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46. 全排列 🟨

题目

LeetCode 中等

题目

给定一个不含重复数字的数组 nums ，返回其 所有可能的全排列 。你可以 按任意顺序 返回答案。

示例 1：
输入：nums = [1,2,3]
输出：[[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]

示例 2：
输入：nums = [0,1]
输出：[[0,1],[1,0]]

题解

递归

  • 时间复杂度：O(n×n!)
  • 空间复杂度：O(n)
js 
function permute(nums) {
  const len = nums.length
  const res = []
  const used = {}

  const _permute = path => {
    console.log('------')
    console.log('path: ', path)

    if (path.length === len) {
      res.push([...path])
    }

    for (let i = 0; i < len; i++) {
      const num = nums[i]

      console.log('num', num, path, used)

      if (used[num] === true) continue
      path.push(num)
      used[num] = true

      console.log('📌 num', num, path, used)

      _permute(path)
      path.pop()
      used[num] = false

      console.log('🫧 num', num, path, used)
    }
  }
  _permute([])

  return res
}

console.log('🌰', permute([1, 2, 3]))
执行结果 
------
path:  []
num 1 [] {}
📌 num 1 [1] {"1":true}
------
path:  [1]
num 1 [1] {"1":true}
num 2 [1] {"1":true}
📌 num 2 [1,2] {"1":true,"2":true}
------
path:  [1,2]
num 1 [1,2] {"1":true,"2":true}
num 2 [1,2] {"1":true,"2":true}
num 3 [1,2] {"1":true,"2":true}
📌 num 3 [1,2,3] {"1":true,"2":true,"3":true}
------
path:  [1,2,3]
num 1 [1,2,3] {"1":true,"2":true,"3":true}
num 2 [1,2,3] {"1":true,"2":true,"3":true}
num 3 [1,2,3] {"1":true,"2":true,"3":true}
🫧 num 3 [1,2] {"1":true,"2":true,"3":false}
🫧 num 2 [1] {"1":true,"2":false,"3":false}
num 3 [1] {"1":true,"2":false,"3":false}
📌 num 3 [1,3] {"1":true,"2":false,"3":true}
------
path:  [1,3]
num 1 [1,3] {"1":true,"2":false,"3":true}
num 2 [1,3] {"1":true,"2":false,"3":true}
📌 num 2 [1,3,2] {"1":true,"2":true,"3":true}
------
path:  [1,3,2]
num 1 [1,3,2] {"1":true,"2":true,"3":true}
num 2 [1,3,2] {"1":true,"2":true,"3":true}
num 3 [1,3,2] {"1":true,"2":true,"3":true}
🫧 num 2 [1,3] {"1":true,"2":false,"3":true}
num 3 [1,3] {"1":true,"2":false,"3":true}
🫧 num 3 [1] {"1":true,"2":false,"3":false}
🫧 num 1 [] {"1":false,"2":false,"3":false}
num 2 [] {"1":false,"2":false,"3":false}
📌 num 2 [2] {"1":false,"2":true,"3":false}
------
path:  [2]
num 1 [2] {"1":false,"2":true,"3":false}
📌 num 1 [2,1] {"1":true,"2":true,"3":false}
------
path:  [2,1]
num 1 [2,1] {"1":true,"2":true,"3":false}
num 2 [2,1] {"1":true,"2":true,"3":false}
num 3 [2,1] {"1":true,"2":true,"3":false}
📌 num 3 [2,1,3] {"1":true,"2":true,"3":true}
------
path:  [2,1,3]
num 1 [2,1,3] {"1":true,"2":true,"3":true}
num 2 [2,1,3] {"1":true,"2":true,"3":true}
num 3 [2,1,3] {"1":true,"2":true,"3":true}
🫧 num 3 [2,1] {"1":true,"2":true,"3":false}
🫧 num 1 [2] {"1":false,"2":true,"3":false}
num 2 [2] {"1":false,"2":true,"3":false}
num 3 [2] {"1":false,"2":true,"3":false}
📌 num 3 [2,3] {"1":false,"2":true,"3":true}
------
path:  [2,3]
num 1 [2,3] {"1":false,"2":true,"3":true}
📌 num 1 [2,3,1] {"1":true,"2":true,"3":true}
------
path:  [2,3,1]
num 1 [2,3,1] {"1":true,"2":true,"3":true}
num 2 [2,3,1] {"1":true,"2":true,"3":true}
num 3 [2,3,1] {"1":true,"2":true,"3":true}
🫧 num 1 [2,3] {"1":false,"2":true,"3":true}
num 2 [2,3] {"1":false,"2":true,"3":true}
num 3 [2,3] {"1":false,"2":true,"3":true}
🫧 num 3 [2] {"1":false,"2":true,"3":false}
🫧 num 2 [] {"1":false,"2":false,"3":false}
num 3 [] {"1":false,"2":false,"3":false}
📌 num 3 [3] {"1":false,"2":false,"3":true}
------
path:  [3]
num 1 [3] {"1":false,"2":false,"3":true}
📌 num 1 [3,1] {"1":true,"2":false,"3":true}
------
path:  [3,1]
num 1 [3,1] {"1":true,"2":false,"3":true}
num 2 [3,1] {"1":true,"2":false,"3":true}
📌 num 2 [3,1,2] {"1":true,"2":true,"3":true}
------
path:  [3,1,2]
num 1 [3,1,2] {"1":true,"2":true,"3":true}
num 2 [3,1,2] {"1":true,"2":true,"3":true}
num 3 [3,1,2] {"1":true,"2":true,"3":true}
🫧 num 2 [3,1] {"1":true,"2":false,"3":true}
num 3 [3,1] {"1":true,"2":false,"3":true}
🫧 num 1 [3] {"1":false,"2":false,"3":true}
num 2 [3] {"1":false,"2":false,"3":true}
📌 num 2 [3,2] {"1":false,"2":true,"3":true}
------
path:  [3,2]
num 1 [3,2] {"1":false,"2":true,"3":true}
📌 num 1 [3,2,1] {"1":true,"2":true,"3":true}
------
path:  [3,2,1]
num 1 [3,2,1] {"1":true,"2":true,"3":true}
num 2 [3,2,1] {"1":true,"2":true,"3":true}
num 3 [3,2,1] {"1":true,"2":true,"3":true}
🫧 num 1 [3,2] {"1":false,"2":true,"3":true}
num 2 [3,2] {"1":false,"2":true,"3":true}
num 3 [3,2] {"1":false,"2":true,"3":true}
🫧 num 2 [3] {"1":false,"2":false,"3":true}
num 3 [3] {"1":false,"2":false,"3":true}
🫧 num 3 [] {"1":false,"2":false,"3":false}
🌰 [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]