LeetCode216 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.

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]]

思路：

我们使用递归的方式进行暴力搜索，一旦发现符合条件的组合就记录下来；注意这里递归的分支是关键，但是也非常的简单直接：当遇到一个数时，选他或是不选他。

class Solution {
public:
    vector<vector<int>> combinationSum3(int k, int n) {
        set<int> left;
        for(int i = 1;i<=9;i++)
            left.insert(i);
        helper(vector<int>(), 0,left,k,n);
        return res;
    }
private:
    vector<vector<int>> res;
    void helper(vector<int> temp, int sum, set<int> left, int k, int n){
        if(left.empty()) return;

        int num = *left.begin();
        set<int> left_new = left;
        left_new.erase(num);
        int sum_new = sum+num;
        vector<int> temp_new = temp;
        temp_new.push_back(num);

        helper(temp, sum, left_new, k, n);
        if(k == temp_new.size() && sum_new == n){
            res.push_back(temp_new);
            return;
        }
        else if(k > temp_new.size() && sum_new > n)
            return;
        else if(k > temp_new.size() && sum_new < n){
            helper(temp_new, sum_new, left_new, k, n);
        }
    }
};