377. Combination Sum IV

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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.

Code

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

        int[] res = new int[target + 1];
        res[0] = 1;
        
        for(int i = 1; i < res.length; i++){
            for(int num : nums){
                if(i - num >= 0){
                    res[i] += res[i - num];
                }
            }
        }

        return res[target];
    }
}

class Solution {
    public int combinationSum4(int[] nums, int target) {
        HashMap<Integer, Integer> map = new HashMap<>();
        Arrays.sort(nums);
        return helper(nums, target, map);
    }

    private int helper(int[] nums, int target, HashMap<Integer, Integer> map) {
        if (map.containsKey(target)) return map.get(target);

        if(target < 0) return 0;
        if(target == 0) return 1;

        int res = 0;
        for(int i = 0; i < nums.length; i++) {
            if(target - nums[i] >= 0) {
                res += helper(nums, target - nums[i], map);
            }
        }

        map.put(target, res);
        return res;
    }
}