<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 solve(vector<vector<int>>& dp,vector<int>& nums, int&target, int& s, int sum, int index)
    {
        if(index>=nums.size())
        {
            if((sum-(s-sum)) == target)
            {
                return 1;
            }
            else
            {
                return 0;
            }
        }

        if(dp[sum][index]!=-1)
        {
            return dp[sum][index];
        }

        dp[sum][index] = solve(dp, nums, target, s,sum+nums[index], index+1) + solve(dp, nums, target, s, sum, index+1);
        return dp[sum][index];
    }
    int findTargetSumWays(vector<int>& nums, int target) {

        int s = 0;
        for(int i=0; i<nums.size() ; i++)
        {
            s+=nums[i];
        }

        vector<vector<int>> dp(s+1, vector<int>(nums.size()+1, -1));
        
        return solve(dp, nums, target , s, 0, 0);
    }
};
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