【刷题-LeetCode】216. Combination Sum III

1. 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]]

解 定义函数f(l, r, n, target)，表示在区间[l, r]之间和为target的n个数，则：

\[f(l, r, n, target) = \bigcup_{i=l}^r f(i+1, r, n-1, target - i)
\]

当n=2时，直接采用双指针搜索

class Solution {
public:
    vector<vector<int>> combinationSum3(int k, int n) {
        vector<bool>nums(10, true);
        return comb(1, 9, k, n);
    }
    vector<vector<int>> comb(int l, int r, int n, int target){
        vector<vector<int>>ans;
        if(n == 2){
            int i = l, j = r;
            while(i < j){
                int tmp = i + j;
                if(tmp == target){
                    ans.push_back({i,j});
                    i++;
                    j--;
                }else if(tmp < target){
                    i++;
                }else{
                    j--;
                }
            }
            return ans;
        }
        for(int i = l; i <= r; ++i){
            vector<vector<int>>tmp_ans = comb(i+1, r, n - 1, target - i);
            if(tmp_ans.size() > 0){
                for(auto &v : tmp_ans){
                    v.insert(v.begin(), i);
                    ans.push_back(v);
                }
            }
        }
        return ans;
    }
};