<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>

// template<> struct std::hash<pair<int, int>>
// {
//     size_t operator()(const pair<int, int> &key) const
//     {
//         return ((int32_t)key.first << 32) | ((int32_t)key.second);
//     }
// };

class Solution {
public:
    int findTargetSumWays(vector<int>& nums, int target) {
        return recurrence(nums, 0, target);
    }

private:
    int recurrence(const vector<int> &nums, int index, int remaining) {
        if (index == nums.size()) {
            return remaining == 0 ? 1 : 0;
        }
        
        if (cache.count(getKey(remaining, index)) > 0) {
            return cache[getKey(remaining, index)];
        }

        int result = 0;
        result = recurrence(nums, index + 1, remaining - nums[index]) 
                + recurrence(nums, index + 1, remaining + nums[index]);
        cache[getKey(remaining, index)] = result;

        return result;
    }

    long long getKey(const int &sum, const int &index) const {
        return ((long long)sum << 32) | ((uint32_t)index);
    }

private:
    unordered_map<long long, int> cache;
};

65961