216. Combination Sum III

Medium (Trung bình) C++ 🔗 Xem trên LeetCode

📋 Đề Bài

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.

 

Example 1:

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

Example 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.

Example 3:

Input: k = 4, n = 1
Output: []
Explanation: There are no valid combinations.
Using 4 different numbers in the range [1,9], the smallest sum we can get is 1+2+3+4 = 10 and since 10 > 1, there are no valid combination.

 

Constraints:

  • 2 <= k <= 9
  • 1 <= n <= 60

🧠 Thuật Toán & Kỹ Thuật

DFS (Tìm kiếm theo chiều sâu)Bit Manipulation (Thao tác bit)
⏱️ Thời gian O(V+E)
💾 Không gian O(V)

💻 Lời Giải

C++ 0216-combination-sum-iii.cpp 
class Solution {
private:
    vector<vector<int>> ans;
    vector<int> tmp;
    
public:
    void dfs(int i, int k, int n) {
        if (n <= 0) {
            if (n == 0 and k == 0) {
                ans.push_back(tmp);
            }
            return;
        }
        for (int j = i; j <= 9; ++j) {
            tmp.push_back(j);
            dfs(j + 1, k - 1, n - j);
            tmp.pop_back();
        }
    }
    vector<vector<int>> combinationSum3(int k, int n) {
        dfs(1, k, n);
        return ans;
    }
};