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)

maxDotProduct.js

/**
 * @param {number[]} nums1
 * @param {number[]} nums2
 * @return {number}
 */
var maxDotProduct = function(nums1, nums2) {
    const m = nums1.length;
    const n = nums2.length;

    // Create a DP table where:
    // dp[i][j] = max dot product using nums1[0..i-1] and nums2[0..j-1]
    //
    // We initialize everything to -Infinity because:
    // - We want to allow negative numbers.
    // - We want to ensure that taking no elements is never considered valid.
    const dp = Array.from({ length: m + 1 }, () =>
        Array(n + 1).fill(-Infinity)
    );

    // Fill the DP table
    for (let i = 1; i <= m; i++) {
        for (let j = 1; j <= n; j++) {
            const product = nums1[i - 1] * nums2[j - 1];

            dp[i][j] = Math.max(
                product,                     // Start a new subsequence with this pair
                dp[i - 1][j - 1] + product,  // Extend previous subsequence
                dp[i][j - 1],                // Skip nums2[j - 1]
                dp[i - 1][j]                 // Skip nums1[i - 1]
            );
        }
    }

    return dp[m][n];
};