377. Combination Sum IV

https://leetcode.com/problems/combination-sum-iv/#/description

 

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?

 

 

Sol:

 

DP.

 

class Solution(object):
    def combinationSum4(self, nums, target):
        """
        :type nums: List[int]
        :type target: int
        :rtype: int
        """
        # DP
        nums.sort()
        dp = [0] * (target + 1)
        dp[0] = 1 # if num == target
        
        # before we figure out the number of ways that add up to target, we figure out the number of ways that add up to target - 1, target - 2, ..., 1.
        for currSum in range(1, target + 1):
            for num in nums:
                if num > currSum:
                    break 
                dp[currSum] += dp[currSum - num]
        return dp[target]