Max Dot Product of Two Subsequences

arraydynamic programming

Problem Statement

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 an 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).

Examples

Example 1

Input: nums1 = [2,1,-2,5], nums2 = [3,0,-6]
Output: 18
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
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
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

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Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicDynamic Programming