Maximum Area of Longest Diagonal Rectangle

Maximum Area of Longest Diagonal Rectangle

What is this problem about?

You are given a 2D array where each element is an array [length, width] representing the dimensions of a rectangle. You need to calculate the length of the diagonal for each rectangle. Your goal is to find the rectangle that has the strictly longest diagonal. If there is a tie (multiple rectangles have the exact same longest diagonal), you must return the maximum area among those tied rectangles.

Why is this asked in interviews?

This is an entry-level Array Traversal and Math problem. It tests basic geometric formulas (Pythagorean theorem) and multi-variable state tracking. Interviewers use it as a warm-up to ensure candidates can write conditional logic that handles tie-breakers without writing messy, convoluted if-else trees.

Algorithmic pattern used

This problem follows a simple Linear Scan (Single Pass) pattern. You iterate through the list of rectangles, maintaining two global tracking variables: max_diagonal and max_area_of_longest_diagonal. For each rectangle, calculate its diagonal squared ($L^2 + W^2$).

• If this diagonal squared is strictly greater than max_diagonal, update max_diagonal and completely overwrite max_area with the current rectangle's area.
• If this diagonal squared is exactly equal to max_diagonal, you update max_area to be the max(max_area, current_area).

Example explanation

Rectangles: [[9, 3], [8, 6]]

• Rectangle 1: [9, 3].
  • Diagonal squared = $9^2 + 3^2 = 81 + 9 = 90$.
  • Area = $9 \times 3 = 27$.
  • This is the first one, so max_diag = 90, max_area = 27.
• Rectangle 2: [8, 6].
  • Diagonal squared = $8^2 + 6^2 = 64 + 36 = 100$.
  • Area = $8 \times 6 = 48$.
  • Since $100 > 90$, this is the new longest diagonal. We overwrite state.
  • max_diag = 100, max_area = 48. Return 48.

If another rectangle had diag = 100 but area = 50, the equality condition would trigger and max_area would bump up to 50.

Common mistakes candidates make

A common mistake is using Math.sqrt() to calculate the exact diagonal length. Floating-point square roots suffer from precision loss. If two diagonals are extremely close in value, a float might evaluate them as equal when they aren't. Because the square root function is strictly increasing, $A > B$ implies $\sqrt{A} > \sqrt{B}$. Therefore, you should always compare the squared diagonal lengths ($L^2 + W^2$) using exact integers to ensure 100% accuracy and faster computation.

Interview preparation tip

When an interview question involves geometric distances, distances between points, or diagonals, avoid Math.sqrt unless the prompt explicitly asks for a float return type. Comparing squared distances using integers is an industry-standard optimization that shows the interviewer you care about both performance and type safety.