46 Permutations

1. Question

Given a collection of distinct numbers, return all possible permutations.
For example, [1,2,3]have the following permutations:
[
[1,2,3],
[1,3,2],
[2,1,3],
[2,3,1],
[3,1,2],
[3,2,1]
]

2. Implementation

(1) Backtracking
class Solution {
public List<List<Integer>> permute(int[] nums) {
List<List<Integer>> res = new ArrayList<>();
List<Integer> permutation = new ArrayList<>();
boolean[] used = new boolean[nums.length];
getPermutations(nums, used, permutation, res);
return res;
}
public void getPermutations(int[] nums, boolean[] used, List<Integer> permutation, List<List<Integer>> res) {
if (permutation.size() == nums.length) {
res.add(new ArrayList<>(permutation));
return;
}
for (int i = 0; i < nums.length; i++) {
if (!used[i]) {
used[i] = true;
permutation.add(nums[i]);
getPermutations(nums, used, permutation, res);
permutation.remove(permutation.size() - 1);
used[i] = false;
}
}
}
}

3. Time & Space Complexity

Backtracking: 时间复杂度O(n!), 空间复杂度O(n!)