# 377 Combination Sum IV

### Problem:

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?

### Solutions:

``````public class Solution {
public int combinationSum4(int[] nums, int target) {
HashMap<Integer, Integer> ans = new HashMap<Integer, Integer>();
return process(ans, nums, target);
}
private int process(HashMap<Integer, Integer> ans, int[] nums, int target){
if (target == 0) {
return 1;
}
if (ans.containsKey(target)) {
return ans.get(target);
}
int count = 0;
for (int i = 0; i < nums.length; i ++) {
if (nums[i] <= target) {
count += process(ans, nums, target - nums[i]);
}
}
ans.put(target, count);
return count;
}

}
``````
``````public class Solution {
public int combinationSum4(int[] nums, int target) {
int[] dp = new int[target + 1];
dp = 1;
for (int i = 1; i <= target; i ++) {
for (int j = 0; j < nums.length; j ++) {
if (i - nums[j] >= 0) {
dp[i] += dp[i - nums[j]];
}
}
}
return dp[target];
}
}
``````