377. Combination Sum IV

Medium

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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?

Solution 1 :

class Solution:
    def combinationSum4(self, nums: List[int], target: int) -> int:
        nums.sort()
        d = {}
        count = 0
        def recursion(target):
            nonlocal count
            if target == 0:
                return 1
            if target < 0:
                return 0
            if target in d:
                return d[target]
            temp = 0
            for num in nums:
                if target >= num:
                    temp += recursion(target-num)
                else:
                    break
            d[target] = temp
            return d[target]
        recursion(target)
        return d[target]

Solution 2 :

class Solution:
    def combinationSum4(self, nums: List[int], target: int) -> int:
        nums.sort() # For Early Exit
        arr = [0]*(target+1)
        for num in nums:
            if num <= target:
                arr[num] = 1
        for i in range(target+1):
            for num in nums:
                if i-num > 0:
                    arr[i] += arr[i-num]
                else:
                    break
        return arr[-1]