<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:
    template <typename T1, typename T2>
    struct PairHash {
        std::size_t operator()(const std::pair<T1, T2>& p) const {
            // Hashes the first element of the pair
            std::size_t h1 = std::hash<T1>{}(p.first);
            // Hashes the second element of the pair
            std::size_t h2 = std::hash<T2>{}(p.second);
            
            // Combine the two hash values
            return h1 ^ (h2 << 1);  // Shift h2 to prevent collisions
        }
    };

    int findTargetSumWays(vector<int>& nums, int target) {
        unordered_map<pair<int, int>, int, PairHash<int, int>> map;
        return findTargetSumWaysHelper(nums, target, 0, map, accumulate(nums.begin(), nums.end(), 0));
    }

    int findTargetSumWaysHelper(vector<int>& nums, int target, int idx, unordered_map<pair<int, int>, int, PairHash<int, int>>& map, int remaining){
        if (idx >= nums.size() || target > remaining){
            return (int)(target == 0);
        }
        pair<int, int> curr = make_pair(idx, target);
        if (map.contains(curr)){
            return map[curr];
        }
        int x = findTargetSumWaysHelper(nums, target - nums[idx], idx + 1, map, remaining - nums[idx]);
        int y = findTargetSumWaysHelper(nums, target + nums[idx], idx + 1, map, remaining - nums[idx]);
        map[curr] = x + y;
        // printf("(%d, %d): %d %d %d ", curr.first, curr.second, x, y, map[curr]);
        return map[curr];
    }
};
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