Leetcode 77. Combinations

Leetcode 77. Combinations

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题目描述

Given two integers n and k, return all possible combinations of k numbers out of 1 … n.

For example,
If n = 4 and k = 2, a solution is:

[
  [2,4],
  [3,4],
  [2,3],
  [1,2],
  [1,3],
  [1,4],
]

输入：最大数字n，组合所需元素数k
输出：k个元素的排列组合

思路

利用DFS，并保存DFS的路径，在递归层满足k时，结束；否则，继续以n个节点的方式展开。由于此处是排列组合，并且不可重复，故此处根据递增的方式展开，同时进行剪支。算法复杂度$O(n^2)$，约n(n+1)/2次。

代码

class Solution {
public:
    vector<vector<int>> ret;
    int dim;

    void backtrack(vector<int> b, int now, int n, int t){
        //meet the require dimension
        if(dim==t){

            //insert current
            b.push_back(now);
            ret.push_back(b);//insert trace
        }else{
            b.push_back(now);
            //next dimension should larger than this
            for(int i = now+1;i<=n;i++){
                backtrack(b,i,n,t+1);
            }
        }
    }
    vector<vector<int>> combine(int n, int k) {
        vector<int> b;
        dim = k;
        for(int i=1;i<=n;i++){
            backtrack(b,i,n,1);
        }

        return ret;
    }
};