<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 solve(vector<int> nums, int total, int idx, vector<vector<int>> &dp) {
        if(idx == 0) {
            if(nums[0] == 0 && total == 0) return 2;

            if(total == 0 || nums[0] == total) return 1;

            return 0;
        }

        if(dp[idx][total] != -1)
            return dp[idx][total];

        int not_take = solve(nums, total, idx - 1, dp);
        
        int take = 0;
        if(total >= nums[idx]) {
            take = solve(nums, total - nums[idx], idx - 1, dp);
        }

        return dp[idx][total] = not_take + take;
    }

    int findTargetSumWays(vector<int>& nums, int target) {
        int n = nums.size();

        int total = 0;

        for(int i = 0; i < n; i++) {
            total += nums[i];
        }

        total -= target;

        if(total < 0 || total % 2 != 0)
            return false;
        
        total /= 2;

        vector<vector<int>> dp(n + 1, vector<int>(total + 1, -1));

        int ans = solve(nums, total, n - 1, dp);

        return ans;
    }
};
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