[Leetcode] Combination Sum III(Medium)
LeetCode 216 - 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
Input: k = 3, n = 7
Output: [[1,2,4]]
Explanation:
1 + 2 + 4 = 7
There are no other valid combinations.
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.
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.
How can we solve this problem?
這題主要關注的點是數字範圍為[1,9]，每個結果中，數字只能使用一次，而且數字必須是順序排列。例如:2,3,4,1,2,5。解決這題我們可以用back-traking大法。只要我們當前的Sum大於n我們就直接退回back track回上一步,因為數值只會越來越大，並不是我們想要的。如果Ans我們所需的k個就直接判斷是否等於n，如果是就直接加入到我們的result即可。
Solution:
class Solution {
vector<vector<int>> res;
vector<int> tmp;
public:
vector<vector<int>> combinationSum3(int k, int n) {
solution(n,k,0,1);
return res;
}
void solution(int n,int k,int sum,int start){
if(k==0){
if(sum == n) res.push_back(tmp);
return;
}
if(sum > n) return;
for(int i = start;i<=9;i++){
tmp.push_back(i);
solution(n,k-1,sum + i,i+1);
tmp.pop_back();
}
}
};