Practice/Google/Leetcode 223. Rectangle Area

Leetcode 223. Rectangle Area

CodingOptional

Problem

You are given the coordinates of two axis-aligned rectangles in a 2D plane. Each rectangle is defined by its bottom-left corner and top-right corner coordinates.

For the first rectangle, you receive: (ax1, ay1) as the bottom-left corner and (ax2, ay2) as the top-right corner.

For the second rectangle, you receive: (bx1, by1) as the bottom-left corner and (bx2, by2) as the top-right corner.

Calculate the total area covered by the two rectangles combined. If the rectangles overlap, count the overlapping region only once.

Requirements

1. Calculate the area of each individual rectangle
2. Determine if the rectangles overlap
3. If they overlap, compute the overlapping area
4. Return the total area covered (sum of both areas minus any overlap)
5. Handle cases where rectangles don't overlap, partially overlap, or one contains the other

Constraints

• -10^4 <= ax1 < ax2 <= 10^4
• -10^4 <= ay1 < ay2 <= 10^4
• -10^4 <= bx1 < bx2 <= 10^4
• -10^4 <= by1 < by2 <= 10^4
• All coordinates are integers

Examples

Example 1:

Input: ax1 = -3, ay1 = 0, ax2 = 3, ay2 = 4, bx1 = 0, by1 = -1, bx2 = 9, by2 = 2 Output: 45 Explanation: First rectangle has area (3-(-3)) * (4-0) = 24. Second rectangle has area (9-0) * (2-(-1)) = 27. They overlap in the region from (0, 0) to (3, 2), which has area 6. Total area = 24 + 27 - 6 = 45.

Example 2:

Input: ax1 = -2, ay1 = -2, ax2 = 2, ay2 = 2, bx1 = 3, by1 = 3, bx2 = 7, by2 = 7 Output: 32 Explanation: First rectangle has area 16, second has area 16. They don't overlap at all, so total area = 16 + 16 = 32.

Example 3:

Input: ax1 = 0, ay1 = 0, ax2 = 5, ay2 = 5, bx1 = 0, by1 = 0, bx2 = 5, by2 = 5 Output: 25 Explanation: Both rectangles are identical with area 25. They completely overlap, so total area = 25.