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?

Optimal Solution

Complexity Optimal Solution

• Time: O(nm)
• Space: O(n)

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

    return dp[target];
}