Perfect Rectangle.py

class Solution:
    def isRectangleCover(self, rectangles: List[List[int]]) -> bool:
        X1, Y1 = float('inf'), float('inf')
        X2, Y2 = -float('inf'), -float('inf')

        points = set()
        actual_area = 0
        for x1, y1, x2, y2 in rectangles:
            # calculate the coords of the potential perfect rectangle
            X1, Y1 = min(X1, x1), min(Y1, y1)
            X2, Y2 = max(X2, x2), max(Y2, y2)
            # add up to the actual_area, so we can check against to see if thers is any part overwritten.
            actual_area += (x2 - x1) * (y2 - y1)
            
            # proving steps in https://labuladong.github.io/algo/4/32/131/
            for p in [(x1, y1), (x1, y2), (x2, y1), (x2, y2)]:
                if p in points: 
                    points.remove(p)
                else:           
                    points.add(p)

        # check the area 
        expected_area = (X2 - X1) * (Y2 - Y1)
        if actual_area != expected_area:
            return False
        
        if len(points) != 4:       
            return False

        if (X1, Y1) not in points: 
            return False
        if (X1, Y2) not in points: 
            return False
        if (X2, Y1) not in points: 
            return False
        if (X2, Y2) not in points: 
            return False

        return True