<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:
        total = sum(nums)
        
        cache = {}
        def gen_exp(i, sum_):
            if (i, sum_) in cache:
                return cache[(i, sum_)]
            if i >= len(nums):
                print(sum_, total)
                return (sum_) - (total - sum_) == target
            # include nums[i] in the positive group
            positive, negative = gen_exp(i + 1, sum_ + nums[i]), gen_exp(i + 1, sum_)
            
            cache[(i, sum_)] = positive + negative
            return cache[(i, sum_)]
        
        return gen_exp(0, 0)
        

            
            


            
            

        # cache[(index, sum_)] -> how many expressions from nums[index] onwards sum to target - sum_?
        cache = {}

        de

        # generate all possible expressions, see which meet criteria
        def gen_exp(i, sum_):
            if (i, sum_) in cache:
                num_expressions[0] += cache[(i, sum_)]
                return
            if i >= len(nums):
                if sum_ == target:
                    num_expressions[0] += 1
                return
            
            old_expressions = num_expressions[0]
            
            gen_exp(i + 1, sum_ + nums[i])
            gen_exp(i + 1, sum_ - nums[i])

            cache[(i, sum_)] = num_expressions[0] - old_expressions
        
        gen_exp(0, 0)
        return num_expressions[0]
35486