<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:
    map<pair<int,int>, int> dp;
    int rec(int lvl, int sum_left, vector<int>&nums){
        if(lvl >= nums.size()){
            if(sum_left == 0)
                return 1;
            return 0;
        }
        if(dp.find({lvl,sum_left}) != dp.end())
            return dp[{lvl,sum_left}];
        int res = 0;
        if(nums[lvl] <= sum_left){
            res += rec(lvl+1,sum_left-nums[lvl],nums);
        }
        res += rec(lvl+1,sum_left,nums);
        return dp[{lvl,sum_left}] = res;
    }
    int findTargetSumWays(vector<int>& nums, int target) {
        int sum = accumulate(nums.begin(), nums.end(), 0);
        int S = 0;
        if((sum+target) % 2 == 0)
            S = (sum+target)/2;
        else    
            return 0;
        return rec(0,S,nums);
    }
};
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