Introduction

In this blog post, we will explore how to solve the LeetCode problem "1465" 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

You are given a rectangular cake of size h x w and two arrays of integers horizontalCuts and verticalCuts where: horizontalCuts[i] is the distance from the top of the rectangular cake to the ith horizontal cut and similarly, and verticalCuts[j] is the distance from the left of the rectangular cake to the jth vertical cut. Return the maximum area of a piece of cake after you cut at each horizontal and vertical position provided in the arrays horizontalCuts and verticalCuts. Since the answer can be a large number, return this modulo 109 + 7. Example 1: Input: h = 5, w = 4, horizontalCuts = [1,2,4], verticalCuts = [1,3] Output: 4 Explanation: The figure above represents the given rectangular cake. Red lines are the horizontal and vertical cuts. After you cut the cake, the green piece of cake has the maximum area. Example 2: Input: h = 5, w = 4, horizontalCuts = [3,1], verticalCuts = [1] Output: 6 Explanation: The figure above represents the given rectangular cake. Red lines are the horizontal and vertical cuts. After you cut the cake, the green and yellow pieces of cake have the maximum area. Example 3: Input: h = 5, w = 4, horizontalCuts = [3], verticalCuts = [3] Output: 9 Constraints: 2 <= h, w <= 109 1 <= horizontalCuts.length <= min(h - 1, 105) 1 <= verticalCuts.length <= min(w - 1, 105) 1 <= horizontalCuts[i] < h 1 <= verticalCuts[i] < w All the elements in horizontalCuts are distinct. All the elements in verticalCuts are distinct.

Explanation

Here's the breakdown of the solution:

• Maximize Gaps: The largest area will be determined by the largest horizontal gap multiplied by the largest vertical gap. We need to find these maximum gaps after making the cuts.
• Sort and Calculate: Sort both horizontalCuts and verticalCuts to easily calculate the differences between adjacent cuts. Include the cake boundaries (0 and h for horizontal, 0 and w for vertical) when calculating the gaps.

• Modulo Arithmetic: Perform the multiplication modulo 10⁹ + 7 to prevent overflow.

• Runtime Complexity: O(n log n + m log m), where n is the length of horizontalCuts and m is the length of verticalCuts due to sorting.

• Storage Complexity: O(1) excluding the input and the space used for sorting (which might be O(n) or O(log n) depending on the sorting algorithm implementation).

Code

    def maxArea(h: int, w: int, horizontalCuts: list[int], verticalCuts: list[int]) -> int:
    """
    Calculates the maximum area of a piece of cake after making horizontal and vertical cuts.

    Args:
        h: The height of the cake.
        w: The width of the cake.
        horizontalCuts: A list of horizontal cut positions.
        verticalCuts: A list of vertical cut positions.

    Returns:
        The maximum area of a piece of cake modulo 10^9 + 7.
    """

    horizontalCuts.sort()
    verticalCuts.sort()

    max_h_gap = max(horizontalCuts[0], h - horizontalCuts[-1])
    for i in range(1, len(horizontalCuts)):
        max_h_gap = max(max_h_gap, horizontalCuts[i] - horizontalCuts[i - 1])

    max_v_gap = max(verticalCuts[0], w - verticalCuts[-1])
    for i in range(1, len(verticalCuts)):
        max_v_gap = max(max_v_gap, verticalCuts[i] - verticalCuts[i - 1])

    return (max_h_gap * max_v_gap) % (10**9 + 7)