5419_dot_product_of_two_subseq.py

'''
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) -> int:
        m,n = len(nums1), len(nums2)
        ht = [[-999999999999 for _ in range(n)] for _ in range(m)]
        for i in range(m):
            for j in range(n):
                ans = nums1[i] * nums2[j]
                if i > 0 and j > 0:
                    ans += max(ht[i-1][j-1], 0)
                if i > 0:
                    ans = max(ans, ht[i-1][j])
                if j > 0:
                    ans = max(ans, ht[i][j-1])
                ht[i][j] = ans
        # for row in ht:
        #     print(row)
        return ht[-1][-1]


s = Solution()
# nums1 = [2,1,-2,5]
# nums2 = [3,0,-6]
nums1 = [3,-2]
nums2 = [2,-6,7]
res = s.maxDotProduct(nums1, nums2)
print(res)