<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:
struct pair_hash {
    template <class T1, class T2>
    size_t operator() (const pair<T1, T2>& p) const {
        auto hash1 = hash<T1>{}(p.first);
        auto hash2 = hash<T2>{}(p.second);
        return hash1 ^ hash2; // Combine the two hash values
    }
};
   unordered_map<pair<int, int>, int, pair_hash> memo;
    int findSumWithMemoiz(vector<int>&nums,int n,int target){
       if (n == 0) {
            return target == 0 ? 1 : 0; // If target is achieved, return 1 way; otherwise, return 0 ways
        }
       pair<int, int> key = {n, target};
        if (memo.find(key) != memo.end()) return memo[key];
        int takenWithPlus=findSumWithMemoiz(nums,n-1,target-nums[n-1]);
        int takenWithMinus=findSumWithMemoiz(nums,n-1,target+nums[n-1]);
        return memo[key]=takenWithMinus+takenWithPlus;
    }
    int findTargetSumWays(vector<int>& nums, int target) {
        int n=nums.size();
        
        int ans=findSumWithMemoiz(nums,n,target);
        if(ans==-1)return 0;
        return ans;
    }
};
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