题目描述

题目链接：216. Combination Sum III

Find all valid combinations of k numbers that sum up to n such that the following conditions are true:

• Only numbers 1 through 9 are used.
• Each number is used at most once.
  Return a list of all possible valid combinations. The list must not contain the same combination twice, and the combinations may be returned in any order.

例子

例子 1

Input: k = 3, n = 7
Output: [[1,2,4]]
Explanation:
1 + 2 + 4 = 7
There are no other valid combinations.

例子 2

Input: k = 3, n = 9
Output: [[1,2,6],[1,3,5],[2,3,4]]
Explanation:
1 + 2 + 6 = 9
1 + 3 + 5 = 9
2 + 3 + 4 = 9
There are no other valid combinations.

例子 3

Input: k = 4, n = 1
Output: []
Explanation: There are no valid combinations. [1,2,1] is not valid because 1 is used twice.

Constraints

• 2 <= k <= 9
• 1 <= n <= 60

解题思路

参考 [Leetcode]40. Combination Sum II(C++)， 思路大同小异，代码如下：

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#include <vector>

class Solution {
public:
    std::vector<std::vector<int>> combinationSum3(int k, int n) {
        k_ = k;
        std::vector<int> comb;
        std::vector<std::vector<int>> result;
        dfs(comb, 1, n, result);
        return result;
    }

private:
    int k_;

    void dfs(std::vector<int>& comb, int idx, int target,
             std::vector<std::vector<int>>& result) {
        if (comb.size() == k_) {
            if (target == 0) {
                result.push_back(comb);
            }
            return;
        }
        if (target < 0) {
            return;
        }
        for (int i = idx; i <= 9; i++) {
            comb.push_back(i);
            dfs(comb, i + 1, target - i, result);
            comb.pop_back();
        }
    }
};

• 时间复杂度: O(n!)
• 空间复杂度: O(n!)

GitHub 代码同步地址： 216.CombinationSumIii.cpp

其他题目：
GitHub: Leetcode-C++-Solution
博客： Leetcode-Solutions