<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(vector<int>& nums, int target, int ind, map<string, int>* memo) {
        if (ind == 0) {
            int n = 0;
            if (target - nums[ind] == 0) n += 1;
            if (target + nums[ind] == 0) n += 1;
            string key = to_string(target) + "@" + to_string(ind);
            (*memo)[key] = n;
            return n;
        }

        string key = to_string(target) + "@" + to_string(ind);

        if (memo->find(key) != memo->end()) {
            return memo->at(key);
        }

        int add = solve(nums, target - nums[ind], ind - 1, memo);
        int sub = solve(nums, target + nums[ind], ind - 1, memo);
        int sum = add + sub;
        (*memo)[key] = sum;
        return sum;
    }

    int findTargetSumWays(vector<int>& nums, int target) {
        int n = nums.size();
        map<string, int>* memo = new map<string, int>();
        int result = solve(nums, target, n - 1, memo);
        delete memo; // Clean up dynamically allocated memory
        return result;
    }
};

    // int solve(vector<int>& nums, int target,int ind,map<string,int>* memo)
    // {
    //     // if(ind==0)
    //     // {
    //     //     int n = 0;
    //     //     if(target-nums[ind] == 0) n+=1;
    //     //     if(target+nums[ind]==0) n+=1;
    //     //     return n;
        
    //     // }
    //     // string key = to_string(target) + "@" + to_string(ind);

    //     // if(memo->find(key)==memo->end()){int s =  *(memo)[key];
    //     // return s;
    //     // }

    //     // int add = solve(nums,target-nums[ind],ind-1,memo);
    //     // int sub = solve(nums,target+nums[ind],ind-1,memo);
    //     // int sum = add+sub;
    //     // *(memo)[key] = sum;
    //     // return sum; 
    //       if (ind == 0) {
    //     int n = 0;
    //     if (target - nums[ind] == 0) n += 1;
    //     if (target + nums[ind] == 0) n += 1;
    //      string key = to_string(target) + "@" + to_string(ind);
    //      (*memo)[key]=n;
    //     return n;
    // }

    // string key = to_string(target) + "@" + to_string(ind);

    // if (memo->find(key) != memo->end()) {
    //     int s = memo->at(key); // Use 'at' to get the value
    //     return s;
    // }

    // int add = solve(nums, target - nums[ind], ind - 1, memo);
    // int sub = solve(nums, target + nums[ind], ind - 1, memo);
    // int sum = add + sub;
    // (*memo)[key] = sum; // Use the subscript operator to set the value
    // return sum;
    // }
    // int findTargetSumWays(vector<int>& nums, int target) {
    //     //one option is add - and 1 is +
    //     int  n = nums.size();
    //     map<string,int>* memo = new map<string,int>();
    //     return solve(nums,target,n-1,memo);
    // }
// };
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