<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>


struct pair_hash {
    template <class T1, class T2>
    std::size_t operator()(const std::pair<T1, T2>& p) const {
        auto hash1 = std::hash<T1>{}(p.first);
        auto hash2 = std::hash<T2>{}(p.second);
        return hash1 ^ hash2; // Combine the two hash values
    }
};

class Solution {
    int n;
    unordered_map<pair<int, int>, int, pair_hash> mp; // Memoization map

public:
    int f(int ind, int target, vector<int>& nums) {
        // Base case: when we've processed all elements
        if (ind == n) {
            return target == 0 ? 1 : 0;
        }

        // Memoization check
        pair<int, int> key = {ind, target};
        if (mp.find(key) != mp.end()) {
            return mp[key]; // Return cached result if exists
        }

        // Recursive calls: choose to add or subtract nums[ind]
        int a = mp.count({ind + 1, target - nums[ind]})
                    ? mp[{ind + 1, target - nums[ind]}]
                    : f(ind + 1, target - nums[ind], nums);
        int b = mp.count({ind + 1, target + nums[ind]})
                    ? mp[{ind + 1, target + nums[ind]}]
                    : f(ind + 1, target + nums[ind], nums);

        // Store result in memoization map
        mp[key] = a + b;

        return mp[key];
    }

    int findTargetSumWays(vector<int>& nums, int target) {
        n = nums.size();
        return f(0, target, nums); // Start recursion from index 0
    }
};

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