Program to find total area covered by two rectangles in Python

Suppose we want to find the total area covered by two rectilinear rectangles in a 2D plane. Here each rectangle is defined by its bottom left corner and top right corner as shown in the figure.

To solve this, we will follow these steps −

• width_1 := |C-A|, height_1 := |D-B|
• width_2 := |G-E|, height_2 := |H-F|
• area := width_1*height_1 + width_2*height_2
• if (G<A) or (E>C) or (F>D) or (H<B), then
  • return area
• otherwise,
  • p := maximum of A, E
  • q := maximum of B, F
  • r := minimum of C, G
  • s := minimum of D, H
  • width_3 := |r-p|
  • height_3 := |s-q|
  • return area - (width_3*height_3)

Example

Let us see the following implementation to get better understanding −

def solve(A, B, C, D, E, F, G, H):    width_1 = abs(C-A)    height_1 = abs(D-B)    width_2 = abs(G-E)    height_2 = abs(H-F)    area = width_1*height_1 + width_2*height_2 if (G<A) or (E>C) or (F>D) or (H<B): return area else: p = max(A,E) q = max(B,F) r = min(C,G) s = min(D,H) width_3 = abs(r-p) height_3 = abs(s-q) return area - (width_3*height_3) A = -3 B = 0 C = 3 D = 4 E = 0 F = -1 G = 9 H = 2 print(solve(A, B, C, D, E, F, G, H))

Input

-3, 0, 3, 4, 0, -1, 9, 2 

Output

45