# \[46]\[中等]\[回溯] 全排列

## 题目描述

[46. 全排列](https://leetcode-cn.com/problems/permutations/)

给定一个 没有重复 数字的序列，返回其所有可能的全排列。

示例:

```
输入: [1,2,3]
输出:
[
  [1,2,3],
  [1,3,2],
  [2,1,3],
  [2,3,1],
  [3,1,2],
  [3,2,1]
]
```

## 解题思路

列举全部排列, 需要使用回溯的方法, 使用DFS的思路, 将元素逐个放入当前列表中, 直到备选列表中元素为空, 说明所有的元素都已经被使用, 从而得到了一种排列情况. 抛弃掉尾部的元素向上回溯, 探索另一种选择对应的情况.

由于列表中的元素没有重复值, 因此不需要考虑结果的重复问题.

```python
class Solution:
    def permute(self, nums: List[int]) -> List[List[int]]:
        results = []

        def dfs(path, residual):
            if len(residual) == 0:
                results.append(path[:])

            for i, num in enumerate(residual):
                path.append(num)
                dfs(path, residual[:i] + residual[i + 1:])
                path.pop()

        dfs([], nums)
        return results
```


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