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MEDIUM

Permutations

Given an array nums of distinct integers, return all the possible permutations. You can return the answer in any order.

Example

Input:

nums = [1,2,3]

Output:

[[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]

Explanation:
All possible permutations of [1,2,3].

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Constraints

• 1 ≤ nums.length ≤ 6
• -10 ≤ nums[i] ≤ 10
• All the integers of nums are unique.

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Solution: Backtracking

• Time Complexity: O(n!)
• Space Complexity: O(n!)

C++

class Solution {
public:
    vector<vector<int>> permute(vector<int>& nums) {
        vector<vector<int>> res;
        vector<int> path;
        vector<bool> used(nums.size(), false);
        function<void()> dfs = [&]() {
            if (path.size() == nums.size()) {
                res.push_back(path);
                return;
            }
            for (int i = 0; i < nums.size(); ++i) {
                if (used[i]) continue;
                used[i] = true;
                path.push_back(nums[i]);
                dfs();
                path.pop_back();
                used[i] = false;
            }
        };
        dfs();
        return res;
    }
};