<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>

def solve(i,nums,tar,dp):
    if i==0:
        ans=0
            
        if tar-nums[i]==0:
            ans+=1
        if tar+nums[i]==0:
            ans+=1
        return ans
    if (i,tar) in dp:
        return dp[(i,tar)]
    plus,minus=0,0
    plus=solve(i-1,nums,tar+nums[i],dp)
    minus=solve(i-1,nums,tar-nums[i],dp)
    ans=plus+minus
    dp[(i,tar)]=ans
    return ans 
class Solution:
    def findTargetSumWays(self, nums: List[int], target: int) -> int:
        n=len(nums)
        s=sum(nums)
        dp={}
        # dp=[[0 for i in range(4002)]for i in range(n)]
        # ans=solve(n-1,nums,target,dp)
        # return ans  
        for i in range(0,n):
            for tar in range(-2000,2001,1):
                dp[(i,tar)]=0
        for tar in range (-1000,1001,1):
            ans=0
            
            if tar-nums[0]==0:
                ans+=1
            if tar+nums[0]==0:
                ans+=1
            dp[(0,tar)]=ans
        
        for i in range(1,n):
            for tar in range(-1000,1001,1):
                plus,minus=0,0
                plus=dp[(i-1,tar+nums[i])]
                minus=dp[(i-1,tar-nums[i])]
                ans=plus+minus
                dp[(i,tar)]=ans
        return dp[(n-1,target)]


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