# Solving Leetcode Interviews in Seconds with AI: Maximum of Absolute Value Expression


	# 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](https://www.chatmagic.app), 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
	```python
	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
	```