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[0] = 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];
    }
}