<p>You are given an integer array <code>nums</code> and an integer <code>target</code>.</p>

<p>You want to build an <strong>expression</strong> out of nums by adding one of the symbols <code>&#39;+&#39;</code> and <code>&#39;-&#39;</code> before each integer in nums and then concatenate all the integers.</p>

<ul>
	<li>For example, if <code>nums = [2, 1]</code>, you can add a <code>&#39;+&#39;</code> before <code>2</code> and a <code>&#39;-&#39;</code> before <code>1</code> and concatenate them to build the expression <code>&quot;+2-1&quot;</code>.</li>
</ul>

<p>Return the number of different <strong>expressions</strong> that you can build, which evaluates to <code>target</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [1,1,1,1,1], target = 3
<strong>Output:</strong> 5
<strong>Explanation:</strong> There are 5 ways to assign symbols to make the sum of nums be target 3.
-1 + 1 + 1 + 1 + 1 = 3
+1 - 1 + 1 + 1 + 1 = 3
+1 + 1 - 1 + 1 + 1 = 3
+1 + 1 + 1 - 1 + 1 = 3
+1 + 1 + 1 + 1 - 1 = 3
</pre>

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

<pre>
<strong>Input:</strong> nums = [1], target = 1
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 20</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 1000</code></li>
	<li><code>0 &lt;= sum(nums[i]) &lt;= 1000</code></li>
	<li><code>-1000 &lt;= target &lt;= 1000</code></li>
</ul>

class Solution {
public:
    int countPartitionsUtil(int ind, int target, vector<int>& arr, vector<vector<int>>& dp) {
        if(ind==0) {
            if(target==0 && arr[0]==0) return 2; 
            if (target==0 || target==arr[0]) return 1; 
            return 0; 
        }
        if(dp[ind][target]!=-1) return dp[ind][target];
        int notTaken=countPartitionsUtil(ind-1,target,arr,dp);
        int taken=0;
        if(arr[ind]<=target) taken=countPartitionsUtil(ind-1,target-arr[ind],arr,dp);
        return dp[ind][target]=(notTaken+taken);
    }
    int findTargetSumWays(vector<int>& arr, int target) {
        int n=arr.size();
        int totSum = 0;
        for(int i=0;i<arr.size();i++) totSum+=arr[i];
        if(totSum-target<0) return 0; 
        if((totSum-target)%2==1) return 0; 
        int s2=(totSum-target)/2; 
        vector<vector<int>>dp(n,vector<int>(s2+1,-1)); 
        return countPartitionsUtil(n-1,s2,arr,dp); 
    }
};
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