卖萌的弱渣

I am stupid, I am hungry.

Combination Sum 4

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
2
3
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7

(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?

Soltuion

  • DP
(Combination-Sum4.java) download
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public class Solution {
    public int combinationSum4(int[] nums, int target) {
        int n = nums.length;
        if (n==0) return 0;
        int[] dp = new int[target+1];
        Arrays.sort(nums);
        for(int i=0; i<dp.length;i++){
            for(int num : nums){
                if(num > i)
                    break;
                if(num == i)
                    dp[i]++;
                else if(num < i)
                    dp[i] += dp[i-num];

            }

        }
        return dp[target];
    }
}