# 377. Combination Sum IV (Medium)

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.
```

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?

Credits:
Special thanks to @pbrother for adding this problem and creating all test cases.

## Solutions

• Java
``````class Solution {
public int combinationSum4(int[] nums, int target) {
if (nums == null || nums.length == 0) {
return 0;
}
return recursion(nums, target);
}

private int recursion(int[] nums, int remainTarget) {
// 当剩余容量为 0 时，说明找到了一个方案
if (remainTarget == 0) {
return 1;
}
int rst = 0;
// 每次 Recursion 都需要遍历整个数组
for (int i = 0; i < nums.length; i++) {
if (remainTarget >= nums[i]) {
rst += recursion(nums, remainTarget - nums[i]);
}
}
return rst;
}
}
``````