<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 find_ans( vector<int>& nums ,int i ,  int target , vector<unordered_map<int,int>>& v)
    {
        
        target  = abs(target);
        if( i ==( nums.size()))
        return (target == 0 ) ; 

        if( v[i].find(target) != v[i].end()) return v[i][target];


        return v[i][target] = find_ans(nums , i+1 , abs(target-nums[i]) , v ) + find_ans(nums, i+1 , abs(target+nums[i]), v);


    }
    int findTargetSumWays(vector<int>& nums, int target) {
        // dp(i  , tar) = dp( i+1 , tar - nums[i]) + dp9

        vector<unordered_map<int,int>> v ; 
        for(int i = 0 ; i < nums.size()  ; i++) v.emplace_back( unordered_map<int,int>());

        return find_ans(nums , 0 , abs(target) , v);         
    }
};
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