Is Maximum Area of Longest Diagonal Rectangle easy or hard?

LeetCode classifies this problem as Easy. The solution only requires understanding the Pythagorean formula for diagonals and performing a linear scan with a tie‑breaking rule based on area.

Maximum Area of Longest Diagonal Rectangle Python/Java solution

Both Python and Java implementations follow the same pattern: loop through the rectangles, compute l*l + w*w, compare it with the current maximum diagonal square, and update the stored area if needed. The logic stays O(n) time and O(1) space regardless of language.

How to solve Maximum Area of Longest Diagonal Rectangle in O(n)?

Iterate through the rectangles once and compute the squared diagonal value l*l + w*w for each pair. Maintain the maximum diagonal square encountered so far and the area of that rectangle. Update the stored result whenever a larger diagonal appears or when the diagonal ties but the area is larger.

What is the best approach for Maximum Area of Longest Diagonal Rectangle?

The best approach is a single linear scan that compares the squared diagonals of each rectangle. For every pair (l, w), compute l*l + w*w and track the maximum value. If two rectangles share the same diagonal square, choose the one with the larger area. This runs in O(n) time with O(1) extra space.

Is Maximum Area of Longest Diagonal Rectangle asked at Google/Amazon/Meta?

This problem represents a common interview pattern involving array traversal and mathematical comparison. Variants that involve comparing geometric properties like diagonals or areas appear in interviews at large companies because they test careful iteration and tie‑breaking logic.

What data structure is used in Maximum Area of Longest Diagonal Rectangle?

The problem primarily uses an array of rectangle dimensions. The algorithm performs a sequential scan of this array while maintaining a few variables for the current best diagonal and area. No additional data structures such as hash maps or trees are required.

What is the time complexity of Maximum Area of Longest Diagonal Rectangle?

The optimal solution runs in O(n) time because each rectangle is processed exactly once during a single pass through the array. Only constant additional variables are used to track the best diagonal and area, giving O(1) space complexity.

Description Hints 1 Solution Video 7:02

3000. Maximum Area of Longest Diagonal Rectangle

Easy45.9% acceptance5 companies

You are given a 2D 0-indexed integer array dimensions.

For all indices i, 0 <= i < dimensions.length, dimensions[i][0] represents the length and dimensions[i][1] represents the width of the rectangle i.

Return the area of the rectangle having the longest diagonal. If there are multiple rectangles with the longest diagonal, return the area of the rectangle having the maximum area.

Example 1:

Input: dimensions = [[9,3],[8,6]]
Output: 48
Explanation: 
For index = 0, length = 9 and width = 3. Diagonal length = sqrt(9 * 9 + 3 * 3) = sqrt(90) ≈ 9.487.
For index = 1, length = 8 and width = 6. Diagonal length = sqrt(8 * 8 + 6 * 6) = sqrt(100) = 10.
So, the rectangle at index 1 has a greater diagonal length therefore we return area = 8 * 6 = 48.

Example 2:

Input: dimensions = [[3,4],[4,3]]
Output: 12
Explanation: Length of diagonal is the same for both which is 5, so maximum area = 12.

Constraints:

1 <= dimensions.length <= 100
dimensions[i].length == 2
1 <= dimensions[i][0], dimensions[i][1] <= 100

Asked at 5 companies

Accenture Atlassian

Google Amazon Meta

Topics

Array

Hints open one at a time

Hint 1

Diagonal of rectangle is sqrt(length² + width²).

7:02

Still stuck?Read 3 approaches, or watch a walkthrough.

Open solution

LanguageLoading editor…

1class Solution:
2    def areaOfMaxDiagonal(self, dimensions: List[List[int]]) -> int:
3        

Starter codePython 3Spaces: 4

Examples

Case 1Case 2

Input

[[9,3],[8,6]]

Input

[[3,4],[4,3]]

Your code is saved on this device.Solution