Introduction

In this blog post, we will explore how to solve the LeetCode problem "3382" 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

There are n points on an infinite plane. You are given two integer arrays xCoord and yCoord where (xCoord[i], yCoord[i]) represents the coordinates of the ith point. Your task is to find the maximum area of a rectangle that: Can be formed using four of these points as its corners. Does not contain any other point inside or on its border. Has its edges parallel to the axes. Return the maximum area that you can obtain or -1 if no such rectangle is possible. Example 1: Input: xCoord = [1,1,3,3], yCoord = [1,3,1,3] Output: 4 Explanation: We can make a rectangle with these 4 points as corners and there is no other point that lies inside or on the border. Hence, the maximum possible area would be 4. Example 2: Input: xCoord = [1,1,3,3,2], yCoord = [1,3,1,3,2] Output: -1 Explanation: There is only one rectangle possible is with points [1,1], [1,3], [3,1] and [3,3] but [2,2] will always lie inside it. Hence, returning -1. Example 3: Input: xCoord = [1,1,3,3,1,3], yCoord = [1,3,1,3,2,2] Output: 2 Explanation: The maximum area rectangle is formed by the points [1,3], [1,2], [3,2], [3,3], which has an area of 2. Additionally, the points [1,1], [1,2], [3,1], [3,2] also form a valid rectangle with the same area. Constraints: 1 <= xCoord.length == yCoord.length <= 2 105 0 <= xCoord[i], yCoord[i] <= 8 107 All the given points are unique.

Explanation

Here's an efficient solution to find the maximum area of a rectangle formed by given points, ensuring no other point lies inside or on its border:

• Iterate through all pairs of points: Treat each pair as a potential diagonal of a rectangle.
• Check for the other two corners: For a pair to be a diagonal, we need to find two other points that form the other two corners of a rectangle whose sides are parallel to the axes.

• Validate the rectangle: If a potential rectangle is found, check if any other point lies inside or on the border of the rectangle. If not, calculate its area and update the maximum area found so far.

• Runtime Complexity: O(n^3), Storage Complexity: O(n)

Code

    def max_rectangle_area(xCoord, yCoord):
    """
    Finds the maximum area of a rectangle formed by four points from the given coordinates,
    ensuring no other point lies inside or on its border.

    Args:
        xCoord: A list of x-coordinates.
        yCoord: A list of y-coordinates.

    Returns:
        The maximum area of a valid rectangle, or -1 if no such rectangle is possible.
    """

    n = len(xCoord)
    points = set(zip(xCoord, yCoord))
    max_area = -1

    for i in range(n):
        for j in range(i + 1, n):
            x1, y1 = xCoord[i], yCoord[i]
            x2, y2 = xCoord[j], yCoord[j]

            if x1 != x2 and y1 != y2:
                # Potential rectangle with (x1, y1) and (x2, y2) as diagonal corners
                if (x1, y2) in points and (x2, y1) in points:
                    # Check if any other point lies inside or on the border
                    valid = True
                    min_x = min(x1, x2)
                    max_x = max(x1, x2)
                    min_y = min(y1, y2)
                    max_y = max(y1, y2)

                    for k in range(n):
                        if k != i and k != j:
                            x, y = xCoord[k], yCoord[k]
                            if min_x <= x <= max_x and min_y <= y <= max_y:
                                valid = False
                                break

                    if valid:
                        area = abs(x1 - x2) * abs(y1 - y2)
                        max_area = max(max_area, area)

    return max_area