Maximum Area of Longest Diagonal Rectangle

Problem Description

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.

Key Insights

• The length of the diagonal of a rectangle can be calculated using the formula: sqrt(length^2 + width^2).
• We need to iterate through the list of rectangles to find the one with the longest diagonal.
• If multiple rectangles have the same longest diagonal, we will choose the one with the largest area (length * width).
• The constraints allow us to perform operations in a straightforward manner since the maximum number of rectangles is small (100).

Space and Time Complexity

Time Complexity: O(n) - We only need to iterate through the list once. Space Complexity: O(1) - We are using a constant amount of space for storing variables.

Solution

To solve the problem, we will use a simple approach:

1. Initialize variables to keep track of the maximum diagonal found and the corresponding maximum area.
2. Loop through each rectangle in the dimensions array.
3. Calculate the diagonal length for each rectangle using the formula.
4. If the current diagonal is longer than the maximum found, update the maximum diagonal and the area.
5. If the diagonal matches the longest found, compare the areas and update the maximum area if needed.
6. Finally, return the area of the rectangle with the longest diagonal (or the largest area if tied).

Code Solutions