How do you solve Maximum Area of Longest Diagonal Rectangle on LeetCode?

Maximum Area of Longest Diagonal Rectangle (LeetCode #3000) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: The diagonal length is calculated using the Pythagorean theorem.

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

The optimal solution for Maximum Area of Longest Diagonal Rectangle runs in O(n) time and uses O(1) space. The time complexity remains O(n) as we still loop through each rectangle once, and the space complexity is O(1) since we only store a few variables.

What is the brute force solution for Maximum Area of Longest Diagonal Rectangle?

The brute force approach for Maximum Area of Longest Diagonal Rectangle is Brute Force, with O(n) time complexity and O(1) space complexity. We can calculate the diagonal length for each rectangle and then compare them to find the one with the longest diagonal. If there are ties, we will check the area to determine the maximum. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Maximum Area of Longest Diagonal Rectangle?

Maximum Area of Longest Diagonal Rectangle uses the following concepts: Array. The recommended patterns to study are: Array, Mathematics.

What are the interview tips for Maximum Area of Longest Diagonal Rectangle?

Always clarify the problem statement and constraints before jumping to code. Think about edge cases, such as when all rectangles have the same diagonal. Discuss your thought process and approach with the interviewer before coding.

What are common mistakes when solving Maximum Area of Longest Diagonal Rectangle?

Forgetting to calculate both diagonal and area for each rectangle. Not handling the case where multiple rectangles have the same diagonal length.

#3000

Maximum Area of Longest Diagonal Rectangle

Easy

ArrayArrayMathematics

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n)	O(n)
Space	O(1)	O(1)

💡

Intuition

Time O(n)Space O(1)

We can achieve the same result in a single pass through the rectangles, calculating the diagonal and area simultaneously, which allows us to keep track of the maximum values efficiently.

⚙️

Algorithm

5 steps

1Step 1: Initialize variables to track the maximum diagonal length and the corresponding maximum area.
2Step 2: Loop through each rectangle in the dimensions array.
3Step 3: Calculate the diagonal length and area in one go.
4Step 4: Update the maximum diagonal and area based on the conditions.
5Step 5: Return the maximum area found.

solution.py14 lines

1import math
2
3def maxAreaOfLongestDiagonal(dimensions):
4    max_diagonal = 0
5    max_area = 0
6    for length, width in dimensions:
7        diagonal = math.sqrt(length ** 2 + width ** 2)
8        area = length * width
9        if diagonal > max_diagonal:
10            max_diagonal = diagonal
11            max_area = area
12        elif diagonal == max_diagonal:
13            max_area = max(max_area, area)
14    return max_area

ℹ

Complexity note: The time complexity remains O(n) as we still loop through each rectangle once, and the space complexity is O(1) since we only store a few variables.

1The diagonal length is calculated using the Pythagorean theorem.
2When diagonals are equal, the area becomes the deciding factor.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.