<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 {
private:
    struct entry_hash {
        size_t operator()(const pair<int, int>& e) const {
            return hash<int>()(e.first) ^ hash<int>()(e.second);
        }
    };

    typedef unordered_map<pair<int, int>, int, entry_hash> tbl;

    int _findTargetSumWays(vector<int>& nums, int i, int target, tbl& t) {
        int ret;
        pair<int, int> k;
        tbl::iterator it;

        k = pair<int, int>(i, target);

        it = t.find(k);
        if (it != end(t))
            return it->second;

        if (i < nums.size()) {
            int val;

            val = nums[i++];
            ret = _findTargetSumWays(nums, i, target + val, t);
            ret += _findTargetSumWays(nums, i, target - val, t);
        } else
            ret = target == 0;

        t[k] = ret;

        return ret;
    }

public:
    int findTargetSumWays(vector<int>& nums, int target) {
        tbl t;

        return _findTargetSumWays(nums, 0, target, t);
    }
};
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