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krahets 2 years ago
parent 969281965e
commit 4eb7734fa9
2 changed files with 164 additions and 38 deletions
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chapter_backtracking/n_queens_problem.md
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chapter_backtracking/permutations_problem.md
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@ -49,16 +49,23 @@ comments: true
int choice = choices[i];
// 剪枝：不允许重复选择元素 且 不允许重复选择相等元素
if (!selected[i]) {
// 尝试
selected[i] = true; // 做出选择
state.add(choice); // 更新状态
// 尝试：做出选择，更新状态
selected[i] = true;
state.add(choice);
backtrack(state, choices, selected, res);
// 回退
selected[i] = false; // 撤销选择
state.remove(state.size() - 1); // 恢复到之前的状态
// 回退：撤销选择，恢复到之前的状态
selected[i] = false;
state.remove(state.size() - 1);
}
}
}
/* 全排列 I */
List<List<Integer>> permutationsI(int[] nums) {
List<List<Integer>> res = new ArrayList<List<Integer>>();
backtrack(new ArrayList<Integer>(), nums, new boolean[nums.length], res);
return res;
}
```
=== "C++"
@ -76,15 +83,24 @@ comments: true
int choice = choices[i];
// 剪枝：不允许重复选择元素 且 不允许重复选择相等元素
if (!selected[i]) {
// 尝试
selected[i] = true; // 做出选择
state.push_back(choice); // 更新状态
// 尝试：做出选择，更新状态
selected[i] = true;
state.push_back(choice);
backtrack(state, choices, selected, res);
// 回退
selected[i] = false; // 撤销选择
state.pop_back(); // 恢复到之前的状态
// 回退：撤销选择，恢复到之前的状态
selected[i] = false;
state.pop_back();
}
}
}
/* 全排列 I */
vector<vector<int>> permutationsI(vector<int> nums) {
vector<int> state;
vector<bool> selected(nums.size(), false);
vector<vector<int>> res;
backtrack(state, nums, selected, res);
return res;
}
```
@ -103,55 +119,101 @@ comments: true
for i, choice in enumerate(choices):
# 剪枝：不允许重复选择元素
if not selected[i]:
# 尝试
selected[i] = True # 做出选择
state.append(choice) # 更新状态
# 尝试：做出选择，更新状态
selected[i] = True
state.append(choice)
backtrack(state, choices, selected, res)
# 回退
selected[i] = False # 撤销选择
state.pop() # 恢复到之前的状态
# 回退：撤销选择，恢复到之前的状态
selected[i] = False
state.pop()
def permutations_i(nums: list[int]) -> list[list[int]]:
"""全排列 I"""
res = []
backtrack(state=[], choices=nums, selected=[False] * len(nums), res=res)
return res
```
=== "Go"
```go title="permutations_i.go"
[class]{}-[func]{backtrack}
[class]{}-[func]{permutationsI}
```
=== "JavaScript"
```javascript title="permutations_i.js"
[class]{}-[func]{backtrack}
[class]{}-[func]{permutationsI}
```
=== "TypeScript"
```typescript title="permutations_i.ts"
[class]{}-[func]{backtrack}
[class]{}-[func]{permutationsI}
```
=== "C"
```c title="permutations_i.c"
[class]{}-[func]{backtrack}
[class]{}-[func]{permutationsI}
```
=== "C#"
```csharp title="permutations_i.cs"
[class]{permutations_i}-[func]{backtrack}
/* 回溯算法：全排列 I */
void backtrack(List<int> state, int[] choices, bool[] selected, List<List<int>> res) {
// 当状态长度等于元素数量时，记录解
if (state.Count == choices.Length) {
res.Add(new List<int>(state));
return;
}
// 遍历所有选择
for (int i = 0; i < choices.Length; i++) {
int choice = choices[i];
// 剪枝：不允许重复选择元素 且 不允许重复选择相等元素
if (!selected[i]) {
// 尝试：做出选择，更新状态
selected[i] = true;
state.Add(choice);
backtrack(state, choices, selected, res);
// 回退：撤销选择，恢复到之前的状态
selected[i] = false;
state.RemoveAt(state.Count - 1);
}
}
}
/* 全排列 I */
List<List<int>> permutationsI(int[] nums) {
List<List<int>> res = new List<List<int>>();
backtrack(new List<int>(), nums, new bool[nums.Length], res);
return res;
}
```
=== "Swift"
```swift title="permutations_i.swift"
[class]{}-[func]{backtrack}
[class]{}-[func]{permutationsI}
```
=== "Zig"
```zig title="permutations_i.zig"
[class]{}-[func]{backtrack}
[class]{}-[func]{permutationsI}
```
需要重点关注的是，我们引入了一个布尔型数组 `selected` ，它的长度与输入数组长度相等，其中 `selected[i]` 表示 `choices[i]` 是否已被选择。我们利用 `selected` 避免某个元素被重复选择，从而实现剪枝。
@ -198,17 +260,24 @@ comments: true
int choice = choices[i];
// 剪枝：不允许重复选择元素 且 不允许重复选择相等元素
if (!selected[i] && !duplicated.contains(choice)) {
// 尝试
// 尝试：做出选择，更新状态
duplicated.add(choice); // 记录选择过的元素值
selected[i] = true; // 做出选择
state.add(choice); // 更新状态
selected[i] = true;
state.add(choice);
backtrack(state, choices, selected, res);
// 回退
selected[i] = false; // 撤销选择
state.remove(state.size() - 1); // 恢复到之前的状态
// 回退：撤销选择，恢复到之前的状态
selected[i] = false;
state.remove(state.size() - 1);
}
}
}
/* 全排列 II */
List<List<Integer>> permutationsII(int[] nums) {
List<List<Integer>> res = new ArrayList<List<Integer>>();
backtrack(new ArrayList<Integer>(), nums, new boolean[nums.length], res);
return res;
}
```
=== "C++"
@ -227,16 +296,25 @@ comments: true
int choice = choices[i];
// 剪枝：不允许重复选择元素 且 不允许重复选择相等元素
if (!selected[i] && duplicated.find(choice) == duplicated.end()) {
// 尝试
// 尝试：做出选择，更新状态
duplicated.emplace(choice); // 记录选择过的元素值
selected[i] = true; // 做出选择
state.push_back(choice); // 更新状态
selected[i] = true;
state.push_back(choice);
backtrack(state, choices, selected, res);
// 回退
selected[i] = false; // 撤销选择
state.pop_back(); // 恢复到之前的状态
// 回退：撤销选择，恢复到之前的状态
selected[i] = false;
state.pop_back();
}
}
}
/* 全排列 II */
vector<vector<int>> permutationsII(vector<int> nums) {
vector<int> state;
vector<bool> selected(nums.size(), false);
vector<vector<int>> res;
backtrack(state, nums, selected, res);
return res;
}
```
@ -256,56 +334,104 @@ comments: true
for i, choice in enumerate(choices):
# 剪枝：不允许重复选择元素 且 不允许重复选择相等元素
if not selected[i] and choice not in duplicated:
# 尝试
# 尝试：做出选择，更新状态
duplicated.add(choice) # 记录选择过的元素值
selected[i] = True # 做出选择
state.append(choice) # 更新状态
selected[i] = True
state.append(choice)
backtrack(state, choices, selected, res)
# 回退
selected[i] = False # 撤销选择
state.pop() # 恢复到之前的状态
# 回退：撤销选择，恢复到之前的状态
selected[i] = False
state.pop()
def permutations_ii(nums: list[int]) -> list[list[int]]:
"""全排列 II"""
res = []
backtrack(state=[], choices=nums, selected=[False] * len(nums), res=res)
return res
```
=== "Go"
```go title="permutations_ii.go"
[class]{}-[func]{backtrack}
[class]{}-[func]{permutationsII}
```
=== "JavaScript"
```javascript title="permutations_ii.js"
[class]{}-[func]{backtrack}
[class]{}-[func]{permutationsII}
```
=== "TypeScript"
```typescript title="permutations_ii.ts"
[class]{}-[func]{backtrack}
[class]{}-[func]{permutationsII}
```
=== "C"
```c title="permutations_ii.c"
[class]{}-[func]{backtrack}
[class]{}-[func]{permutationsII}
```
=== "C#"
```csharp title="permutations_ii.cs"
[class]{permutations_ii}-[func]{backtrack}
/* 回溯算法：全排列 II */
void backtrack(List<int> state, int[] choices, bool[] selected, List<List<int>> res) {
// 当状态长度等于元素数量时，记录解
if (state.Count == choices.Length) {
res.Add(new List<int>(state));
return;
}
// 遍历所有选择
ISet<int> duplicated = new HashSet<int>();
for (int i = 0; i < choices.Length; i++) {
int choice = choices[i];
// 剪枝：不允许重复选择元素 且 不允许重复选择相等元素
if (!selected[i] && !duplicated.Contains(choice)) {
// 尝试：做出选择，更新状态
duplicated.Add(choice); // 记录选择过的元素值
selected[i] = true;
state.Add(choice);
backtrack(state, choices, selected, res);
// 回退：撤销选择，恢复到之前的状态
selected[i] = false;
state.RemoveAt(state.Count - 1);
}
}
}
/* 全排列 II */
List<List<int>> permutationsII(int[] nums) {
List<List<int>> res = new List<List<int>>();
backtrack(new List<int>(), nums, new bool[nums.Length], res);
return res;
}
```
=== "Swift"
```swift title="permutations_ii.swift"
[class]{}-[func]{backtrack}
[class]{}-[func]{permutationsII}
```
=== "Zig"
```zig title="permutations_ii.zig"
[class]{}-[func]{backtrack}
[class]{}-[func]{permutationsII}
```
注意，虽然 `selected` 和 `duplicated` 都起到剪枝的作用，但他们剪掉的是不同的分支：

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