1401-Circle-and-Rectangle-Overlapping.py

'''
Given a circle represented as (radius, x_center, y_center) 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 are any point (xi, yi) such that belongs to the circle and the rectangle at the same time.

 

Example 1:
Input: radius = 1, x_center = 0, y_center = 0, x1 = 1, y1 = -1, x2 = 3, y2 = 1
Output: true
Explanation: Circle and rectangle share the point (1,0) 

Example 2:
Input: radius = 1, x_center = 0, y_center = 0, x1 = -1, y1 = 0, x2 = 0, y2 = 1
Output: true

Example 3:
Input: radius = 1, x_center = 1, y_center = 1, x1 = -3, y1 = -3, x2 = 3, y2 = 3
Output: true

Example 4:
Input: radius = 1, x_center = 1, y_center = 1, x1 = 1, y1 = -3, x2 = 2, y2 = -1
Output: false
 

Constraints:

1 <= radius <= 2000
-10^4 <= x_center, y_center, x1, y1, x2, y2 <= 10^4
x1 < x2
y1 < y2
'''
class Solution:
    def checkOverlap(self, radius: int, x_center: int, y_center: int, x1: int, y1: int, x2: int, y2: int) -> bool:
        corners = [(x1,y1), (x2,y1), (x2,y2), (x1, y2)]
        for (x, y) in corners:
            if (x_center - x)**2 + (y_center - y)**2 <= radius**2:
                return True

        for x in [x1, x2]:
            if x_center-radius <= x <= x_center+radius and y1<=y_center<=y2:
                return True
        for y in [y1, y2]:
            if y_center-radius <= y <= y_center+radius and x1<=x_center<=x2:
                return True
				
        if x1<=x_center<=x2 and y1<=y_center<=y2:
            return True
        return False