Medium
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).
Example 1:
Input: ax1 = -3, ay1 = 0, ax2 = 3, ay2 = 4, bx1 = 0, by1 = -1, bx2 = 9, by2 = 2 Output: 45
Example 2:
Input: ax1 = -2, ay1 = -2, ax2 = 2, ay2 = 2, bx1 = -2, by1 = -2, bx2 = 2, by2 = 2 Output: 16
Constraints:
-104 <= ax1 <= ax2 <= 104-104 <= ay1 <= ay2 <= 104-104 <= bx1 <= bx2 <= 104-104 <= by1 <= by2 <= 104
class Solution:
def computeArea(self, ax1: int, ay1: int, ax2: int, ay2: int, bx1: int, by1: int, bx2: int, by2: int) -> int:
# area1 = abs(ax1-ax2) * abs(ay1-ay2)
# area2 = abs(bx1-bx2) * abs(by1-by2)
# total = area1+area2
# print(total, area1, area2)
area_of_a = (ay2 - ay1) * (ax2 - ax1)
area_of_b = (by2 - by1) * (bx2 - bx1)
# calculate x overlap
left = max(ax1, bx1)
right = min(ax2, bx2)
x_overlap = right - left
# calculate y overlap
top = min(ay2, by2)
bottom = max(ay1, by1)
y_overlap = top - bottom
area_of_overlap = 0
# if the rectangles overlap each other, then calculate
# the area of the overlap
if x_overlap > 0 and y_overlap > 0:
area_of_overlap = x_overlap * y_overlap
# area_of_overlap is counted twice when in the summation of
# area_of_a and area_of_b, so we need to subtract it from the
# total, to get the toal area covered by both the rectangles
total_area = area_of_a + area_of_b - area_of_overlap
return total_area