Combination sum III

Time: O(KxC(N,K)); Space: O(K); medium

Find all possible combinations of k numbers that add up to a number n, given that only numbers from 1 to 9 can be used and each combination should be a unique set of numbers.

Notes:

• All numbers will be positive integers.

• The solution set must not contain duplicate combinations.

Example 1:

Input: k = 3, n = 7

Output: [[1,2,4]]

Example 2:

Input: k = 3, n = 9

Output: [[1,2,6], [1,3,5], [2,3,4]]

class Solution1(object):
    """
    Time: O(K*C(N,K))
    Space: O(K)
    """
    def combinationSum3(self, k, n):
        """
        :type k: int
        :type n: int
        :rtype: List[List[int]]
        """
        result = []
        self.combinationSumRecu(result, [], 1, k, n)
        return result

    def combinationSumRecu(self, result, intermediate, start, k, target):
        if k == 0 and target == 0:
            result.append(list(intermediate))
        elif k < 0:
            return

        while start < 10 and start * k + k * (k - 1) / 2 <= target:
            intermediate.append(start)
            self.combinationSumRecu(result, intermediate, start + 1, k - 1, target - start)
            intermediate.pop()
            start += 1

s = Solution1()

k = 3
n = 7
assert s.combinationSum3(k, n) ==  [[1,2,4]]

k = 3
n = 9
assert s.combinationSum3(k, n) == [[1,2,6], [1,3,5], [2,3,4]]

See also:

https://leetcode.com/problems/combination-sum-iii

https://www.lintcode.com/problem/combination-sum-iii/description