<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 {
public:
    int dp[505][505];
    int solve(int i,int j,vector<int>&num1,vector<int>&num2){
        if(i==num1.size()) return 0;
        if(j==num2.size()) return 0;
        if(dp[i][j]!=-1) return dp[i][j];
        int ans=-1e9;
        int val=num1[i]*num2[j];
        ans=max({ans,val+solve(i+1,j+1,num1,num2)});
        ans=max({ans,solve(i+1,j,num1,num2),solve(i,j+1,num1,num2)});
        return dp[i][j]=ans;
    }
    int maxDotProduct(vector<int>& nums1, vector<int>& nums2) {
        memset(dp,-1,sizeof(dp));
        int val=solve(0,0,nums1,nums2);
        if(val>0) return val;
        else {
            vector<int>v;
            for(int i=0;i<nums1.size();i++){
                for(int j=0;j<nums2.size();j++){
                    v.push_back(nums1[i]*nums2[j]);
                }
            }
            sort(v.begin(),v.end());
            return v[v.size()-1];
        }
    }
};
13500