<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 findTargetSumWays(vector<int>& nums, int target) {
        int totalSum = 0;
        for (int num : nums) {
            totalSum += num;
        }
        
        if (target > totalSum || (totalSum - target) % 2 != 0) {
            return 0;
        }
        
        int n = nums.size();
        vector<vector<int>> dp(n, vector<int>(2 * totalSum + 1, -1));
        return f(n - 1, nums, target, 0, dp, totalSum);
    }

    int f(int index, vector<int>& nums, int target, int sum, vector<vector<int>>& dp, int totalSum) {
        if (index < 0) {
            return sum == target ? 1 : 0;
        }

        if (dp[index][sum + totalSum] != -1) {
            return dp[index][sum + totalSum];
        }

        int positive = f(index - 1, nums, target, sum + nums[index], dp, totalSum);
        int negative = f(index - 1, nums, target, sum - nums[index], dp, totalSum);

        dp[index][sum + totalSum] = positive + negative;
        return dp[index][sum + totalSum];
    }
};

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