Introduction

In this blog post, we will explore how to solve the LeetCode problem "3047" 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 exist n rectangles in a 2D plane with edges parallel to the x and y axis. You are given two 2D integer arrays bottomLeft and topRight where bottomLeft[i] = [a_i, b_i] and topRight[i] = [c_i, d_i] represent the bottom-left and top-right coordinates of the ith rectangle, respectively. You need to find the maximum area of a square that can fit inside the intersecting region of at least two rectangles. Return 0 if such a square does not exist. Example 1: Input: bottomLeft = [[1,1],[2,2],[3,1]], topRight = [[3,3],[4,4],[6,6]] Output: 1 Explanation: A square with side length 1 can fit inside either the intersecting region of rectangles 0 and 1 or the intersecting region of rectangles 1 and 2. Hence the maximum area is 1. It can be shown that a square with a greater side length can not fit inside any intersecting region of two rectangles. Example 2: Input: bottomLeft = [[1,1],[1,3],[1,5]], topRight = [[5,5],[5,7],[5,9]] Output: 4 Explanation: A square with side length 2 can fit inside either the intersecting region of rectangles 0 and 1 or the intersecting region of rectangles 1 and 2. Hence the maximum area is 2 * 2 = 4. It can be shown that a square with a greater side length can not fit inside any intersecting region of two rectangles. Example 3: Input: bottomLeft = [[1,1],[2,2],[1,2]], topRight = [[3,3],[4,4],[3,4]] Output: 1 Explanation: A square with side length 1 can fit inside the intersecting region of any two rectangles. Also, no larger square can, so the maximum area is 1. Note that the region can be formed by the intersection of more than 2 rectangles. Example 4: Input: bottomLeft = [[1,1],[3,3],[3,1]], topRight = [[2,2],[4,4],[4,2]] Output: 0 Explanation: No pair of rectangles intersect, hence, the answer is 0. Constraints: n == bottomLeft.length == topRight.length 2 <= n <= 103 bottomLeft[i].length == topRight[i].length == 2 1 <= bottomLeft[i][0], bottomLeft[i][1] <= 107 1 <= topRight[i][0], topRight[i][1] <= 107 bottomLeft[i][0] < topRight[i][0] bottomLeft[i][1] < topRight[i][1]

Explanation

Here's the breakdown of the solution:

• Find Intersections: Iterate through all pairs of rectangles, compute the intersection rectangle for each pair. The intersection's bottom-left x and y coordinates are the maximum of the corresponding coordinates of the two rectangles, and the intersection's top-right x and y coordinates are the minimum of the corresponding coordinates of the two rectangles.
• Determine Maximum Square Side: For each intersection rectangle, determine the largest possible square side length that can fit within it. This is the minimum of the intersection's width and height.

• Maximize Area: Maintain a running maximum of the square of the side lengths found in the previous step. Return this maximum area.

• Runtime Complexity: O(n^2), where n is the number of rectangles due to the nested loops for intersection calculation. Storage Complexity: O(1) as we only use a few variables to store intermediate results and the maximum area.

Code

    def max_square_area(bottomLeft, topRight):
    """
    Finds the maximum area of a square that can fit inside the intersecting region of at least two rectangles.

    Args:
        bottomLeft: A list of lists, where bottomLeft[i] = [a_i, b_i] represents the bottom-left coordinates of the ith rectangle.
        topRight: A list of lists, where topRight[i] = [c_i, d_i] represents the top-right coordinates of the ith rectangle.

    Returns:
        The maximum area of a square that can fit inside the intersecting region of at least two rectangles.
        Returns 0 if such a square does not exist.
    """

    n = len(bottomLeft)
    max_area = 0

    for i in range(n):
        for j in range(i + 1, n):
            # Calculate the intersection rectangle
            intersection_bottom_left_x = max(bottomLeft[i][0], bottomLeft[j][0])
            intersection_bottom_left_y = max(bottomLeft[i][1], bottomLeft[j][1])
            intersection_top_right_x = min(topRight[i][0], topRight[j][0])
            intersection_top_right_y = min(topRight[i][1], topRight[j][1])

            # Check if the rectangles intersect
            if intersection_bottom_left_x < intersection_top_right_x and \
               intersection_bottom_left_y < intersection_top_right_y:

                # Calculate the width and height of the intersection
                intersection_width = intersection_top_right_x - intersection_bottom_left_x
                intersection_height = intersection_top_right_y - intersection_bottom_left_y

                # Calculate the maximum possible side length of a square within the intersection
                side_length = min(intersection_width, intersection_height)

                # Update the maximum area
                max_area = max(max_area, side_length * side_length)

    return max_area