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Grokking the Coding Interview Patterns in C#

Solution: Rectangle Area

Explore how to calculate the total area covered by two axis-aligned rectangles in a 2D plane, including cases where they overlap. Understand the step-by-step process to find individual areas, determine horizontal and vertical overlaps, and compute the final combined area without double counting. This lesson teaches you a methodical approach to solve geometric problems using simple arithmetic operations with constant time and space complexity.

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Statement

You are given the coordinates of two axis-aligned rectangles in a 2D plane. Your task is to calculate the total area covered by both rectangles.

  • The first rectangle is specified by the coordinates of its bottom-left corner (ax1, ay1) and top-right corner (ay1, ay2).

  • Similarly, the second rectangle is defined by its bottom-left corner (bx1, by1) and top-right corner (bx2, by2).

Note: The rectangles may overlap.

Constraints:

  • −104≤-10^4 \leq ax1 ≤ \leq ax2 ≤104\leq 10^4 ...