Practice/Apple/Leetcode 3000. Maximum Area of Longest Diagonal Rectangle

Leetcode 3000. Maximum Area of Longest Diagonal Rectangle

CodingOptional

Problem

You are given an array of rectangles where each rectangle is represented by a pair of integers [length, width]. Your task is to identify the rectangle that has the longest diagonal. If multiple rectangles share the same longest diagonal length, return the area of the one with the maximum area among them.

The diagonal of a rectangle with dimensions length and width can be computed using the Pythagorean theorem. To avoid floating-point arithmetic, compare the squared values of diagonals (length² + width²) instead of computing square roots.

Return the area (length × width) of the selected rectangle.

Requirements

1. Find the rectangle with the longest diagonal by comparing diagonal² values
2. If multiple rectangles have the same longest diagonal, select the one with maximum area
3. Return the area of the selected rectangle as an integer
4. Handle edge cases including single rectangles and ties

Constraints

• 1 ≤ dimensions.length ≤ 1000
• dimensions[i].length == 2
• 1 ≤ length, width ≤ 1000
• Time complexity should be O(n) where n is the number of rectangles
• Space complexity should be O(1)

Examples

Example 1:

` Input: dimensions = [[9, 3], [8, 6], [4, 7]] Output: 48 Explanation:

• Rectangle [9, 3]: diagonal² = 81 + 9 = 90, area = 27
• Rectangle [8, 6]: diagonal² = 64 + 36 = 100, area = 48
• Rectangle [4, 7]: diagonal² = 16 + 49 = 65, area = 28 The longest diagonal is 100, so we return area 48. `

Example 2:

Input: dimensions = [[3, 4], [4, 3]] Output: 12 Explanation: Both rectangles have diagonal² = 25 and area = 12. Since they tie on both diagonal and area, return 12.

Example 3:

` Input: dimensions = [[10, 4], [8, 7], [6, 9]] Output: 56 Explanation:

• Rectangle [10, 4]: diagonal² = 116, area = 40
• Rectangle [8, 7]: diagonal² = 113, area = 56
• Rectangle [6, 9]: diagonal² = 117, area = 54 The longest diagonal is 117, so we return area 54. `