<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:
    def findTargetSumWays(self, nums: List[int], target: int) -> int:
        s = sum(nums)
        dp = {}


        def recursive(i,sm):
            # if i>0 and dp[i][2*sm]:
            #     return dp[i][sm]
            # if i==0:
            #     ans = 0
            #     if sm-nums[i]==target:
            #         dp[i][sm+sm-nums[i]] +=1
            #         ans+=1
            #     if sm+nums[i]==target:
            #         dp[i][sm+sm+nums[i]] +=1
            #         ans+=1

            #     return ans

            if (i,sm) in dp:
                return dp[(i,sm)]
            if i==0:
                if sm-nums[i]==target and sm+nums[i]==target:
                    return 2
                elif sm-nums[i]==target or sm+nums[i]==target:
                    return 1
                else:
                    return 0

            left = recursive(i-1,sm+nums[i])
            right = recursive(i-1,sm-nums[i])
            
            dp[(i,sm)] = left+right
            return dp[(i,sm)]

            # dp[i][2*sm] = left+right
            # return dp[i][2*sm]

        x =  recursive(len(nums)-1,0)

        # print(dp)
        return x
29926