<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:
        totalSum = sum(nums)
        if target not in range(-totalSum, totalSum + 1):
            return 0
        
        # ## RC ##
        # ## APPROACH : DP ##
        # ## INTUITION : THINK LIKE SUBSET SUM PROBLEM (tushor roy DP solution) Leetcode 416. Partition equal subset sum ##
        # # but here  1. our target can range from -totalSum to +totalSum
        # #           2. and we dont include True directly from above sequence, coz it is not subsequence we are looking for. so here consider if and only if previous value exists
        # # [1,1,1,1,1]

        # if(target not in range(-1 * totalSum, totalSum + 1)):
        #     return 0
        # dp [[0 for _ in range(total * 2 + 1)] for _ in range(len(nums))]




        memo = {}
        def helper(index, cur_sum):
            #memoization
            if (index, cur_sum) in memo:
                return memo[(index, cur_sum)]
            #base case
            if index == (len(nums)):
                return 1 if cur_sum == target else 0
            
            add = helper(index + 1, cur_sum + nums[index])
            subtract = helper(index + 1, cur_sum - nums[index])
            # return add + subtract
            memo[(index, cur_sum)] = add + subtract
            return memo[(index, cur_sum)]

        return helper(0, 0)
36528