Leetcode #1465: Maximum Area of a Piece of Cake After Horizontal and Vertical Cuts
In this guide, we solve Leetcode #1465 Maximum Area of a Piece of Cake After Horizontal and Vertical Cuts in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
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.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Greedy, Array, Sorting
Intuition
A locally optimal choice leads to a globally optimal result for this structure.
That means we can commit to decisions as we scan without backtracking.
Approach
Sort or preprocess if needed, then repeatedly take the best available local choice.
Maintain the minimal state necessary to validate the greedy decision.
Steps:
- Sort or preprocess as needed.
- Iterate and pick the best local option.
- Track the current solution.
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
The time complexity is , where and are the lengths of horizontalCuts and verticalCuts, respectively. The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.