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377. Combination Sum IV

Array Dynamic Programming

Problem - Combination Sum IV

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?

Solutions

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

Submission Stats:

  • Runtime: 40 ms (74.20%)
  • Memory: 18 MB (26.50%)