46. Permutations

题目描述：

Given a collection of distinct integers, return all possible permutations.

Example:

Input: [1,2,3]
Output:
[
  [1,2,3],
  [1,3,2],
  [2,1,3],
  [2,3,1],
  [3,1,2],
  [3,2,1]
]

解题思路：

用回溯法。使用额外空间记录每个数值是否已经使用。

代码：

class Solution {
public:
    vector<vector<int>> permute(vector<int>& nums) {
        int size = nums.size();
        vector<int> flag(size, 0);
        vector<vector<int> > ret;
        vector<int> tmp;
        tmp.reserve(size);   
        permute(size, flag, tmp, ret);
        for (int i = 0; i < ret.size(); i++) {
            for (int j = 0; j < size; j++) {
                ret[i][j] = nums[ret[i][j]];
            }
        }
        return ret;
    }
    void permute(int size, vector<int>& flag, vector<int>& tmp, vector<vector<int> >& ret) {
        if (accumulate(flag.begin(), flag.end(), 0) == size) {
            ret.push_back(tmp);
        }
        for (int i = 0; i < size; i++) {
            if (flag[i])
                continue;
            flag[i] = 1;
            tmp.push_back(i);
            permute(size, flag, tmp, ret);
            tmp.pop_back();
            flag[i] = 0;
        }
    }
};

 改进版本：

class Solution {
public:
    vector<vector<int>> permute(vector<int>& nums) {
        int size = nums.size();
        vector<int> flag(size, 0);
        vector<vector<int> > ret;
        vector<int> tmp;
        tmp.reserve(size);   
        permute(size, nums, flag, tmp, ret);
        /*for (int i = 0; i < ret.size(); i++) {
            for (int j = 0; j < size; j++) {
                ret[i][j] = nums[ret[i][j]];
            }
        }*/
        return ret;
    }
    void permute(int size, const vector<int>& nums, vector<int>& flag, vector<int>& tmp, vector<vector<int> >& ret) {
        if (accumulate(flag.begin(), flag.end(), 0) == size) {
            ret.push_back(tmp);
            return;
        }
        for (int i = 0; i < size; i++) {
            if (flag[i])
                continue;
            flag[i] = 1;
            tmp.push_back(nums[i]);
            permute(size, nums, flag, tmp, ret);
            tmp.pop_back();
            flag[i] = 0;
        }
    }
};