<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(int ind,int sign,vector<int> &arr,int target,vector<vector<vector<int>>> &dp){
        int n = arr.size();
        if(ind == n-1){
            if(sign == 0){
                return target + arr[ind] == 0;
            }else{
                return target - arr[ind] == 0;
            }
        }

        if(target+1000 < 0 || target+1000 > 3000){
            cout<<target<<endl;
             return -1;
        }

        if(dp[ind][sign][target+1000] != -1) return dp[ind][sign][target+1000];

        int pve = 0, nve = 0;

        if(sign == 0){
            pve = solve(ind+1,1,arr,target + arr[ind],dp);
            nve = solve(ind+1,0,arr,target + arr[ind],dp);
        }else{
            pve = solve(ind+1,1,arr,target - arr[ind],dp);
            nve = solve(ind+1,0,arr,target - arr[ind],dp);
        }
        
        return dp[ind][sign][target+1000] = pve+nve;
    }

    int findTargetSumWays(vector<int>& nums, int target) {
        int n = nums.size();
        vector<vector<vector<int>>> dp(n,vector<vector<int>>(2,vector<int>(3001,-1)));

        return solve(0,0,nums,target,dp) + solve(0,1,nums,target,dp);
    }
};
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