Max Dot Product of Two Subsequences

Description

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

Solution(javascript)

/**
 * @param {number[]} nums1
 * @param {number[]} nums2
 * @return {number}
 */
const maxDotProduct = function (nums1, nums2) {
  let max = -Infinity
  const memo = {}
  const aux = (index1, index2) => {
    const key = `${index1}-${index2}`
    if (memo[key] !== undefined) {
      return memo[key]
    }
    if (index1 >= nums1.length || index2 >= nums2.length) {
      return 0
    }
    memo[key] = Math.max(
      nums1[index1] * nums2[index2] + aux(index1 + 1, index2 + 1),
      aux(index1, index2 + 1),
      aux(index1 + 1, index2),
    )
    return memo[key]
  }
  for (let i = 0; i < nums1.length; i++) {
    for (let j = 0; j < nums2.length; j++) {
      max = Math.max(
        max,
        nums1[i] * nums2[j] + aux(i + 1, j + 1),
      )
    }
  }
  return max
}