<p>Given two arrays <code>nums1</code>&nbsp;and <code><font face="monospace">nums2</font></code><font face="monospace">.</font></p>

<p>Return the maximum dot product&nbsp;between&nbsp;<strong>non-empty</strong> subsequences of nums1 and nums2 with the same length.</p>

<p>A subsequence of a array is a new array which is formed from the original array by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. (ie,&nbsp;<code>[2,3,5]</code>&nbsp;is a subsequence of&nbsp;<code>[1,2,3,4,5]</code>&nbsp;while <code>[1,5,3]</code>&nbsp;is not).</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums1 = [2,1,-2,5], nums2 = [3,0,-6]
<strong>Output:</strong> 18
<strong>Explanation:</strong> Take subsequence [2,-2] from nums1 and subsequence [3,-6] from nums2.
Their dot product is (2*3 + (-2)*(-6)) = 18.</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums1 = [3,-2], nums2 = [2,-6,7]
<strong>Output:</strong> 21
<strong>Explanation:</strong> Take subsequence [3] from nums1 and subsequence [7] from nums2.
Their dot product is (3*7) = 21.</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums1 = [-1,-1], nums2 = [1,1]
<strong>Output:</strong> -1
<strong>Explanation: </strong>Take subsequence [-1] from nums1 and subsequence [1] from nums2.
Their dot product is -1.</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums1.length, nums2.length &lt;= 500</code></li>
	<li><code>-1000 &lt;= nums1[i], nums2[i] &lt;= 1000</code></li>
</ul>

class Solution {
    int dp[500][500];
public:
   int product(int indexi, int indexj, vector<int> &nums1, vector<int> &nums2)
   {
       if(indexi>=nums1.size() || indexj>=nums2.size())
       {
           return  0 ; 
       }
       if(dp[indexi][indexj]!=-1)
             return dp[indexi][indexj];
       int ans1 = INT_MIN , ans2 =INT_MIN,  ans3 =INT_MIN, ans4 = INT_MIN ;
       ans3 = nums1[indexi]*nums2[indexj]+product(indexi+1, indexj+1, nums1,nums2);
        ans2 = product(indexi,indexj+1,nums1,nums2);
       ans1 = product(indexi+1,indexj+1,nums1,nums2);
       ans4  = product(indexi+1,indexj,nums1,nums2);
      

       return dp[indexi][indexj]=max({ans1,ans2,ans3,ans4});
   }
    int maxDotProduct(vector<int>& nums1, vector<int>& nums2) {

        int  maxi = INT_MIN;
        int n = nums1.size();
        int m = nums2.size();
        for(int i = 0;i<n;i++)
        {
            for(int j = 0;j<m;j++)
            {
                maxi = max(maxi,nums1[i]*nums2[j]);
            }
        }
        memset(dp,-1,sizeof(dp));
        int res = product(0,0,nums1,nums2);
        return res==0?maxi:res;
        
    }
};
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