## DEV Community

Abhishek Chaudhary

Posted on

# 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 <= 9`
• `1 <= n <= 60`

SOLUTION:

``````class Solution:
def getSums(self, comb, target, p, res):
if target < 0:
return
if p == len(comb):
if target == 0:
res.append(comb[1:])
return
for i in range(comb[p - 1] + 1, 10):
comb[p] = i
self.getSums(comb, target - i, p + 1, res)

def combinationSum3(self, k: int, n: int) -> List[List[int]]:
comb = [0] * (k + 1)
res = []
self.getSums(comb, n, 1, res)
return res
``````