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Rectangle Area

Difficulty: Medium

Problem Description

Given the coordinates of two rectilinear rectangles in a 2D plane, return the total area covered by the two rectangles. The first rectangle is defined by its bottom-left corner (ax1, ay1) and its top-right corner (ax2, ay2). The second rectangle is defined by its bottom-left corner (bx1, by1) and its top-right corner (bx2, by2).

Key Insights

  • The area of a rectangle can be calculated using the formula: width * height.
  • To find the total area covered by both rectangles, we need to calculate the area of each rectangle separately and then account for any overlapping area.
  • The overlapping area can be determined by finding the intersection coordinates of the two rectangles.
  • If there is no overlap, the total area will simply be the sum of the areas of both rectangles.

Space and Time Complexity

Time Complexity: O(1)
Space Complexity: O(1)

Solution

To solve the problem, we will:

  1. Calculate the area of the first rectangle using the coordinates (ax1, ay1) and (ax2, ay2).
  2. Calculate the area of the second rectangle using the coordinates (bx1, by1) and (bx2, by2).
  3. Determine the overlapping area by finding the maximum of the bottom-left corners and the minimum of the top-right corners for both rectangles.
  4. If there is an overlap, calculate the area of the overlapping rectangle.
  5. Subtract the overlapping area from the total area of both rectangles to get the final result.

We will use basic arithmetic operations and comparisons to achieve this, ensuring a constant time complexity.

Code Solutions

def computeArea(ax1, ay1, ax2, ay2, bx1, by1, bx2, by2):
    # Calculate the area of both rectangles
    area1 = (ax2 - ax1) * (ay2 - ay1)
    area2 = (bx2 - bx1) * (by2 - by1)

    # Calculate the overlapping coordinates
    overlap_width = max(0, min(ax2, bx2) - max(ax1, bx1))
    overlap_height = max(0, min(ay2, by2) - max(ay1, by1))

    # Calculate the area of the overlapping rectangle
    overlap_area = overlap_width * overlap_height

    # Return the total area covered by both rectangles
    return area1 + area2 - overlap_area
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