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46. Permutations ​

题目 ​

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]]

 

Constraints:

  • 1 <= nums.length <= 6
  • -10 <= nums[i] <= 10
  • All the integers of nums are unique.
Related Topics
  • 数组
  • 回溯

  • 👍 3128
  • 👎 0

    • 思路 ​

    • python 中的 shallow copy 数组可使用 list[:] 进行拷贝
    • 回溯的本质是递归加穷举， 用一个等长数组记录是否使用过的位数感觉很巧妙

    解法 ​

    py
    # leetcode submit region begin(Prohibit modification and deletion)
class Solution:
    def permute(self, nums: List[int]) -> List[List[int]]:
        res = []

        def backtrack(path, used):
            if len(path) == len(nums):
                res.append(path[:])
                return

            for i,  num in enumerate(nums):
                if not used[i]:
                    used[i] = True
                    path.append(num)
                    backtrack(path, used)
                    path.pop()
                    used[i] = False

        backtrack([], [False] * len(nums))
        return res


        
# leetcode submit region end(Prohibit modification and deletion)

    复杂度分析 ​

    • 时间复杂度 O(N * N)
    • 空间复杂度 O(N * N!)