Union Area Calculation

The task is to write a Java program that calculates the total area of the union of N given rectangles, where each rectangle's edges are parallel to the axis. The rectangles may intersect or be inside each other. The complexity should not be O(n^2). The input format consists of the number of rectangles followed by the coordinates of each rectangle (x1, x2, y1, y2) in the format , , etc. The output is a single number representing the total area of the union.

Area of rectangles union
- Given N rectangles with edges parallel to axis, calculate the area of the union of all rectangles.
- A rectangle is specified by giving its smallest and largest x- and y-coordinates x1, x2, y1,
y2, where x1 < x2 and y1 < y2.
- Bottom left corner is at (x1, y1) and the upper right corner at (x2, y2).
- The area of this rectangle is given by the formula (x2 – x1)*(y2 – y1)
Rectangles may intersect each other or may even be inside each other.
- The task is to write a program in Java that reads n rectangles and return the total area.
- The complexity should not be O(n2).
The format of the input is:
- <Number of rectangles>
- <x1> <x2><y1>y2>
- <x1> <x2><y1>y2>
- ……
Output file should contain 1 number - the resulting area of the rectangles' union