1 Description #
source: https://leetcode.com/problems/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.
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 <= 91 <= n <= 60
2 Solution #
class Solution {
public:
vector<vector<int>> combinationSum3(int k, int n) {
// Time complexity: (10 - 1) * (10 -2) * .. * (10 -k)
// Space complexity:
// faster than 100.00% of C++ online submissions for Combination Sum III.
std::vector<std::vector<int>> result;
std::vector<int> path;
backtrack(k, n, 1, result, path);
return result;
}
private:
void backtrack(int k, int target, int start, std::vector<std::vector<int>>& result, std::vector<int>& path){
if(k < 0 || target < 0){
return;
}
if (k == 0 && target == 0){
result.push_back(path);
}
for(int i = start; i < 10; i++){
path.push_back(i);
backtrack(k - 1, target - i, i + 1, result, path);
path.pop_back();
}
}
};