Find all valid combinations of k
numbers that sum up to n
such that the following conditions are true:
- Only numbers
1
through9
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
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