chore: add daily leetcode post 46.全排列

Author: longsizhuo

app/docs/CommunityShare/Leetcode/46.全排列.md

@@ -0,0 +1,82 @@
+---
+title: 46.permutations
+date: 24/3/2025
+tags:
+  - Python
+  - '9021'
+  - tree
+abbrlink: d567a4cd
+---
+
+# Description:
+Given an array nums of distinct integers, return all the possible permutations. You can return the answer in any order.
+
+Example 1:
+
+Input: nums = [1,2,3]
+Output: [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]
+Example 2:
+
+Input: nums = [0,1]
+Output: [[0,1],[1,0]]
+Example 3:
+
+Input: nums = [1]
+Output: [[1]]
+
+
+# Thinking:
+This question is more like a tree problem.
+like the tree below:
+```shell
+dfs(0): nums = [1,2,3]
+|
+|-- i=0: swap(0,0) -> [1,2,3]
+|   |
+|   |-- dfs(1)
+|       |-- i=1: swap(1,1) -> [1,2,3]
+|       |   |-- dfs(2): append [1,2,3]
+|       |-- i=2: swap(1,2) -> [1,3,2]
+|           |-- dfs(2): append [1,3,2]
+|
+|-- i=1: swap(0,1) -> [2,1,3]
+|   |
+|   |-- dfs(1)
+|       |-- i=1: swap(1,1) -> [2,1,3]
+|       |   |-- dfs(2): append [2,1,3]
+|       |-- i=2: swap(1,2) -> [2,3,1]
+|           |-- dfs(2): append [2,3,1]
+|
+|-- i=2: swap(0,2) -> [3,2,1]
+    |
+    |-- dfs(1)
+        |-- i=1: swap(1,1) -> [3,2,1]
+        |   |-- dfs(2): append [3,2,1]
+        |-- i=2: swap(1,2) -> [3,1,2]
+            |-- dfs(2): append [3,1,2]
+
+```
+We swap the current position index with each possible candidate `i` from `index` to the end. They can be seen as left and right pointers: `index` determines which position we're filling, and `i` tries different numbers to place there.
+
+Before the recursive call, we swap `nums[i]` and `nums[index]` to try placing a new number at position index. If we reach the last position (`index == len(nums) - 1`), we add the current permutation to the answer list. 
+After recursion, we swap back to restore the original state (backtracking).
+
+# Code:
+```python
+class Solution:
+    def permute(self, nums: List[int]) -> List[List[int]]:
+        # index
+        def dfs(index):
+            # Reach the last element
+            if index == len(nums) - 1:
+                res.append(list(nums))
+                return
+            for i in range(index, len(nums)):
+                nums[i], nums[index] = nums[index], nums[i]
+                dfs(index + 1)
+                nums[i], nums[index] = nums[index], nums[i]
+
+        res = []
+        dfs(0)
+        return res
+```