From def8da66171e440fcfc263bb508772d2cd8c1afc Mon Sep 17 00:00:00 2001 From: krahets Date: Wed, 10 May 2023 19:47:30 +0800 Subject: [PATCH] Prepare 1.0.0b3 release --- README.md | 2 +- .../backtracking_algorithm.md | 246 ++++++++++++++++-- .../permutations_ii.png | Bin 62284 -> 63341 bytes .../permutations_ii_pruning.png | Bin 80436 -> 81181 bytes .../permutations_ii_pruning_summary.png | Bin 74933 -> 76523 bytes .../permutations_problem.md | 16 +- 6 files changed, 236 insertions(+), 28 deletions(-) diff --git a/README.md b/README.md index d5291bd48..2bebeff48 100644 --- a/README.md +++ b/README.md @@ -24,7 +24,7 @@ 阅读网页版   |   - + 下载 PDF 版

diff --git a/docs/chapter_backtracking/backtracking_algorithm.md b/docs/chapter_backtracking/backtracking_algorithm.md index 0eb0711e1..af5381a10 100644 --- a/docs/chapter_backtracking/backtracking_algorithm.md +++ b/docs/chapter_backtracking/backtracking_algorithm.md @@ -272,24 +272,232 @@ 设 `state` 为问题的当前状态,`choices` 表示当前状态下可以做出的选择,则可得到以下回溯算法的框架代码。 -```python -def backtrack(state, choices, res): - """回溯算法框架""" - # 判断是否为解 - if is_solution(state): - # 记录解 - record_solution(state, res) - return - # 遍历所有选择 - for choice in choices: - # 剪枝:判断选择是否合法 - if is_valid(state, choice): - # 尝试:做出选择,更新状态 - make_choice(state, choice) - backtrack(state, choices, res) - # 回退:撤销选择,恢复到之前的状态 - undo_choice(state, choice) -``` +=== "Java" + + ```java title="" + /* 回溯算法框架 */ + void backtrack(State state, List choices, List res) { + // 判断是否为解 + if (isSolution(state)) { + // 记录解 + recordSolution(state, res); + return; + } + // 遍历所有选择 + for (Choice choice : choices) { + // 剪枝:判断选择是否合法 + if (isValid(state, choice)) { + // 尝试:做出选择,更新状态 + makeChoice(state, choice); + backtrack(state, choices, res); + // 回退:撤销选择,恢复到之前的状态 + undoChoice(state, choice); + } + } + } + ``` + +=== "C++" + + ```cpp title="" + /* 回溯算法框架 */ + void backtrack(State *state, vector &choices, vector &res) { + // 判断是否为解 + if (isSolution(state)) { + // 记录解 + recordSolution(state, res); + return; + } + // 遍历所有选择 + for (Choice choice : choices) { + // 剪枝:判断选择是否合法 + if (isValid(state, choice)) { + // 尝试:做出选择,更新状态 + makeChoice(state, choice); + backtrack(state, choices, res); + // 回退:撤销选择,恢复到之前的状态 + undoChoice(state, choice); + } + } + } + ``` + +=== "Python" + + ```python title="" + def backtrack(state: State, choices: list[choice], res: list[state]) -> None: + """回溯算法框架""" + # 判断是否为解 + if is_solution(state): + # 记录解 + record_solution(state, res) + return + # 遍历所有选择 + for choice in choices: + # 剪枝:判断选择是否合法 + if is_valid(state, choice): + # 尝试:做出选择,更新状态 + make_choice(state, choice) + backtrack(state, choices, res) + # 回退:撤销选择,恢复到之前的状态 + undo_choice(state, choice) + ``` + +=== "Go" + + ```go title="" + /* 回溯算法框架 */ + func backtrack(state *State, choices []Choice, res *[]State) { + // 判断是否为解 + if isSolution(state) { + // 记录解 + recordSolution(state, res) + return + } + // 遍历所有选择 + for _, choice := range choices { + // 剪枝:判断选择是否合法 + if isValid(state, choice) { + // 尝试:做出选择,更新状态 + makeChoice(state, choice) + backtrack(state, choices, res) + // 回退:撤销选择,恢复到之前的状态 + undoChoice(state, choice) + } + } + } + ``` + +=== "JavaScript" + + ```javascript title="" + /* 回溯算法框架 */ + function backtrack(state, choices, res) { + // 判断是否为解 + if (isSolution(state)) { + // 记录解 + recordSolution(state, res); + return; + } + // 遍历所有选择 + for (let choice of choices) { + // 剪枝:判断选择是否合法 + if (isValid(state, choice)) { + // 尝试:做出选择,更新状态 + makeChoice(state, choice); + backtrack(state, choices, res); + // 回退:撤销选择,恢复到之前的状态 + undoChoice(state, choice); + } + } + } + ``` + +=== "TypeScript" + + ```typescript title="" + /* 回溯算法框架 */ + function backtrack(state: State, choices: Choice[], res: State[]): void { + // 判断是否为解 + if (isSolution(state)) { + // 记录解 + recordSolution(state, res); + return; + } + // 遍历所有选择 + for (let choice of choices) { + // 剪枝:判断选择是否合法 + if (isValid(state, choice)) { + // 尝试:做出选择,更新状态 + makeChoice(state, choice); + backtrack(state, choices, res); + // 回退:撤销选择,恢复到之前的状态 + undoChoice(state, choice); + } + } + } + ``` + +=== "C" + + ```c title="" + /* 回溯算法框架 */ + void backtrack(State *state, Choice *choices, int numChoices, State *res, int numRes) { + // 判断是否为解 + if (isSolution(state)) { + // 记录解 + recordSolution(state, res, numRes); + return; + } + // 遍历所有选择 + for (int i = 0; i < numChoices; i++) { + // 剪枝:判断选择是否合法 + if (isValid(state, &choices[i])) { + // 尝试:做出选择,更新状态 + makeChoice(state, &choices[i]); + backtrack(state, choices, numChoices, res, numRes); + // 回退:撤销选择,恢复到之前的状态 + undoChoice(state, &choices[i]); + } + } + } + ``` + +=== "C#" + + ```csharp title="" + /* 回溯算法框架 */ + void backtrack(State state, List choices, List res) { + // 判断是否为解 + if (isSolution(state)) { + // 记录解 + recordSolution(state, res); + return; + } + // 遍历所有选择 + foreach (Choice choice in choices) { + // 剪枝:判断选择是否合法 + if (isValid(state, choice)) { + // 尝试:做出选择,更新状态 + makeChoice(state, choice); + backtrack(state, choices, res); + // 回退:撤销选择,恢复到之前的状态 + undoChoice(state, choice); + } + } + } + ``` + +=== "Swift" + + ```swift title="" + /* 回溯算法框架 */ + func backtrack(state: inout State, choices: [Choice], res: inout [State]) { + // 判断是否为解 + if isSolution(state: state) { + // 记录解 + recordSolution(state: state, res: &res) + return + } + // 遍历所有选择 + for choice in choices { + // 剪枝:判断选择是否合法 + if isValid(state: state, choice: choice) { + // 尝试:做出选择,更新状态 + makeChoice(state: &state, choice: choice) + backtrack(state: &state, choices: choices, res: &res) + // 回退:撤销选择,恢复到之前的状态 + undoChoice(state: &state, choice: choice) + } + } + } + ``` + +=== "Zig" + + ```zig title="" + + ``` 下面,我们尝试基于此框架来解决例题三。在例题三中,状态 `state` 是节点遍历路径,选择 `choices` 是当前节点的左子节点和右子节点,结果 `res` 是路径列表,实现代码如下所示。 @@ -453,7 +661,7 @@ def backtrack(state, choices, res): [class]{}-[func]{backtrack} ``` -相较于基于前序遍历的实现代码,基于回溯算法框架的实现代码虽然显得啰嗦,但通用性更好,适用于各种不同的回溯算法问题。实际上,**所有回溯问题都可以在该框架下解决**。我们只需要根据问题特点来定义框架中的各个变量,实现各个方法即可。 +相较于基于前序遍历的实现代码,基于回溯算法框架的实现代码虽然显得啰嗦,但通用性更好。实际上,**所有回溯问题都可以在该框架下解决**。我们需要根据具体问题来定义 `state` 和 `choices` ,并实现框架中的各个方法。 ## 典型例题 diff --git a/docs/chapter_backtracking/permutations_problem.assets/permutations_ii.png b/docs/chapter_backtracking/permutations_problem.assets/permutations_ii.png index 3003a32b94710cae063460993ea591783d24a0eb..3635e717bd6c1d31ea164731ccb0971d938dbcd6 100644 GIT binary patch literal 63341 zcmeEu2U}Cy)^3O(ML~*)h!jDJAiYTwq$(W(L^^`hP(*qM3rJUy7NkQcAq1s&1d-k$ z^dcPs0i^f4aG&#idwYJsz0ZA)KBTP7wKC^iW4`kpW4t4wn(9iVB)3RFAQ0)3$MV`B z5CQNK+)D%oo@5x6@qi~h7i}e3P+|A&72wSq%coDQ)YL$nz-uB90Ujmj(nS;CKM3#E z?~^Z1QO2YDpV!)W9RF$qTr>-ka|-v3@P4gBxc1faA_ z|9%bb1zLjw$`wJWZy6T@M5{h=zxBMp2$Da@x)u3B>sF`Ve))yE!JKn 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