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// https://leetcode.com/problems/rectangle-area

// T: O(1)

// S: O(1)

public class RectangleArea {

private record Point(int x, int y) {}

private static class Rectangle {

public final int xl;

public final int xr;

public final int yb;

public final int yt;

public final int area;

Rectangle(Point lowerLeft, Point upperRight) {

xl = lowerLeft.x;

xr = upperRight.x;

yb = lowerLeft.y;

yt = upperRight.y;

area = (upperRight.x - lowerLeft.x) * (upperRight.y - lowerLeft.y);

}

public static Rectangle from(int x1, int y1, int x2, int y2) {

final Point a1 = new Point(x1, y1);

final Point a2 = new Point(x2, y2);

return new Rectangle(a1, a2);

}

public Rectangle intersection(Rectangle other) {

final int intersectionXl = Math.max(xl, other.xl);

final int intersectionXr = Math.max(intersectionXl, Math.min(xr, other.xr));

final int intersectionYb = Math.max(yb, other.yb);

final int intersectionYt = Math.max(intersectionYb, Math.min(yt, other.yt));

if (intersectionXl > intersectionXr || intersectionYb > intersectionYt) {

return null;

}

return Rectangle.from(intersectionXl, intersectionYb, intersectionXr, intersectionYt);

}

}

public static int computeArea(int ax1, int ay1, int ax2, int ay2, int bx1, int by1, int bx2, int by2) {

final Rectangle rectangle1 = Rectangle.from(ax1, ay1, ax2, ay2);

final Rectangle rectangle2 = Rectangle.from(bx1, by1, bx2, by2);

final Rectangle intersection = rectangle1.intersection(rectangle2);

return rectangle1.area + rectangle2.area - (intersection == null ? 0 : intersection.area);

}

}