LeetCode——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. Solution

递归求解。

Basic idea: permutation of A[1..n] equals to
A[1] + permutation of (A[1..n] - A[1])
A[2] + permutation of (A[1..n] - A[2])
...
A[n] + permutation of (A[1..n] - A[n]).

3. Code

class Solution {
public:
    vector<vector<int>> permute(vector<int>& nums) {
        vector<vector<int>> res;
        permuteCore(nums, 0, res);
        return res;
    }
    void permuteCore(vector<int>& nums, int start, vector<vector<int>>& res) {
        if (start >= nums.size()) {  // 已经遍历到最后一个数字
            res.push_back(nums);
            return;
        }
        // 依次和开始的数字交换
        for (int i = start; i < nums.size(); i++) {
            swap(nums[start], nums[i]);
            permuteCore(nums,start + 1, res);
            swap(nums[start], nums[i]);   // 还原
        }
     }
};