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hello-algo/docs-en/chapter_computational_compl.../space_complexity.md

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translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
# Space Complexity
"Space complexity" is used to measure the growth trend of the memory space occupied by an algorithm as the amount of data increases. This concept is very similar to time complexity, except that "running time" is replaced with "occupied memory space".
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
## Space Related to Algorithms
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
The memory space used by an algorithm during its execution mainly includes the following types.
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
- **Input Space**: Used to store the input data of the algorithm.
- **Temporary Space**: Used to store variables, objects, function contexts, and other data during the algorithm's execution.
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
- **Output Space**: Used to store the output data of the algorithm.
Generally, the scope of space complexity statistics includes both "Temporary Space" and "Output Space".
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
Temporary space can be further divided into three parts.
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
- **Temporary Data**: Used to save various constants, variables, objects, etc., during the algorithm's execution.
- **Stack Frame Space**: Used to save the context data of the called function. The system creates a stack frame at the top of the stack each time a function is called, and the stack frame space is released after the function returns.
- **Instruction Space**: Used to store compiled program instructions, which are usually negligible in actual statistics.
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
When analyzing the space complexity of a program, **we typically count the Temporary Data, Stack Frame Space, and Output Data**, as shown in the figure below.
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
![Space Types Used in Algorithms](space_complexity.assets/space_types.png)
The relevant code is as follows:
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
=== "Python"
```python title=""
class Node:
"""Classes""""
def __init__(self, x: int):
self.val: int = x # node value
self.next: Node | None = None # reference to the next node
def function() -> int:
""""Functions"""""
# Perform certain operations...
return 0
def algorithm(n) -> int: # input data
A = 0 # temporary data (constant, usually in uppercase)
b = 0 # temporary data (variable)
node = Node(0) # temporary data (object)
c = function() # Stack frame space (call function)
return A + b + c # output data
```
=== "C++"
```cpp title=""
/* Structures */
struct Node {
int val;
Node *next;
Node(int x) : val(x), next(nullptr) {}
};
/* Functions */
int func() {
// Perform certain operations...
return 0;
}
int algorithm(int n) { // input data
const int a = 0; // temporary data (constant)
int b = 0; // temporary data (variable)
Node* node = new Node(0); // temporary data (object)
int c = func(); // stack frame space (call function)
return a + b + c; // output data
}
```
=== "Java"
```java title=""
/* Classes */
class Node {
int val;
Node next;
Node(int x) { val = x; }
}
/* Functions */
int function() {
// Perform certain operations...
return 0;
}
int algorithm(int n) { // input data
final int a = 0; // temporary data (constant)
int b = 0; // temporary data (variable)
Node node = new Node(0); // temporary data (object)
int c = function(); // stack frame space (call function)
return a + b + c; // output data
}
```
=== "C#"
```csharp title=""
/* Classes */
class Node {
int val;
Node next;
Node(int x) { val = x; }
}
/* Functions */
int Function() {
// Perform certain operations...
return 0;
}
int Algorithm(int n) { // input data
const int a = 0; // temporary data (constant)
int b = 0; // temporary data (variable)
Node node = new(0); // temporary data (object)
int c = Function(); // stack frame space (call function)
return a + b + c; // output data
}
```
=== "Go"
```go title=""
/* Structures */
type node struct {
val int
next *node
}
/* Create node structure */
func newNode(val int) *node {
return &node{val: val}
}
/* Functions */
func function() int {
// Perform certain operations...
return 0
}
func algorithm(n int) int { // input data
const a = 0 // temporary data (constant)
b := 0 // temporary storage of data (variable)
newNode(0) // temporary data (object)
c := function() // stack frame space (call function)
return a + b + c // output data
}
```
=== "Swift"
```swift title=""
/* Classes */
class Node {
var val: Int
var next: Node?
init(x: Int) {
val = x
}
}
/* Functions */
func function() -> Int {
// Perform certain operations...
return 0
}
func algorithm(n: Int) -> Int { // input data
let a = 0 // temporary data (constant)
var b = 0 // temporary data (variable)
let node = Node(x: 0) // temporary data (object)
let c = function() // stack frame space (call function)
return a + b + c // output data
}
```
=== "JS"
```javascript title=""
/* Classes */
class Node {
val;
next;
constructor(val) {
this.val = val === undefined ? 0 : val; // node value
this.next = null; // reference to the next node
}
}
/* Functions */
function constFunc() {
// Perform certain operations
return 0;
}
function algorithm(n) { // input data
const a = 0; // temporary data (constant)
let b = 0; // temporary data (variable)
const node = new Node(0); // temporary data (object)
const c = constFunc(); // Stack frame space (calling function)
return a + b + c; // output data
}
```
=== "TS"
```typescript title=""
/* Classes */
class Node {
val: number;
next: Node | null;
constructor(val?: number) {
this.val = val === undefined ? 0 : val; // node value
this.next = null; // reference to the next node
}
}
/* Functions */
function constFunc(): number {
// Perform certain operations
return 0;
}
function algorithm(n: number): number { // input data
const a = 0; // temporary data (constant)
let b = 0; // temporary data (variable)
const node = new Node(0); // temporary data (object)
const c = constFunc(); // Stack frame space (calling function)
return a + b + c; // output data
}
```
=== "Dart"
```dart title=""
/* Classes */
class Node {
int val;
Node next;
Node(this.val, [this.next]);
}
/* Functions */
int function() {
// Perform certain operations...
return 0;
}
int algorithm(int n) { // input data
const int a = 0; // temporary data (constant)
int b = 0; // temporary data (variable)
Node node = Node(0); // temporary data (object)
int c = function(); // stack frame space (call function)
return a + b + c; // output data
}
```
=== "Rust"
```rust title=""
use std::rc::Rc;
use std::cell::RefCell;
/* Structures */
struct Node {
val: i32,
next: Option<Rc<RefCell<Node>>>,
}
/* Creating a Node structure */
impl Node {
fn new(val: i32) -> Self {
Self { val: val, next: None }
}
}
/* Functions */
fn function() -> i32 {
// Perform certain operations...
return 0;
}
fn algorithm(n: i32) -> i32 { // input data
const a: i32 = 0; // temporary data (constant)
let mut b = 0; // temporary data (variable)
let node = Node::new(0); // temporary data (object)
let c = function(); // stack frame space (call function)
return a + b + c; // output data
}
```
=== "C"
```c title=""
/* Functions */
int func() {
// Perform certain operations...
return 0;
}
int algorithm(int n) { // input data
const int a = 0; // temporary data (constant)
int b = 0; // temporary data (variable)
int c = func(); // stack frame space (call function)
return a + b + c; // output data
}
```
=== "Zig"
```zig title=""
```
## Calculation Method
The method for calculating space complexity is roughly similar to that of time complexity, with the only change being the shift of the statistical object from "number of operations" to "size of used space".
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
However, unlike time complexity, **we usually only focus on the worst-case space complexity**. This is because memory space is a hard requirement, and we must ensure that there is enough memory space reserved under all input data.
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
Consider the following code, the term "worst-case" in worst-case space complexity has two meanings.
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
1. **Based on the worst input data**: When $n < 10$, the space complexity is $O(1)$; but when $n > 10$, the initialized array `nums` occupies $O(n)$ space, thus the worst-case space complexity is $O(n)$.
2. **Based on the peak memory used during the algorithm's execution**: For example, before executing the last line, the program occupies $O(1)$ space; when initializing the array `nums`, the program occupies $O(n)$ space, hence the worst-case space complexity is $O(n)$.
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
=== "Python"
```python title=""
def algorithm(n: int):
a = 0 # O(1)
b = [0] * 10000 # O(1)
if n > 10:
nums = [0] * n # O(n)
```
=== "C++"
```cpp title=""
void algorithm(int n) {
int a = 0; // O(1)
vector<int> b(10000); // O(1)
if (n > 10)
vector<int> nums(n); // O(n)
}
```
=== "Java"
```java title=""
void algorithm(int n) {
int a = 0; // O(1)
int[] b = new int[10000]; // O(1)
if (n > 10)
int[] nums = new int[n]; // O(n)
}
```
=== "C#"
```csharp title=""
void Algorithm(int n) {
int a = 0; // O(1)
int[] b = new int[10000]; // O(1)
if (n > 10) {
int[] nums = new int[n]; // O(n)
}
}
```
=== "Go"
```go title=""
func algorithm(n int) {
a := 0 // O(1)
b := make([]int, 10000) // O(1)
var nums []int
if n > 10 {
nums := make([]int, n) // O(n)
}
fmt.Println(a, b, nums)
}
```
=== "Swift"
```swift title=""
func algorithm(n: Int) {
let a = 0 // O(1)
let b = Array(repeating: 0, count: 10000) // O(1)
if n > 10 {
let nums = Array(repeating: 0, count: n) // O(n)
}
}
```
=== "JS"
```javascript title=""
function algorithm(n) {
const a = 0; // O(1)
const b = new Array(10000); // O(1)
if (n > 10) {
const nums = new Array(n); // O(n)
}
}
```
=== "TS"
```typescript title=""
function algorithm(n: number): void {
const a = 0; // O(1)
const b = new Array(10000); // O(1)
if (n > 10) {
const nums = new Array(n); // O(n)
}
}
```
=== "Dart"
```dart title=""
void algorithm(int n) {
int a = 0; // O(1)
List<int> b = List.filled(10000, 0); // O(1)
if (n > 10) {
List<int> nums = List.filled(n, 0); // O(n)
}
}
```
=== "Rust"
```rust title=""
fn algorithm(n: i32) {
let a = 0; // O(1)
let b = [0; 10000]; // O(1)
if n > 10 {
let nums = vec![0; n as usize]; // O(n)
}
}
```
=== "C"
```c title=""
void algorithm(int n) {
int a = 0; // O(1)
int b[10000]; // O(1)
if (n > 10)
int nums[n] = {0}; // O(n)
}
```
=== "Zig"
```zig title=""
```
**In recursive functions, stack frame space must be taken into count**. Consider the following code:
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
=== "Python"
```python title=""
def function() -> int:
# Perform certain operations
return 0
def loop(n: int):
"""Loop O(1)"""""
for _ in range(n):
function()
def recur(n: int) -> int:
"""Recursion O(n)"""""
if n == 1: return
return recur(n - 1)
```
=== "C++"
```cpp title=""
int func() {
// Perform certain operations
return 0;
}
/* Cycle O(1) */
void loop(int n) {
for (int i = 0; i < n; i++) {
func();
}
}
/* Recursion O(n) */
void recur(int n) {
if (n == 1) return;
return recur(n - 1);
}
```
=== "Java"
```java title=""
int function() {
// Perform certain operations
return 0;
}
/* Cycle O(1) */
void loop(int n) {
for (int i = 0; i < n; i++) {
function();
}
}
/* Recursion O(n) */
void recur(int n) {
if (n == 1) return;
return recur(n - 1);
}
```
=== "C#"
```csharp title=""
int Function() {
// Perform certain operations
return 0;
}
/* Cycle O(1) */
void Loop(int n) {
for (int i = 0; i < n; i++) {
Function();
}
}
/* Recursion O(n) */
int Recur(int n) {
if (n == 1) return 1;
return Recur(n - 1);
}
```
=== "Go"
```go title=""
func function() int {
// Perform certain operations
return 0
}
/* Cycle O(1) */
func loop(n int) {
for i := 0; i < n; i++ {
function()
}
}
/* Recursion O(n) */
func recur(n int) {
if n == 1 {
return
}
recur(n - 1)
}
```
=== "Swift"
```swift title=""
@discardableResult
func function() -> Int {
// Perform certain operations
return 0
}
/* Cycle O(1) */
func loop(n: Int) {
for _ in 0 ..< n {
function()
}
}
/* Recursion O(n) */
func recur(n: Int) {
if n == 1 {
return
}
recur(n: n - 1)
}
```
=== "JS"
```javascript title=""
function constFunc() {
// Perform certain operations
return 0;
}
/* Cycle O(1) */
function loop(n) {
for (let i = 0; i < n; i++) {
constFunc();
}
}
/* Recursion O(n) */
function recur(n) {
if (n === 1) return;
return recur(n - 1);
}
```
=== "TS"
```typescript title=""
function constFunc(): number {
// Perform certain operations
return 0;
}
/* Cycle O(1) */
function loop(n: number): void {
for (let i = 0; i < n; i++) {
constFunc();
}
}
/* Recursion O(n) */
function recur(n: number): void {
if (n === 1) return;
return recur(n - 1);
}
```
=== "Dart"
```dart title=""
int function() {
// Perform certain operations
return 0;
}
/* Cycle O(1) */
void loop(int n) {
for (int i = 0; i < n; i++) {
function();
}
}
/* Recursion O(n) */
void recur(int n) {
if (n == 1) return;
return recur(n - 1);
}
```
=== "Rust"
```rust title=""
fn function() -> i32 {
// Perform certain operations
return 0;
}
/* Cycle O(1) */
fn loop(n: i32) {
for i in 0..n {
function();
}
}
/* Recursion O(n) */
void recur(n: i32) {
if n == 1 {
return;
}
recur(n - 1);
}
```
=== "C"
```c title=""
int func() {
// Perform certain operations
return 0;
}
/* Cycle O(1) */
void loop(int n) {
for (int i = 0; i < n; i++) {
func();
}
}
/* Recursion O(n) */
void recur(int n) {
if (n == 1) return;
return recur(n - 1);
}
```
=== "Zig"
```zig title=""
```
The time complexity of both `loop()` and `recur()` functions is $O(n)$, but their space complexities differ.
- The `loop()` function calls `function()` $n$ times in a loop, where each iteration's `function()` returns and releases its stack frame space, so the space complexity remains $O(1)$.
- The recursive function `recur()` will have $n$ instances of unreturned `recur()` existing simultaneously during its execution, thus occupying $O(n)$ stack frame space.
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
## Common Types
Let the size of the input data be $n$, the following chart displays common types of space complexities (arranged from low to high).
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
$$
\begin{aligned}
O(1) < O(\log n) < O(n) < O(n^2) < O(2^n) \newline
\text{Constant Order} < \text{Logarithmic Order} < \text{Linear Order} < \text{Quadratic Order} < \text{Exponential Order}
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
\end{aligned}
$$
![Common Types of Space Complexity](space_complexity.assets/space_complexity_common_types.png)
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
### Constant Order $O(1)$
Constant order is common in constants, variables, objects that are independent of the size of input data $n$.
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
Note that memory occupied by initializing variables or calling functions in a loop, which is released upon entering the next cycle, does not accumulate over space, thus the space complexity remains $O(1)$:
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
```src
[file]{space_complexity}-[class]{}-[func]{constant}
```
### Linear Order $O(n)$
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
Linear order is common in arrays, linked lists, stacks, queues, etc., where the number of elements is proportional to $n$:
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
```src
[file]{space_complexity}-[class]{}-[func]{linear}
```
As shown below, this function's recursive depth is $n$, meaning there are $n$ instances of unreturned `linear_recur()` function, using $O(n)$ size of stack frame space:
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
```src
[file]{space_complexity}-[class]{}-[func]{linear_recur}
```
![Recursive Function Generating Linear Order Space Complexity](space_complexity.assets/space_complexity_recursive_linear.png)
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
### Quadratic Order $O(n^2)$
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
Quadratic order is common in matrices and graphs, where the number of elements is quadratic to $n$:
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
```src
[file]{space_complexity}-[class]{}-[func]{quadratic}
```
As shown below, the recursive depth of this function is $n$, and in each recursive call, an array is initialized with lengths $n$, $n-1$, $\dots$, $2$, $1$, averaging $n/2$, thus overall occupying $O(n^2)$ space:
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
```src
[file]{space_complexity}-[class]{}-[func]{quadratic_recur}
```
![Recursive Function Generating Quadratic Order Space Complexity](space_complexity.assets/space_complexity_recursive_quadratic.png)
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
### Exponential Order $O(2^n)$
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
Exponential order is common in binary trees. Observe the below image, a "full binary tree" with $n$ levels has $2^n - 1$ nodes, occupying $O(2^n)$ space:
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
```src
[file]{space_complexity}-[class]{}-[func]{build_tree}
```
![Full Binary Tree Generating Exponential Order Space Complexity](space_complexity.assets/space_complexity_exponential.png)
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
### Logarithmic Order $O(\log n)$
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
Logarithmic order is common in divide-and-conquer algorithms. For example, in merge sort, an array of length $n$ is recursively divided in half each round, forming a recursion tree of height $\log n$, using $O(\log n)$ stack frame space.
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
Another example is converting a number to a string. Given a positive integer $n$, its number of digits is $\log_{10} n + 1$, corresponding to the length of the string, thus the space complexity is $O(\log_{10} n + 1) = O(\log n)$.
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
## Balancing Time and Space
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
Ideally, we aim for both time complexity and space complexity to be optimal. However, in practice, optimizing both simultaneously is often difficult.
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
**Lowering time complexity usually comes at the cost of increased space complexity, and vice versa**. The approach of sacrificing memory space to improve algorithm speed is known as "space-time tradeoff"; the reverse is known as "time-space tradeoff".
translation: English Translation of the chapter of preface(part), introduction and complexity analysis(part) (#994) * Translate 1.0.0b6 release with the machine learning translator. * Update Dockerfile A few translation improvements. * Fix a badge logo. * Fix EN translation of chapter_appendix/terminology.md (#913) * Update README.md * Update README.md * translation: Refined the automated translation of README (#932) * refined the automated translation of README * Update index.md * Update mkdocs-en.yml --------- Co-authored-by: Yudong Jin <krahets@163.com> * translate: Embellish chapter_computational_complexity/index.md (#940) * translation: Update chapter_computational_complexity/performance_evaluation.md (#943) * Update performance_evaluation.md * Update performance_evaluation.md * Update performance_evaluation.md change 'methods' to 'approaches' on line 15 * Update performance_evaluation.md on line 21, change the sentence to 'the results could be the opposite on another computer with different specifications.' * Update performance_evaluation.md delete two short sentence on line 5 and 6 * Update performance_evaluation.md change `unavoidable` to `inevitable` on line 48 * Update performance_evaluation.md small changes on line 23 * translation: Update terminology and improve readability in preface summary (#954) * Update terminology and improve readability in preface summary This commit made a few adjustments in the 'summary.md' file for clearer and more accessible language. "Brushing tool library" was replaced with "Coding Toolkit" to better reflect common terminology. Also, advice for beginners in algorithm learning journey was reformulated to imply a more positive approach avoiding detours and common pitfalls. The section related to the discussion forum was rewritten to sound more inviting to readers. * Format * Optimize the translation of chapter_introduction/algorithms_are_everywhere. * Add .gitignore to Java subfolder. * Update the button assets. * Fix the callout * translation: chapter_computational_complexity/summary to en (#953) * translate chapter_computational_complexity/summary * minor format * Update summary.md with comment * Update summary.md * Update summary.md * translation: chapter_introduction/what_is_dsa.md (#962) * Optimize translation of what_is_dsa.md * Update * translation: chapter_introduction/summary.md (#963) * Translate chapter_introduction/summary.md * Update * translation: Update README.md (#964) * Update en translation of README.md * Update README.md * translation: update space_complexity.md (#970) * update space_complexity.md * the rest of translation piece * Update space_complexity.md --------- Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/index.md (#971) * Update index.md sorry, first time doing this... now this is the final change. changes: title of the chapter is shorter. refined the abstract. * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_data_structure/classification_of_data_structure.md (#980) * update classification_of_data_structure.md * Update classification_of_data_structure.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * translation: Update chapter_introduction/algorithms_are_everywhere.md (#972) * Update algorithms_are_everywhere.md changed or refined parts of the words and sentences including tips. Some of them I didnt change that much because im worried that it might not meet the requirement of accuracy. some other ones i changed a lot to make it sound better, but also kind of following the same wording as the CN version * Update algorithms_are_everywhere.md re-edited the dictionary part from Piyin to just normal Eng dictionary. again thank you very much hpstory for you suggestion. * Update algorithms_are_everywhere.md --------- Co-authored-by: Yudong Jin <krahets@163.com> * Prepare merging into main branch. * Update buttons * Update Dockerfile * Update index.md * Update index.md * Update README * Fix index.md * Fix mkdocs-en.yml --------- Co-authored-by: Yuelin Xin <sc20yx2@leeds.ac.uk> Co-authored-by: Phoenix Xie <phoenixx0415@gmail.com> Co-authored-by: Sizhuo Long <longsizhuo@gmail.com> Co-authored-by: Spark <qizhang94@outlook.com> Co-authored-by: Thomas <thomasqiu7@gmail.com> Co-authored-by: ThomasQiu <thomas.qiu@mnfgroup.limited> Co-authored-by: K3v123 <123932560+K3v123@users.noreply.github.com> Co-authored-by: Jin <36914748+yanedie@users.noreply.github.com>
11 months ago
The choice depends on which aspect we value more. In most cases, time is more precious than space, so "space-time tradeoff" is often the more common strategy. Of course, controlling space complexity is also very important when dealing with large volumes of data.