Introduction

In this blog post, we will explore how to solve the LeetCode problem "1131" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

Given two arrays of integers with equal lengths, return the maximum value of: |arr1[i] - arr1[j]| + |arr2[i] - arr2[j]| + |i - j| where the maximum is taken over all 0 <= i, j < arr1.length. Example 1: Input: arr1 = [1,2,3,4], arr2 = [-1,4,5,6] Output: 13 Example 2: Input: arr1 = [1,-2,-5,0,10], arr2 = [0,-2,-1,-7,-4] Output: 20 Constraints: 2 <= arr1.length == arr2.length <= 40000 -10^6 <= arr1[i], arr2[i] <= 10^6

Explanation

Here's the approach to solve this problem efficiently:

• Transform the Problem: Remove absolute values by considering all possible sign combinations. There are four possible combinations of signs for the terms inside the absolute values: (arr1[i] - arr1[j]), (arr2[i] - arr2[j]), and (i - j).
• Simplify and Re-arrange: For each combination, rearrange the expression |arr1[i] - arr1[j]| + |arr2[i] - arr2[j]| + |i - j| to eliminate subtractions using min/max operations. The transformed expression will have the form arr1[i] + arr2[i] + i - (arr1[j] + arr2[j] + j) (or variations with different sign combinations). Therefore, we only need to maintain min/max value of the terms with index j and compute the expression for all indices i.

• Iterate and Optimize: Iterate through each of the four possible sign combinations, calculate the required maximum value for each, and take the overall maximum across all combinations.

• Runtime Complexity: O(N), where N is the length of the input arrays. Storage Complexity: O(1).

Code

    def max_abs_sum(arr1, arr2):
    """
    Calculates the maximum value of |arr1[i] - arr1[j]| + |arr2[i] - arr2[j]| + |i - j|.

    Args:
        arr1: The first array of integers.
        arr2: The second array of integers.

    Returns:
        The maximum value.
    """

    n = len(arr1)
    max_val = 0

    # Four possible combinations of signs
    combinations = [
        (1, 1, 1),
        (1, 1, -1),
        (1, -1, 1),
        (1, -1, -1),
        (-1, 1, 1),
        (-1, 1, -1),
        (-1, -1, 1),
        (-1, -1, -1)
    ]

    for sign_a1, sign_a2, sign_idx in combinations:
        max_sum = float('-inf')
        min_sum = float('inf')

        for i in range(n):
            curr_sum = sign_a1 * arr1[i] + sign_a2 * arr2[i] + sign_idx * i
            max_sum = max(max_sum, curr_sum)
            min_sum = min(min_sum, curr_sum)

        max_val = max(max_val, max_sum - min_sum)

    return max_val