223. Rectangle Area

Problem

Find the total area covered by two rectilinear rectangles in a 2D plane.

Each rectangle is defined by its bottom left corner and top right corner as shown in the figure.

Example:

Input: A = -3, B = 0, C = 3, D = 4, E = 0, F = -1, G = 9, H = 2
Output: 45

Note:

Assume that the total area is never beyond the maximum possible value of int.

Problem Summary

Calculate the total area formed by the overlap of two rectilinear rectangles on a 2D plane. Each rectangle is represented by the coordinates of its bottom-left vertex and top-right vertex, as shown in the figure. Note: Assume that the rectangle area will not exceed the range of int.

Solution Approach

• Given the coordinates of two rectangles, find the total area covered by these two rectangles on the coordinate axes.
• Geometry problem. Since there are only 2 rectangles, just follow the problem statement. First calculate the areas of the two rectangles separately, add them together, and then subtract the overlapping area of the two rectangles.

Code

package leetcode

func computeArea(A int, B int, C int, D int, E int, F int, G int, H int) int {
	X0, Y0, X1, Y1 := max(A, E), max(B, F), min(C, G), min(D, H)
	return area(A, B, C, D) + area(E, F, G, H) - area(X0, Y0, X1, Y1)
}

func area(x0, y0, x1, y1 int) int {
	l, h := x1-x0, y1-y0
	if l <= 0 || h <= 0 {
		return 0
	}
	return l * h
}