feat: Add the section of permutations problem. (#476)

* Add the section of permutations problem.

* Update permutations_problem.md

codes/python/chapter_backtracking/permutations_ii.py

@@ -0,0 +1,45 @@
+"""
+File: permutations_ii.py
+Created Time: 2023-04-15
+Author: Krahets (krahets@163.com)
+"""
+
+import sys, os.path as osp
+
+sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
+from modules import *
+
+
+def backtrack(
+    state: list[int], choices: list[int], selected: list[bool], res: list[list[int]]
+):
+    """回溯算法：全排列 II"""
+    # 当状态长度等于元素数量时，记录解
+    if len(state) == len(choices):
+        res.append(list(state))
+        return
+    # 遍历所有选择
+    duplicated = set[int]()
+    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
+            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
+            backtrack(state, choices, selected, res)
+            # 回退
+            selected[i] = False  # 撤销选择
+            state.pop()  # 恢复到之前的状态
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    nums = [1, 2, 2]
+    res = []
+
+    # 回溯算法
+    backtrack(state=[], choices=nums, selected=[False] * len(nums), res=res)
+
+    print(f"输入数组 nums = {nums}")
+    print(f"所有排列 res = {res}")