216. Combination Sum III

 

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.

Ensure that numbers within the set are sorted in ascending order.

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]]

Credits:
Special thanks to @mithmatt for adding this problem and creating all test cases.

 

这道题题是组合之和系列的第三道题,跟之前两道 Combination SumCombination Sum II 都不太一样,那两道的联系比较紧密,变化不大,而这道跟它们最显著的不同就是这道题的个数是固定的,为k。个人认为这道题跟那道 Combinations 更相似一些,但是那道题只是排序,对k个数字之和又没有要求。所以实际上这道题是它们的综合体,两者杂糅到一起就是这道题的解法了,n是k个数字之和,如果n小于0,则直接返回,如果n正好等于0,而且此时out中数字的个数正好为k,说明此时是一个正确解,将其存入结果res中,具体实现参见代码入下:

 

class Solution {
public:
    vector<vector<int> > combinationSum3(int k, int n) {
        vector<vector<int> > res;
        vector<int> out;
        combinationSum3DFS(k, n, 1, out, res);
        return res;
    }
    void combinationSum3DFS(int k, int n, int level, vector<int> &out, vector<vector<int> > &res) {
        if (n < 0) return;
        if (n == 0 && out.size() == k) res.push_back(out);
        for (int i = level; i <= 9; ++i) {
            out.push_back(i);
            combinationSum3DFS(k, n - i, i + 1, out, res);
            out.pop_back();
        }
    }
};

 

类似题目:

Combination Sum IV 

Combination Sum II

Combination Sum

 

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