Combination Sum IV.py

'''
 Given an integer array with all positive numbers and no duplicates, find the number of possible combinations that add up to a positive integer target.

Example:

nums = [1, 2, 3]
target = 4

The possible combination ways are:
(1, 1, 1, 1)
(1, 1, 2)
(1, 2, 1)
(1, 3)
(2, 1, 1)
(2, 2)
(3, 1)

Note that different sequences are counted as different combinations.

Therefore the output is 7.

Follow up:
What if negative numbers are allowed in the given array?
How does it change the problem?
What limitation we need to add to the question to allow negative numbers?

Credits:
Special thanks to @pbrother for adding this problem and creating all test cases.
'''

class Solution(object):
    def combinationSum4(self, nums, target):
        """
        :type nums: List[int]
        :type target: int
        :rtype: int
        """
        dic = {}
        return self.dfs(nums, target, dic)
    
    def dfs(self, nums, target, dic):
        if target == 0:
            return 1
        
        if target in dic:
            return dic[target]
        
        tmp = 0
        for num in nums:
            if target >= num:
                tmp += self.dfs(nums, target - num, dic)
        
        dic[target] = tmp
        return dic[target]