Combination sum iv

class Solution:
    def combinationSum4(self, nums: List[int], target: int) -> int:
        n = len(nums)
        dp = [0] * (target + 1)
        dp[0] = 1
        for i in range(1, target + 1):
            for j in range(n):
                if i - nums[j] >= 0:
                    dp[i] += dp[i - nums[j]]
        # print(dp)
        return dp[target]

Combination Sum IV

Difficulty: Medium

Given an array of distinct integers nums and a target integer target, return the number of possible combinations that add up to target.

The test cases are generated so that the answer can fit in a 32-bit integer.

 

Example 1:

Input: nums = [1,2,3], target = 4
Output: 7
Explanation:
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.

Example 2:

Input: nums = [9], target = 3
Output: 0

 

Constraints:

  • 1 <= nums.length <= 200
  • 1 <= nums[i] <= 1000
  • All the elements of nums are unique.
  • 1 <= target <= 1000

 

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?