diff --git a/docs/chapter_backtracking/n_queens_problem.md b/docs/chapter_backtracking/n_queens_problem.md index ed7c8e536..2c9c2864a 100644 --- a/docs/chapter_backtracking/n_queens_problem.md +++ b/docs/chapter_backtracking/n_queens_problem.md @@ -44,6 +44,6 @@ [file]{n_queens}-[class]{}-[func]{n_queens} ``` -逐行放置 $n$ 次，考虑列约束，则从第一行到最后一行分别有 $n$、$n-1$、$\dots$、$2$、$1$ 个选择，使用 $O(n!)$ 时间；当保存解时，需要复制矩阵 `state` 并添加进 `res` ，复制操作使用 $O(n^2)$ 时间；因此总体时间复杂度为 $O(n! \cdot n^2)$ 。实际上，根据对角线约束的剪枝也能够大幅缩小搜索空间，因而搜索效率往往优于以上时间复杂度。 +逐行放置 $n$ 次，考虑列约束，则从第一行到最后一行分别有 $n$、$n-1$、$\dots$、$2$、$1$ 个选择，使用 $O(n!)$ 时间。当记录解时，需要复制矩阵 `state` 并添加进 `res` ，复制操作使用 $O(n^2)$ 时间。因此，**总体时间复杂度为 $O(n! \cdot n^2)$** 。实际上，根据对角线约束的剪枝也能够大幅缩小搜索空间，因而搜索效率往往优于以上时间复杂度。 数组 `state` 使用 $O(n^2)$ 空间，数组 `cols`、`diags1` 和 `diags2` 皆使用 $O(n)$ 空间。最大递归深度为 $n$ ，使用 $O(n)$ 栈帧空间。因此，**空间复杂度为 $O(n^2)$** 。 diff --git a/docs/chapter_data_structure/number_encoding.assets/1s_2s_complement.png b/docs/chapter_data_structure/number_encoding.assets/1s_2s_complement.png index 369b894ce..16b7ba6ef 100644 Binary files a/docs/chapter_data_structure/number_encoding.assets/1s_2s_complement.png and b/docs/chapter_data_structure/number_encoding.assets/1s_2s_complement.png differ diff --git a/docs/chapter_introduction/algorithms_are_everywhere.assets/greedy_change.png b/docs/chapter_introduction/algorithms_are_everywhere.assets/greedy_change.png index 59b05ed17..fa970c15c 100644 Binary files a/docs/chapter_introduction/algorithms_are_everywhere.assets/greedy_change.png and b/docs/chapter_introduction/algorithms_are_everywhere.assets/greedy_change.png differ diff --git a/docs/chapter_preface/suggestions.md b/docs/chapter_preface/suggestions.md index 30c510feb..421f32acd 100644 --- a/docs/chapter_preface/suggestions.md +++ b/docs/chapter_preface/suggestions.md @@ -220,7 +220,7 @@ git clone https://github.com/krahets/hello-algo.git 从总体上看，我们可以将学习数据结构与算法的过程划分为三个阶段。 1. **阶段一：算法入门**。我们需要熟悉各种数据结构的特点和用法，学习不同算法的原理、流程、用途和效率等方面的内容。 -2. **阶段二：刷算法题**。建议从热门题目开刷，如“[剑指 Offer](https://leetcode.cn/studyplan/coding-interviews/)”和“[LeetCode Hot 100](https://leetcode.cn/studyplan/top-100-liked/)”，先积累至少 100 道题目，熟悉主流的算法问题。初次刷题时，“知识遗忘”可能是一个挑战，但请放心，这是很正常的。我们可以按照“艾宾浩斯遗忘曲线”来复习题目，通常在进行 3～5 轮的重复后，就能将其牢记在心。 +2. **阶段二：刷算法题**。建议从热门题目开刷，推荐的题单、题解和刷题计划和请见此 [GitHub 仓库](https://github.com/krahets/LeetCode-Book)。初次刷题时，“知识遗忘”可能是一个挑战，但请放心，这是很正常的。我们可以按照“艾宾浩斯遗忘曲线”来复习题目，通常在进行 3～5 轮的重复后，就能将其牢记在心。 3. **阶段三：搭建知识体系**。在学习方面，我们可以阅读算法专栏文章、解题框架和算法教材，以不断丰富知识体系。在刷题方面，可以尝试采用进阶刷题策略，如按专题分类、一题多解、一解多题等，相关的刷题心得可以在各个社区找到。 如下图所示，本书内容主要涵盖“阶段一”，旨在帮助你更高效地展开阶段二和阶段三的学习。 diff --git a/docs/chapter_sorting/quick_sort.assets/pivot_division_step1.png b/docs/chapter_sorting/quick_sort.assets/pivot_division_step1.png index cae41606f..242ff0d0a 100644 Binary files a/docs/chapter_sorting/quick_sort.assets/pivot_division_step1.png and b/docs/chapter_sorting/quick_sort.assets/pivot_division_step1.png differ diff --git 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