377. Combination Sum IV

辣鸡题目 

也没说取模啊

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.

class Solution {
public:
    int combinationSum4(vector<int>& nums, int target) {
        int dp[20000];
        memset(dp, 0, sizeof(dp));
        dp[0] = 1;
        for (int i = 1; i <= target; i ++) {
            for (int j = 0; j < nums.size(); j ++) {
                if (nums[j] <= i) {
                    if (dp[i-nums[j]]) {
                        //printf("i=%d,j=%d,dp[i-nums[j]]=%d,dp[i]=%d\n",i,j,dp[i-nums[j]],dp[i]);
                        dp[i] = dp[i]%100000000000 + dp[i - nums[j]]%100000000000;
                    }
                }
            }
        }
        return dp[target];
    }
};