Maximum Area of a Piece of Cake After Horizontal and Vertical Cuts — LeetCode 1465 Python Solution

The problem

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.

Example

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.

Python solution

class Solution:
    def maxArea(
        self, h: int, w: int, horizontalCuts: List[int], verticalCuts: List[int]
    ) -> int:
        horizontalCuts.extend([0, h])
        verticalCuts.extend([0, w])
        horizontalCuts.sort()
        verticalCuts.sort()
        x = max(b - a for a, b in pairwise(horizontalCuts))
        y = max(b - a for a, b in pairwise(verticalCuts))
        return (x * y) % (10**9 + 7)

Complexity

Pattern: Greedy

Take the locally best option every time — when you can prove that never costs you later. LeetCode 1465. Maximum Area of a Piece of Cake After Horizontal and Vertical Cuts is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Greedy.

The greedy guide has the Python template for the pattern and the 346 LeetCode problems that use it.

Related problems