<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:
        N = len(nums)
        total = sum(nums)
        if (total+target)%2!=0:
            return 0
        cap = (total+target)//2
        # print(cap)
        # dp = [[0]*(cap+1) for _ in range(N)]
        dp = {}
        count = []
        nums.sort(reverse=True)
        def solve(n, cap):
            if n==0:
                if cap ==0:
                    return 1
                else:
                    return 0
               
           
                
               
            elif (n,cap) in dp:
                return dp[(n,cap)]
            else:
                item=nums[n-1]
                if item <= cap:
                    c1 = solve(n-1,cap-item)
                    c2 = solve(n-1,cap)
                    c = c1 + c2
                else:
                    if cap==0:
                        c=1
                    else:
                        c=0
                   
                dp[(n,cap)]=c
                return c
        #solve(N,cap)
        # print(dp)
       
        return solve(N,cap)
        
        
              
        
        
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