<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 index, int target, vector<int> & nums,  vector< unordered_map<int, int>> & dp){
        
        if(index == 0){
            if(target == nums[0] && target == - nums[0]) return 2;
            return (target == nums[0] || target == -nums[0]);
        }
        
        if( dp[index].find(target)!= dp[index].end()) return dp[index][target];
        int nottake = solve(index - 1, target + nums[index], nums, dp);
        int take = solve(index - 1, target - nums[index], nums, dp);
        
        return dp[index][target] = take + nottake;
    }
    int findTargetSumWays(vector<int>& nums, int target) {
     
        int n = nums.size();
         vector< unordered_map<int, int>> dp(n);
         return solve(n-1,target, nums, dp);
//         int sum = 0 ;
//         dp[0][-nums[0]] = 1;
//         dp[0][nums[0]] = 1;
//         for(int i = 0; i <n ; i++) dp[i][0] =1;
//         for(int index = 1; index < n; index ++){
//             for(int t = -1000 ; t <= 1000 ; t++){
                
//                 int sub = dp[index-1][t + nums[index]];
//                 int add = dp[index -1][t - nums[index]];
                
//                 dp[index][t] = sub + add;
//             }
//         }
//         return dp[n-1][target];
    }
};
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