<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>

typedef vector<vector<int>> vvi;
class Solution {
public:
    int findTargetSumWays(vector<int>& nums, int target) {
        
        // Backtracking to generate all permutations 
        // That can give 2^n


        int sum = 0;
        int size = nums.size();
        //int ans=0;
        int total=0;

        for(auto n:nums)    total+=n;

        vector<vector<int>> cache(size);
        // index - 0 to size
        // sum - will be -sum to sum
        for(int i=0;i<size;i++)
            for(int j=0;j<=2*total;j++)
                cache[i].push_back(-1); 
        return helper(0,sum,nums,target,cache,total);

        //return ans;
    }

    int helper(int index,int sum,vector<int>& nums,int &target,vvi& cache,int &total)
    {
        //cout<<sum<<index<<endl;
        // if already calculated 
        
        if(index==nums.size() )
        {
            if(sum==target){
                return 1;
            }
            return 0;
        }

        if(cache[index][sum+total]!=-1)
            return cache[index][sum+total];

        cache[index][sum+total] = helper(index+1,sum+nums[index],nums,target,cache,total)+helper(index+1,sum-nums[index],nums,target,cache,total);
        return cache[index][sum+total];
    }
};
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