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Sort the coding languages by applications. (#721)

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Yudong Jin
2023-09-04 03:19:08 +08:00
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docs/chapter_backtracking/backtracking_algorithm.md
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@@ -10,10 +10,10 @@
对于此题，我们前序遍历这颗树，并判断当前节点的值是否为 $7$ ，若是则将该节点的值加入到结果列表 `res` 之中。相关过程实现如下图和以下代码所示。
=== "Java"
=== "Python"
```java title="preorder_traversal_i_compact.java"
[class]{preorder_traversal_i_compact}-[func]{preOrder}
```python title="preorder_traversal_i_compact.py"
[class]{}-[func]{pre_order}
```
=== "C++"
@@ -22,10 +22,16 @@
[class]{}-[func]{preOrder}
```
=== "Python"
=== "Java"
```python title="preorder_traversal_i_compact.py"
[class]{}-[func]{pre_order}
```java title="preorder_traversal_i_compact.java"
[class]{preorder_traversal_i_compact}-[func]{preOrder}
```
=== "C#"
```csharp title="preorder_traversal_i_compact.cs"
[class]{preorder_traversal_i_compact}-[func]{preOrder}
```
=== "Go"
@@ -34,6 +40,12 @@
[class]{}-[func]{preOrderI}
```
=== "Swift"
```swift title="preorder_traversal_i_compact.swift"
[class]{}-[func]{preOrder}
```
=== "JS"
```javascript title="preorder_traversal_i_compact.js"
@@ -46,30 +58,6 @@
[class]{}-[func]{preOrder}
```
=== "C"
```c title="preorder_traversal_i_compact.c"
[class]{}-[func]{preOrder}
```
=== "C#"
```csharp title="preorder_traversal_i_compact.cs"
[class]{preorder_traversal_i_compact}-[func]{preOrder}
```
=== "Swift"
```swift title="preorder_traversal_i_compact.swift"
[class]{}-[func]{preOrder}
```
=== "Zig"
```zig title="preorder_traversal_i_compact.zig"
[class]{}-[func]{preOrder}
```
=== "Dart"
```dart title="preorder_traversal_i_compact.dart"
@@ -82,6 +70,18 @@
[class]{}-[func]{pre_order}
```
=== "C"
```c title="preorder_traversal_i_compact.c"
[class]{}-[func]{preOrder}
```
=== "Zig"
```zig title="preorder_traversal_i_compact.zig"
[class]{}-[func]{preOrder}
```
![在前序遍历中搜索节点](backtracking_algorithm.assets/preorder_find_nodes.png)
## 尝试与回退
@@ -98,10 +98,10 @@
在例题一代码的基础上，我们需要借助一个列表 `path` 记录访问过的节点路径。当访问到值为 $7$ 的节点时，则复制 `path` 并添加进结果列表 `res` 。遍历完成后，`res` 中保存的就是所有的解。
=== "Java"
=== "Python"
```java title="preorder_traversal_ii_compact.java"
[class]{preorder_traversal_ii_compact}-[func]{preOrder}
```python title="preorder_traversal_ii_compact.py"
[class]{}-[func]{pre_order}
```
=== "C++"
@@ -110,10 +110,16 @@
[class]{}-[func]{preOrder}
```
=== "Python"
=== "Java"
```python title="preorder_traversal_ii_compact.py"
[class]{}-[func]{pre_order}
```java title="preorder_traversal_ii_compact.java"
[class]{preorder_traversal_ii_compact}-[func]{preOrder}
```
=== "C#"
```csharp title="preorder_traversal_ii_compact.cs"
[class]{preorder_traversal_ii_compact}-[func]{preOrder}
```
=== "Go"
@@ -122,6 +128,12 @@
[class]{}-[func]{preOrderII}
```
=== "Swift"
```swift title="preorder_traversal_ii_compact.swift"
[class]{}-[func]{preOrder}
```
=== "JS"
```javascript title="preorder_traversal_ii_compact.js"
@@ -134,30 +146,6 @@
[class]{}-[func]{preOrder}
```
=== "C"
```c title="preorder_traversal_ii_compact.c"
[class]{}-[func]{preOrder}
```
=== "C#"
```csharp title="preorder_traversal_ii_compact.cs"
[class]{preorder_traversal_ii_compact}-[func]{preOrder}
```
=== "Swift"
```swift title="preorder_traversal_ii_compact.swift"
[class]{}-[func]{preOrder}
```
=== "Zig"
```zig title="preorder_traversal_ii_compact.zig"
[class]{}-[func]{preOrder}
```
=== "Dart"
```dart title="preorder_traversal_ii_compact.dart"
@@ -170,6 +158,18 @@
[class]{}-[func]{pre_order}
```
=== "C"
```c title="preorder_traversal_ii_compact.c"
[class]{}-[func]{preOrder}
```
=== "Zig"
```zig title="preorder_traversal_ii_compact.zig"
[class]{}-[func]{preOrder}
```
在每次“尝试”中，我们通过将当前节点添加进 `path` 来记录路径；而在“回退”前，我们需要将该节点从 `path` 中弹出，**以恢复本次尝试之前的状态**。
观察下图所示的过程，**我们可以将尝试和回退理解为“前进”与“撤销”**，两个操作是互为逆向的。
@@ -217,10 +217,10 @@
为了满足以上约束条件，**我们需要添加剪枝操作**：在搜索过程中，若遇到值为 $3$ 的节点，则提前返回，停止继续搜索。
=== "Java"
=== "Python"
```java title="preorder_traversal_iii_compact.java"
[class]{preorder_traversal_iii_compact}-[func]{preOrder}
```python title="preorder_traversal_iii_compact.py"
[class]{}-[func]{pre_order}
```
=== "C++"
@@ -229,10 +229,16 @@
[class]{}-[func]{preOrder}
```
=== "Python"
=== "Java"
```python title="preorder_traversal_iii_compact.py"
[class]{}-[func]{pre_order}
```java title="preorder_traversal_iii_compact.java"
[class]{preorder_traversal_iii_compact}-[func]{preOrder}
```
=== "C#"
```csharp title="preorder_traversal_iii_compact.cs"
[class]{preorder_traversal_iii_compact}-[func]{preOrder}
```
=== "Go"
@@ -241,6 +247,12 @@
[class]{}-[func]{preOrderIII}
```
=== "Swift"
```swift title="preorder_traversal_iii_compact.swift"
[class]{}-[func]{preOrder}
```
=== "JS"
```javascript title="preorder_traversal_iii_compact.js"
@@ -253,30 +265,6 @@
[class]{}-[func]{preOrder}
```
=== "C"
```c title="preorder_traversal_iii_compact.c"
[class]{}-[func]{preOrder}
```
=== "C#"
```csharp title="preorder_traversal_iii_compact.cs"
[class]{preorder_traversal_iii_compact}-[func]{preOrder}
```
=== "Swift"
```swift title="preorder_traversal_iii_compact.swift"
[class]{}-[func]{preOrder}
```
=== "Zig"
```zig title="preorder_traversal_iii_compact.zig"
[class]{}-[func]{preOrder}
```
=== "Dart"
```dart title="preorder_traversal_iii_compact.dart"
@@ -289,6 +277,18 @@
[class]{}-[func]{pre_order}
```
=== "C"
```c title="preorder_traversal_iii_compact.c"
[class]{}-[func]{preOrder}
```
=== "Zig"
```zig title="preorder_traversal_iii_compact.zig"
[class]{}-[func]{preOrder}
```
剪枝是一个非常形象的名词。如下图所示，在搜索过程中，**我们“剪掉”了不满足约束条件的搜索分支**，避免许多无意义的尝试，从而提高了搜索效率。
![根据约束条件剪枝](backtracking_algorithm.assets/preorder_find_constrained_paths.png)
@@ -299,30 +299,26 @@
在以下框架代码中，`state` 表示问题的当前状态，`choices` 表示当前状态下可以做出的选择。
=== "Java"
=== "Python"
```java title=""
/* 回溯算法框架 */
void backtrack(State state, List<Choice> choices, List<State> res) {
// 判断是否为解
if (isSolution(state)) {
// 记录解
recordSolution(state, res);
// 停止继续搜索
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 title=""
def backtrack(state: State, choices: list[choice], res: list[state]):
"""回溯算法框架"""
# 判断是否为解
if is_solution(state):
# 记录解
record_solution(state, res)
# 停止继续搜索
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)
```
=== "C++"
@@ -351,26 +347,56 @@
}
```
=== "Python"
=== "Java"
```python title=""
def backtrack(state: State, choices: list[choice], res: list[state]):
"""回溯算法框架"""
# 判断是否为解
if is_solution(state):
# 记录解
record_solution(state, res)
# 停止继续搜索
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 title=""
/* 回溯算法框架 */
void backtrack(State state, List<Choice> choices, List<State> res) {
// 判断是否为解
if (isSolution(state)) {
// 记录解
recordSolution(state, res);
// 停止继续搜索
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#"
```csharp title=""
/* 回溯算法框架 */
void backtrack(State state, List<Choice> choices, List<State> res) {
// 判断是否为解
if (isSolution(state)) {
// 记录解
recordSolution(state, res);
// 停止继续搜索
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);
}
}
}
```
=== "Go"
@@ -399,6 +425,32 @@
}
```
=== "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)
// 停止继续搜索
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)
}
}
}
```
=== "JS"
```javascript title=""
@@ -451,90 +503,6 @@
}
```
=== "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);
// 停止继续搜索
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<Choice> choices, List<State> res) {
// 判断是否为解
if (isSolution(state)) {
// 记录解
recordSolution(state, res);
// 停止继续搜索
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)
// 停止继续搜索
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=""
```
=== "Dart"
```dart title=""
@@ -567,22 +535,54 @@
```
=== "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);
// 停止继续搜索
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]);
}
}
}
```
=== "Zig"
```zig title=""
```
接下来，我们基于框架代码来解决例题三。状态 `state` 为节点遍历路径，选择 `choices` 为当前节点的左子节点和右子节点，结果 `res` 是路径列表。
=== "Java"
=== "Python"
```java title="preorder_traversal_iii_template.java"
[class]{preorder_traversal_iii_template}-[func]{isSolution}
```python title="preorder_traversal_iii_template.py"
[class]{}-[func]{is_solution}
[class]{preorder_traversal_iii_template}-[func]{recordSolution}
[class]{}-[func]{record_solution}
[class]{preorder_traversal_iii_template}-[func]{isValid}
[class]{}-[func]{is_valid}
[class]{preorder_traversal_iii_template}-[func]{makeChoice}
[class]{}-[func]{make_choice}
[class]{preorder_traversal_iii_template}-[func]{undoChoice}
[class]{}-[func]{undo_choice}
[class]{preorder_traversal_iii_template}-[func]{backtrack}
[class]{}-[func]{backtrack}
```
=== "C++"
@@ -601,20 +601,36 @@
[class]{}-[func]{backtrack}
```
=== "Python"
=== "Java"
```python title="preorder_traversal_iii_template.py"
[class]{}-[func]{is_solution}
```java title="preorder_traversal_iii_template.java"
[class]{preorder_traversal_iii_template}-[func]{isSolution}
[class]{}-[func]{record_solution}
[class]{preorder_traversal_iii_template}-[func]{recordSolution}
[class]{}-[func]{is_valid}
[class]{preorder_traversal_iii_template}-[func]{isValid}
[class]{}-[func]{make_choice}
[class]{preorder_traversal_iii_template}-[func]{makeChoice}
[class]{}-[func]{undo_choice}
[class]{preorder_traversal_iii_template}-[func]{undoChoice}
[class]{}-[func]{backtrack}
[class]{preorder_traversal_iii_template}-[func]{backtrack}
```
=== "C#"
```csharp title="preorder_traversal_iii_template.cs"
[class]{preorder_traversal_iii_template}-[func]{isSolution}
[class]{preorder_traversal_iii_template}-[func]{recordSolution}
[class]{preorder_traversal_iii_template}-[func]{isValid}
[class]{preorder_traversal_iii_template}-[func]{makeChoice}
[class]{preorder_traversal_iii_template}-[func]{undoChoice}
[class]{preorder_traversal_iii_template}-[func]{backtrack}
```
=== "Go"
@@ -633,6 +649,22 @@
[class]{}-[func]{backtrackIII}
```
=== "Swift"
```swift title="preorder_traversal_iii_template.swift"
[class]{}-[func]{isSolution}
[class]{}-[func]{recordSolution}
[class]{}-[func]{isValid}
[class]{}-[func]{makeChoice}
[class]{}-[func]{undoChoice}
[class]{}-[func]{backtrack}
```
=== "JS"
```javascript title="preorder_traversal_iii_template.js"
@@ -665,70 +697,6 @@
[class]{}-[func]{backtrack}
```
=== "C"
```c title="preorder_traversal_iii_template.c"
[class]{}-[func]{isSolution}
[class]{}-[func]{recordSolution}
[class]{}-[func]{isValid}
[class]{}-[func]{makeChoice}
[class]{}-[func]{undoChoice}
[class]{}-[func]{backtrack}
```
=== "C#"
```csharp title="preorder_traversal_iii_template.cs"
[class]{preorder_traversal_iii_template}-[func]{isSolution}
[class]{preorder_traversal_iii_template}-[func]{recordSolution}
[class]{preorder_traversal_iii_template}-[func]{isValid}
[class]{preorder_traversal_iii_template}-[func]{makeChoice}
[class]{preorder_traversal_iii_template}-[func]{undoChoice}
[class]{preorder_traversal_iii_template}-[func]{backtrack}
```
=== "Swift"
```swift title="preorder_traversal_iii_template.swift"
[class]{}-[func]{isSolution}
[class]{}-[func]{recordSolution}
[class]{}-[func]{isValid}
[class]{}-[func]{makeChoice}
[class]{}-[func]{undoChoice}
[class]{}-[func]{backtrack}
```
=== "Zig"
```zig title="preorder_traversal_iii_template.zig"
[class]{}-[func]{isSolution}
[class]{}-[func]{recordSolution}
[class]{}-[func]{isValid}
[class]{}-[func]{makeChoice}
[class]{}-[func]{undoChoice}
[class]{}-[func]{backtrack}
```
=== "Dart"
```dart title="preorder_traversal_iii_template.dart"
@@ -761,6 +729,38 @@
[class]{}-[func]{backtrack}
```
=== "C"
```c title="preorder_traversal_iii_template.c"
[class]{}-[func]{isSolution}
[class]{}-[func]{recordSolution}
[class]{}-[func]{isValid}
[class]{}-[func]{makeChoice}
[class]{}-[func]{undoChoice}
[class]{}-[func]{backtrack}
```
=== "Zig"
```zig title="preorder_traversal_iii_template.zig"
[class]{}-[func]{isSolution}
[class]{}-[func]{recordSolution}
[class]{}-[func]{isValid}
[class]{}-[func]{makeChoice}
[class]{}-[func]{undoChoice}
[class]{}-[func]{backtrack}
```
根据题意，我们在找到值为 7 的节点后应该继续搜索，**因此需要将记录解之后的 `return` 语句删除**。下图对比了保留或删除 `return` 语句的搜索过程。
![保留与删除 return 的搜索过程对比](backtracking_algorithm.assets/backtrack_remove_return_or_not.png)