<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:
        suffixes = defaultdict()
        zeroes = nums.count(0)
        nums = list(filter(lambda x : x != 0, nums))
        if nums == []:
            return 2**zeroes
        suffixes[len(nums) - 1] = {nums[-1]: 1, -1 * nums[-1]: 1}

        res = 0
        def backtrack(i):
            if i == -1:
                return
            else:
                suffixes[i] = defaultdict()
                for key, value in suffixes[i + 1].items():
                    pos = nums[i] + key
                    neg = -1 * nums[i] + key
                    suffixes[i][pos] = value + suffixes[i].get(pos, 0)
                    suffixes[i][neg] = value + suffixes[i].get(neg, 0)
                backtrack(i - 1)
        backtrack(len(nums) - 2)
        return suffixes[0].get(target, 0) * (2**zeroes)
27841