Given two arrays nums1 and nums2.
Return the maximum dot product between non-empty subsequences of nums1 and nums2 with the same length.
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, [2,3,5] is a subsequence of [1,2,3,4,5] while [1,5,3] is not).
Example 1:
Input: nums1 = [2,1,-2,5], nums2 = [3,0,-6]
Output: 18
Explanation: Take subsequence [2,-2] from nums1 and subsequence [3,-6] from nums2.
Their dot product is (2*3 + (-2)*(-6)) = 18.
Example 2:
Input: nums1 = [3,-2], nums2 = [2,-6,7]
Output: 21
Explanation: Take subsequence [3] from nums1 and subsequence [7] from nums2.
Their dot product is (3*7) = 21.
Example 3:
Input: nums1 = [-1,-1], nums2 = [1,1]
Output: -1
Explanation: Take subsequence [-1] from nums1 and subsequence [1] from nums2.
Their dot product is -1.
Constraints:
1 <= nums1.length, nums2.length <= 500
-1000 <= nums1[i], nums2[i] <= 1000
class Solution:
    def maxDotProduct(self, nums1, nums2):
        if all(x >= 0 for x in nums1) and all(y <= 0 for y in nums2):
            return min(nums1) * max(nums2)
        if all(x <= 0 for x in nums1) and all(y >= 0 for y in nums2):
            return max(nums1) * min(nums2)
        a, b = len(nums1), len(nums2)
        dp = [[0 for _ in range(b)] for _ in range(a)]
        for i in range(a):
            for j in range(b):
                dp[i][j] = nums1[i] * nums2[j]
                if i: dp[i][j] = max(dp[i][j], dp[i-1][j])
                if j: dp[i][j] = max(dp[i][j], dp[i][j-1])
                if i and j: dp[i][j] = max(dp[i][j], nums1[i] * nums2[j] + dp[i-1][j-1])
        return dp[a-1][b-1]
class Solution:
    def maxDotProduct(self, nums1, nums2):
        if all(x >= 0 for x in nums1) and all(y <= 0 for y in nums2):
            return min(nums1) * max(nums2)
        if all(x <= 0 for x in nums1) and all(y >= 0 for y in nums2):
            return max(nums1) * min(nums2)
        a, b = len(nums1), len(nums2)
        dp = [[0 for _ in range(b)] for _ in range(a)]
        for i in range(a):
            for j in range(b):
                dp[i][j] = nums1[i] * nums2[j]
                if i: dp[i][j] = max(dp[i][j], dp[i-1][j])
                if j: dp[i][j] = max(dp[i][j], dp[i][j-1])
                if i and j: dp[i][j] = max(dp[i][j], nums1[i] * nums2[j] + dp[i-1][j-1])
        return dp[a-1][b-1]