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Update the code of permutations I and II
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3 changed files with 72 additions and 22 deletions
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@ -11,7 +11,7 @@ namespace hello_algo.chapter_backtracking;
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public class permutations_i {
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/* 回溯算法:全排列 I */
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public static void backtrack(List<int> state, int[] choices, bool[] selected, List<List<int>> res) {
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static 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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@ -22,24 +22,29 @@ public class permutations_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
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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.RemoveAt(state.Count - 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.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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static 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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[Test]
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public void Test() {
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int[] nums = { 1, 2, 3 };
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// 回溯算法
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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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List<List<int>> res = permutationsI(nums);
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Console.WriteLine("输入数组 nums = " + string.Join(", ", nums));
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Console.WriteLine("所有排列 res = ");
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@ -11,7 +11,7 @@ namespace hello_algo.chapter_backtracking;
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public class permutations_ii {
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/* 回溯算法:全排列 II */
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public static void backtrack(List<int> state, int[] choices, bool[] selected, List<List<int>> res) {
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static 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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@ -23,25 +23,30 @@ public class permutations_ii {
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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.RemoveAt(state.Count - 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.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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static 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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[Test]
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public void Test() {
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int[] nums = { 1, 2, 2 };
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// 回溯算法
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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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List<List<int>> res = permutationsII(nums);
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Console.WriteLine("输入数组 nums = " + string.Join(", ", nums));
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Console.WriteLine("所有排列 res = ");
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@ -32,60 +32,80 @@
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```java title="permutations_i.java"
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[class]{permutations_i}-[func]{backtrack}
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[class]{permutations_i}-[func]{permutationsI}
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```
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=== "C++"
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```cpp title="permutations_i.cpp"
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[class]{}-[func]{backtrack}
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[class]{}-[func]{permutationsI}
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```
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=== "Python"
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```python title="permutations_i.py"
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[class]{}-[func]{backtrack}
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[class]{}-[func]{permutations_i}
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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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[class]{permutations_i}-[func]{permutationsI}
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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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@ -114,60 +134,80 @@
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```java title="permutations_ii.java"
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[class]{permutations_ii}-[func]{backtrack}
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[class]{permutations_ii}-[func]{permutationsII}
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```
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=== "C++"
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```cpp title="permutations_ii.cpp"
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[class]{}-[func]{backtrack}
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[class]{}-[func]{permutationsII}
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```
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=== "Python"
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```python title="permutations_ii.py"
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[class]{}-[func]{backtrack}
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[class]{}-[func]{permutations_ii}
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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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[class]{permutations_ii}-[func]{permutationsII}
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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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