leetcode 377 - Combination Sum IV

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

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?

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class Solution {
public:
int combinationSum4(vector<int>& nums, int target) {
vector<unsigned long> dp(target + 1);

dp[0] = 1;

for (int t = 1; t <= target; t++) {
dp[t] = 0;

for (int num : nums) {
if (t - num < 0)
continue;

dp[t] += dp[t - num];
}
}

return dp[target];
}
};