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?

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

Solution

public class Solution {
    public int combinationSum4(int[] nums, int target) {
        if (nums == null || nums.length == 0 || target <= 0) return 0;

        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];
    }
}