mirror of
https://github.com/krahets/hello-algo.git
synced 2024-12-26 23:06:31 +08:00
build
This commit is contained in:
krahets
parent
969281965e
commit
4eb7734fa9
2 changed files with 164 additions and 38 deletions
0
chapter_backtracking/n_queens_problem.md
Normal file
0
chapter_backtracking/n_queens_problem.md
Normal file
|
|
@ -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++"
|
||||
|
|
@ -76,16 +83,25 @@ 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]) {
|
||||
// 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;
|
||||
}
|
||||
```
|
||||
|
||||
=== "Python"
|
||||
|
|
@ -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++"
|
||||
|
|
@ -227,17 +296,26 @@ 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;
|
||||
}
|
||||
```
|
||||
|
||||
=== "Python"
|
||||
|
|
@ -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：
|
||||
|
|
|
|||
Loading…
Reference in a new issue