Circle and Rectangle Overlapping

Problem Description

You are given a circle represented as (radius, xCenter, yCenter) and an axis-aligned rectangle represented as (x1, y1, x2, y2), where (x1, y1) are the coordinates of the bottom-left corner, and (x2, y2) are the coordinates of the top-right corner of the rectangle. Return true if the circle and rectangle are overlapped otherwise return false. In other words, check if there is any point (xi, yi) that belongs to the circle and the rectangle at the same time.

Key Insights

• The circle is defined by its center and radius.
• The rectangle is defined by its bottom-left and top-right corners.
• Overlapping occurs if any part of the circle extends into the rectangle or vice versa.
• To determine overlap, we can check the distance from the circle's center to the closest point on the rectangle.

Space and Time Complexity

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

Solution

To determine if the circle and rectangle overlap, we can use the following approach:

1. Identify the closest point on the rectangle to the circle's center.
2. Calculate the distance between the circle's center and this closest point.
3. If this distance is less than or equal to the radius of the circle, they overlap; otherwise, they do not.

We can use basic geometric calculations to find the closest point on the rectangle and use the distance formula to check the overlap.

Code Solutions