1458. Max Dot Product of Two Subsequences

Description

Given two arrays nums1 and

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

 

Solutions

Solution: Dynamic Programming

• Time complexity: O(mn)
• Space complexity: O(mn)

 

JavaScript

/**
 * @param {number[]} nums1
 * @param {number[]} nums2
 * @return {number}
 */
const maxDotProduct = function (nums1, nums2) {
  const m = nums1.length;
  const n = nums2.length;
  const dp = Array.from({ length: m }, () => new Array(n).fill(null));

  const maxSubProduct = (index1, index2) => {
    if (index1 >= m || index2 >= n) return Number.MIN_SAFE_INTEGER;
    if (dp[index1][index2] !== null) return dp[index1][index2];

    const product = nums1[index1] * nums2[index2];
    const current = product + maxSubProduct(index1 + 1, index2 + 1);
    const skip1 = maxSubProduct(index1 + 1, index2);
    const skip2 = maxSubProduct(index1, index2 + 1);
    const result = Math.max(product, current, skip1, skip2);

    dp[index1][index2] = result;

    return result;
  };

  return maxSubProduct(0, 0);
};