problem

377. Combination Sum IV
Given an array of distinct integers nums and a target integer target, return the number of possible combinations that add up to target.

The test cases are generated so that the answer can fit in a 32-bit integer.

Example 1:

Input: nums = [1,2,3], target = 4
Output: 7
Explanation:
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.

Example 2:

Input: nums = [9], target = 3
Output: 0

approach 1 recursive TLE

class Solution {
public:
    int combinationSum4(vector<int>& nums, int target) {
        if(target == 0) return 1;
        if(target < 0) return 0;
        int res = 0;
        for(auto x : nums)
            res += combinationSum4(nums, target - x);
        return res;
    }
};

approach 2 dp

class Solution {
public:
    vector<int> dp;
    int rec(vector<int>& nums, int target){
        if(target == 0) return 1;
        if(dp[target] != -1) return dp[target];
        int res = 0;
        for(auto x : nums){
            if(target - x >= 0)
                res += dp[target - x] = rec(nums, target - x);
        }
        return res;
    }
    int combinationSum4(vector<int>& nums, int target) {
        dp = vector<int>(target+1, -1);
        return rec(nums, target);
    }
};