This is my Solution of Assignment 1 - Problem 3 from the Computer Science Course CS106A of Prof. Mehran Sahami at the STANFORD University.

CheckerboardKarel_v2.java

/*
 * File: CheckerboardKarel_v2.java
 * ----------------------------
 * When you finish writing it, the CheckerboardKarel class should draw
 * a checkerboard using beepers, as described in Assignment 1.  You
 * should make sure that your program works for all of the sample
 * worlds supplied in the starter folder.
 */
 
import stanford.karel.*;
 
public class CheckerboardKarel_v2 extends SuperKarel {
 
 
	public void run() {
		/* fills a checkerboard of ANY SIZE.
		 * 
		 * Pre-condition:	Karel starts at 1,1 facing EAST
		 */
 
		while( leftIsClear() ) {
			fillLine();
			goLineUp();
            ReturnToStartOfLine();	
		}
		fillLine(); // dot forget to fill the last line too.
	}
 
 
	private void fillLine() {
		/* Fills a whole Line with either Pattern1 or Pattern2
		 * depending on what kind of Pattern has been set on the
		 * last line (1 row down)
		 * 
		 * PRE-CONDITION:	Karel @ Field1 of a Row facing EAST
		 * 
		 * POST-CONDITION:	Karel filled the whole line with a Beeper-Pattern
		 * 					sitting on the last Field of a Row, facing East.
		 */
 
		// check if last line starts with a beeper
		if( LastLineStartsWithBeeper() ) {
			fillLineWithPattern2();
		} else {
			fillLineWithPattern1();
		}
	}
 
	private boolean LastLineStartsWithBeeper() {
		/* Returns TRUE or FALSE if the Last Line (one Line UNDER actual position
		 * starts with a Beeper or not. 
		 * 
		 * PRE-CONDITION:	Karel @ Field1 on ANY ROW facing EAST
		 * 
		 * POST-CONDITION:	No possition change.
		 */
		if (rightIsBlocked() ) { // special Test while on FIRST LINE
			return false;
		} else {
			turnRight();
			move();
			if ( beepersPresent() ) {
				turnAround();
				move();
				turnRight();
				return true;
			} else {
				turnAround();
				move();
				turnRight();
				return false;
			}
		}
	}
 
 
	private void fillLineWithPattern1() {
		/* Fills a whole Line with Pattern1
		 * 
		 * PRE-CONDITION:	Karel looks either EAST or WEST at the first
		 * 					Field of a Row. 
		 * 
		 * POST-CONDITION:	Karel filled the whole line with a Beeper-Pattern 1
		 * 					which means, starting with a Beeper at Field1,
		 * 					then skipping the next field, and so on.
		 */
		while( frontIsClear() ) {
			putBeeper();
			move();
			// Front STILL clear?? Then do another Step.
			if( frontIsClear() ) {
				move();
			}
		}
	}
 
	private void fillLineWithPattern2() {
		/* Fills a whole Line with Pattern2
		 * 
		 * PRE-CONDITION:	Karel looks either EAST or WEST at the first
		 * 					Field of a Row. 
		 * 
		 * POST-CONDITION:	Karel filled the whole line with a Beeper-Pattern 2
		 * 					which means, starting with an empty Field1,
		 * 					then placing a beeper on the next field, and so on.
		 */
		while( frontIsClear() ) {
			move();
			putBeeper();
			// Front STILL clear?? Then do another Step.
			if( frontIsClear() ) {
				move();
			}
		}
	}
 
 
	private void ReturnToStartOfLine() {
		/* Returns Karel to FIRST FIELD of a Row, facing EAST
		 * 
		 * PRE-CONDITION:	Karel facing EAST on any Row on ANY FIELD.
		 * 
		 * POST-CONDITION:	Karel facing East at FIRST FIELD of the Row.
		 */
		turnAround();
		while( frontIsClear() ) {
			move();
		}
		turnAround();
	}
 
 
	private void goLineUp() {
		/* Karel climbs one rown UP
		 * 
		 * PRE-CONDITION:	Karel facing EAST
		 * 
		 * POST-CONDITION:	Karel facing East, climbed one Row up.
		 */
		turnLeft();
		move();
		turnRight();
	}
}

— Axel Werner 2011-02-05 17:40