216. Combination Sum III

problem description

Find all possible combinations of k numbers that add up to a number n, given that only numbers from 1 to 9 can be used and each combination should be a unique set of numbers.

Note:

All numbers will be positive integers. The solution set must not contain duplicate combinations.

Example 1:

Input: k = 3, n = 7
Output: [[1,2,4]]

Example 2:

Input: k = 3, n = 9
Output: [[1,2,6], [1,3,5], [2,3,4]]

algorithm thought

组合问题，直接用回溯法解决，中间加入剪枝，如果sum已经大于n了，就可以不用继续往下求解了

code

class Solution {
public:
    vector<vector<int>> combinationSum3(int k, int n) {
        vector<vector<int>> res;
        vector<int> tmp;
        help(res,k,n,tmp,0,1);
        return res;
    }
    void help(vector<vector<int>>&res,int k,int n,vector<int>&tmp,int sum,int pos){
        if(tmp.size()==k){
            if(sum==n){
                res.push_back(tmp);
            }
            return;
        }
        for(int i=pos;i<10;++i){
            //cout<<pos<<'-'<<i<<' ';
            if(sum+i>n)
                return;
            tmp.push_back(i);
            help(res,k,n,tmp,sum+i,i+1);
            tmp.pop_back();
        }
    }
};

algorithm analysis

遍历求解3个数的组合，时间复杂度 O(C(9,k))-> O(9^k), 空间复杂度: k