<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:
        nums.sort()

        memo = dict()

        cumu = [0]
        for x in nums:
            cumu.append(x+cumu[-1])
        cumu.pop(0)

        if cumu[-1]<target or cumu[-1]%2!=abs(target)%2:
            return 0

        def bt(nums,n,target):
            if n==0:
                if target==0:
                    return 1
                else:
                    return 0

                
            
            if (n,target) in memo:
                return memo[n,target]
            
            first = 0
            second = 0
            if nums[n-1]==0:
                if -cumu[n-1] <= target <= cumu[n-1]:
                    first = second = bt(nums,n-1,target)
            else:
                if -cumu[n-1] <= target-nums[n-1] <= cumu[n-1]:
                    first = bt(nums,n-1,target-nums[n-1])
                if -cumu[n-1] <= target+nums[n-1] <= cumu[n-1]:
                    second = bt(nums,n-1,target+nums[n-1])

            memo[n,target] = first+second
            return first+second
            
        return bt(nums,len(nums),target)
18458