<p>Given an array of <strong>distinct</strong> integers <code>nums</code> and a target integer <code>target</code>, return <em>the number of possible combinations that add up to</em>&nbsp;<code>target</code>.</p>

<p>The test cases are generated so that the answer can fit in a <strong>32-bit</strong> integer.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3], target = 4
<strong>Output:</strong> 7
<strong>Explanation:</strong>
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.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [9], target = 3
<strong>Output:</strong> 0
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 200</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 1000</code></li>
	<li>All the elements of <code>nums</code> are <strong>unique</strong>.</li>
	<li><code>1 &lt;= target &lt;= 1000</code></li>
</ul>

<p>&nbsp;</p>
<p><strong>Follow up:</strong> 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?</p>

class Solution {
public:
    int combinationSum4(vector<int>& nums, int target) {
        int n = nums.size();
        vector<vector<int>>dp(n+1,vector<int>(target+1,-1));
        return Sum(nums,n,target,dp);
    }
    int Sum(vector<int>&nums,int n,int target,vector<vector<int>>&dp)
    {
        if(target == 0)
            return 1;
        if(n==0)
            return 0;
        if(dp[n][target] != -1)
            return dp[n][target];
        int sum=0;
        for(int i=0;i<n;i++){
            if(nums[i] <= target)
                sum += Sum(nums,n,target-nums[i],dp);
        }
        return dp[n][target] = sum;
    }
};
9300