题目大意：输出所有用k个数的和为n的组合。可以使用的元素是1到9。

Problem:

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.

[[1,2,4]]

[[1,2,6], [1,3,5], [2,3,4]]

Idea:

DFS + backtracking

bit

Solution:

C++

// Author: Huahua
// Runtime: 0 ms
class Solution {
public:
    vector<vector<int>> combinationSum3(int k, int n) {
        vector<vector<int>> ans;
        vector<int> cur;
        dfs(k, n, 1, cur, ans);
        return ans;
    }
private:
    // Use k numbers (>= s) to sum up to n
    void dfs(int k, int n, int s, 
             vector<int>& cur, vector<vector<int>>& ans) {
        if (k == 0) {
            if (n == 0) ans.push_back(cur);
            return;
        }
        
        for (int i = s; i <= 9; ++i) {
            if (i > n) return;
            cur.push_back(i);
            dfs(k - 1, n - i, i + 1, cur, ans);
            cur.pop_back();
        }
    }
};

C++ / binary

class Solution {
public:
    vector<vector<int>> combinationSum3(int k, int n) {
        vector<vector<int>> ans;
        
        // 2^9, generate all combinations of [1 .. 9]
        for (int i = 0; i < (1 << 9); ++i) {
            vector<int> cur;
            int sum = 0;
            // Use j if (j - 1)-th bit is 1
            for (int j = 1; j <= 9; ++j)
                if (i & (1 << (j - 1))) {
                    sum += j;
                    cur.push_back(j);
                }
            if (sum == n && cur.size() == k) 
                ans.push_back(cur);
        }
        
        return ans;
    }
};

Python

class Solution:
    def combinationSum3(self, k, n):
        def dfs(k, n, s, cur, ans):
            if k == 0 and n == 0: 
                ans.append(list(cur))
            for i in range(s, min(n + 1, 10)):
                dfs(k - 1, n - i, i + 1, cur + [i], ans)
        
        ans = []        
        dfs(k, n, 1, [], ans)
        return ans

Related problems:

• [解题报告] LeetCode 39. Combination Sum
• [解题报告] LeetCode 40. Combination Sum II

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