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. [1,2,1] is not valid because 1 is used twice.
Example 4:
Input: k = 3, n = 2
Output: []
Explanation: There are no valid combinations.
Example 5:
Input: k = 9, n = 45
Output: [[1,2,3,4,5,6,7,8,9]]
Explanation:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
There are no other valid combinations.
Constraints:
- 2 <= k <= 9
- 1 <= n <= 60
Solution
class Solution {
List<List<Integer>> res = new ArrayList<>();
public List<List<Integer>> combinationSum3(int k, int n) {
List<Integer> current = new ArrayList<>();
search(k, n, 1, current);
return res;
}
void search(int k, int n, int start, List<Integer> current) {
if (n < 0) return;
if (current.size() > k) return;
if (n == 0 && current.size() == k) {
res.add(new ArrayList<>(current));
return;
}
for (int i = start; i < 10; i++) {
int remainder = n - i;
if (remainder < 0) continue;
current.add(i);
search(k, remainder, i + 1, current);
current.remove(current.size() - 1);
}
}
}