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chapter_backtracking/n_queens_problem.md
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chapter_backtracking/n_queens_problem.md
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@ -49,16 +49,23 @@ comments: true
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int choice = choices[i];
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// 剪枝：不允许重复选择元素 且 不允许重复选择相等元素
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if (!selected[i]) {
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// 尝试
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selected[i] = true; // 做出选择
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state.add(choice); // 更新状态
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// 尝试：做出选择，更新状态
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selected[i] = true;
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state.add(choice);
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backtrack(state, choices, selected, res);
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// 回退
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selected[i] = false; // 撤销选择
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state.remove(state.size() - 1); // 恢复到之前的状态
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// 回退：撤销选择，恢复到之前的状态
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selected[i] = false;
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state.remove(state.size() - 1);
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}
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}
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}
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/* 全排列 I */
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List<List<Integer>> permutationsI(int[] nums) {
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List<List<Integer>> res = new ArrayList<List<Integer>>();
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backtrack(new ArrayList<Integer>(), nums, new boolean[nums.length], res);
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return res;
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}
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```
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=== "C++"
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@ -76,16 +83,25 @@ comments: true
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int choice = choices[i];
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// 剪枝：不允许重复选择元素 且 不允许重复选择相等元素
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if (!selected[i]) {
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// 尝试
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selected[i] = true; // 做出选择
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state.push_back(choice); // 更新状态
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// 尝试：做出选择，更新状态
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selected[i] = true;
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state.push_back(choice);
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backtrack(state, choices, selected, res);
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// 回退
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selected[i] = false; // 撤销选择
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state.pop_back(); // 恢复到之前的状态
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// 回退：撤销选择，恢复到之前的状态
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selected[i] = false;
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state.pop_back();
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}
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}
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}
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/* 全排列 I */
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vector<vector<int>> permutationsI(vector<int> nums) {
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vector<int> state;
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vector<bool> selected(nums.size(), false);
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vector<vector<int>> res;
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backtrack(state, nums, selected, res);
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return res;
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}
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```
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=== "Python"
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@ -103,55 +119,101 @@ comments: true
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for i, choice in enumerate(choices):
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# 剪枝：不允许重复选择元素
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if not selected[i]:
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# 尝试
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selected[i] = True # 做出选择
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state.append(choice) # 更新状态
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# 尝试：做出选择，更新状态
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selected[i] = True
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state.append(choice)
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backtrack(state, choices, selected, res)
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# 回退
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selected[i] = False # 撤销选择
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state.pop() # 恢复到之前的状态
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# 回退：撤销选择，恢复到之前的状态
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selected[i] = False
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state.pop()
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def permutations_i(nums: list[int]) -> list[list[int]]:
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"""全排列 I"""
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res = []
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backtrack(state=[], choices=nums, selected=[False] * len(nums), res=res)
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return res
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```
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=== "Go"
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```go title="permutations_i.go"
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[class]{}-[func]{backtrack}
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[class]{}-[func]{permutationsI}
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```
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=== "JavaScript"
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```javascript title="permutations_i.js"
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[class]{}-[func]{backtrack}
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[class]{}-[func]{permutationsI}
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```
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=== "TypeScript"
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```typescript title="permutations_i.ts"
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[class]{}-[func]{backtrack}
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[class]{}-[func]{permutationsI}
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```
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=== "C"
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```c title="permutations_i.c"
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[class]{}-[func]{backtrack}
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[class]{}-[func]{permutationsI}
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```
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=== "C#"
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```csharp title="permutations_i.cs"
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[class]{permutations_i}-[func]{backtrack}
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/* 回溯算法：全排列 I */
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void backtrack(List<int> state, int[] choices, bool[] selected, List<List<int>> res) {
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// 当状态长度等于元素数量时，记录解
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if (state.Count == choices.Length) {
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res.Add(new List<int>(state));
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return;
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}
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// 遍历所有选择
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for (int i = 0; i < choices.Length; i++) {
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int choice = choices[i];
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// 剪枝：不允许重复选择元素 且 不允许重复选择相等元素
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if (!selected[i]) {
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// 尝试：做出选择，更新状态
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selected[i] = true;
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state.Add(choice);
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backtrack(state, choices, selected, res);
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// 回退：撤销选择，恢复到之前的状态
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selected[i] = false;
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state.RemoveAt(state.Count - 1);
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}
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}
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}
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/* 全排列 I */
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List<List<int>> permutationsI(int[] nums) {
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List<List<int>> res = new List<List<int>>();
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backtrack(new List<int>(), nums, new bool[nums.Length], res);
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return res;
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}
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```
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=== "Swift"
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```swift title="permutations_i.swift"
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[class]{}-[func]{backtrack}
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[class]{}-[func]{permutationsI}
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```
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=== "Zig"
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```zig title="permutations_i.zig"
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[class]{}-[func]{backtrack}
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[class]{}-[func]{permutationsI}
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```
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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。
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@ -198,17 +260,24 @@ comments: true
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int choice = choices[i];
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// 剪枝：不允许重复选择元素 且 不允许重复选择相等元素
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if (!selected[i] && !duplicated.contains(choice)) {
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// 尝试
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// 尝试：做出选择，更新状态
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duplicated.add(choice); // 记录选择过的元素值
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selected[i] = true; // 做出选择
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state.add(choice); // 更新状态
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selected[i] = true;
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state.add(choice);
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backtrack(state, choices, selected, res);
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// 回退
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selected[i] = false; // 撤销选择
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state.remove(state.size() - 1); // 恢复到之前的状态
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// 回退：撤销选择，恢复到之前的状态
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selected[i] = false;
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state.remove(state.size() - 1);
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}
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}
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}
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/* 全排列 II */
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List<List<Integer>> permutationsII(int[] nums) {
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List<List<Integer>> res = new ArrayList<List<Integer>>();
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backtrack(new ArrayList<Integer>(), nums, new boolean[nums.length], res);
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return res;
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}
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```
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=== "C++"
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@ -227,17 +296,26 @@ comments: true
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int choice = choices[i];
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// 剪枝：不允许重复选择元素 且 不允许重复选择相等元素
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if (!selected[i] && duplicated.find(choice) == duplicated.end()) {
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// 尝试
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// 尝试：做出选择，更新状态
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duplicated.emplace(choice); // 记录选择过的元素值
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selected[i] = true; // 做出选择
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state.push_back(choice); // 更新状态
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selected[i] = true;
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state.push_back(choice);
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backtrack(state, choices, selected, res);
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// 回退
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selected[i] = false; // 撤销选择
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state.pop_back(); // 恢复到之前的状态
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// 回退：撤销选择，恢复到之前的状态
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selected[i] = false;
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state.pop_back();
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}
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}
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}
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/* 全排列 II */
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vector<vector<int>> permutationsII(vector<int> nums) {
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vector<int> state;
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vector<bool> selected(nums.size(), false);
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vector<vector<int>> res;
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backtrack(state, nums, selected, res);
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return res;
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}
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```
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=== "Python"
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@ -256,56 +334,104 @@ comments: true
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for i, choice in enumerate(choices):
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# 剪枝：不允许重复选择元素 且 不允许重复选择相等元素
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if not selected[i] and choice not in duplicated:
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# 尝试
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# 尝试：做出选择，更新状态
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duplicated.add(choice) # 记录选择过的元素值
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selected[i] = True # 做出选择
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state.append(choice) # 更新状态
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selected[i] = True
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state.append(choice)
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backtrack(state, choices, selected, res)
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# 回退
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selected[i] = False # 撤销选择
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state.pop() # 恢复到之前的状态
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# 回退：撤销选择，恢复到之前的状态
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selected[i] = False
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state.pop()
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def permutations_ii(nums: list[int]) -> list[list[int]]:
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"""全排列 II"""
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res = []
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backtrack(state=[], choices=nums, selected=[False] * len(nums), res=res)
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return res
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```
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=== "Go"
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```go title="permutations_ii.go"
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[class]{}-[func]{backtrack}
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[class]{}-[func]{permutationsII}
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```
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=== "JavaScript"
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```javascript title="permutations_ii.js"
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[class]{}-[func]{backtrack}
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[class]{}-[func]{permutationsII}
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```
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=== "TypeScript"
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```typescript title="permutations_ii.ts"
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[class]{}-[func]{backtrack}
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[class]{}-[func]{permutationsII}
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```
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=== "C"
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```c title="permutations_ii.c"
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[class]{}-[func]{backtrack}
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[class]{}-[func]{permutationsII}
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```
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=== "C#"
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```csharp title="permutations_ii.cs"
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[class]{permutations_ii}-[func]{backtrack}
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/* 回溯算法：全排列 II */
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void backtrack(List<int> state, int[] choices, bool[] selected, List<List<int>> res) {
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// 当状态长度等于元素数量时，记录解
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if (state.Count == choices.Length) {
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res.Add(new List<int>(state));
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return;
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}
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// 遍历所有选择
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ISet<int> duplicated = new HashSet<int>();
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for (int i = 0; i < choices.Length; i++) {
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int choice = choices[i];
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// 剪枝：不允许重复选择元素 且 不允许重复选择相等元素
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if (!selected[i] && !duplicated.Contains(choice)) {
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// 尝试：做出选择，更新状态
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duplicated.Add(choice); // 记录选择过的元素值
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selected[i] = true;
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state.Add(choice);
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backtrack(state, choices, selected, res);
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// 回退：撤销选择，恢复到之前的状态
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selected[i] = false;
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state.RemoveAt(state.Count - 1);
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}
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}
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}
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/* 全排列 II */
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List<List<int>> permutationsII(int[] nums) {
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List<List<int>> res = new List<List<int>>();
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backtrack(new List<int>(), nums, new bool[nums.Length], res);
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return res;
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}
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```
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=== "Swift"
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```swift title="permutations_ii.swift"
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[class]{}-[func]{backtrack}
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[class]{}-[func]{permutationsII}
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```
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=== "Zig"
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```zig title="permutations_ii.zig"
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[class]{}-[func]{backtrack}
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[class]{}-[func]{permutationsII}
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```
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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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