<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:
    def maxDotProduct(self, nums1, nums2):
        dp = [[-1] * len(nums2) for _ in range(len(nums1))]
        nums1Size = len(nums1)
        nums2Size = len(nums2)

        def calculateDotProduct(idx1, idx2):
            if idx1 == nums1Size or idx2 == nums2Size:
                return 0

            if dp[idx1][idx2] != -1:
                return dp[idx1][idx2]

            option1 = nums1[idx1] * nums2[idx2] + calculateDotProduct(idx1 + 1, idx2 + 1)
            option2 = calculateDotProduct(idx1, idx2 + 1)
            option3 = calculateDotProduct(idx1 + 1, idx2)

            dp[idx1][idx2] = max(option1, option2, option3)
            return dp[idx1][idx2]

        firstMax = float('-inf')
        secondMax = float('-inf')
        firstMin = float('inf')
        secondMin = float('inf')

        for num in nums1:
            firstMax = max(firstMax, num)
            firstMin = min(firstMin, num)

        for num in nums2:
            secondMax = max(secondMax, num)
            secondMin = min(secondMin, num)

        if (firstMax < 0 and secondMin > 0) or (firstMin > 0 and secondMax < 0):
            return max(firstMax * secondMin, firstMin * secondMax)

        return calculateDotProduct(0, 0)
21700