377. Combination Sum IV

LeetCode 377. Combination Sum IV

Description

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

The answer is guaranteed to 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?

Tags

Dynamic Programming

Solution

We initialize an array dp of length target + 1, where dp[i] represents the number of possible combinations that add up to i.

• The edge case is dp[0] = 1 refers to the only case that no elements are selected;

• For each i, from 1 to target, add dp[i-num] onto dp[i] only if i >= num;

• return dp[target].

Complexity

• Time complexity: $O(target\times n)$

• Space complexity: $O(target)$

Code

func combinationSum4(nums []int, target int) int {
	dp := make([]int, target+1)
	dp[0] = 1
	for i := 1; i <= target; i++ {
		for _, num := range nums {
			if i >= num {
				dp[i] += dp[i-num]
			}
		}
	}
	return dp[target]
}

Reference

1. 组合总和 Ⅳ