This is my Solution of Assignment 1 - Problem 4 from the Computer Science Course CS106A of Prof. Mehran Sahami at the STANFORD University.

MidpointFindingKarel.java

/*
 * File: MidpointFindingKarel.java
 * -------------------------------
 * When you finish writing it, the MidpointFindingKarel class should
 * leave a beeper on the corner closest to the center of 1st Street
 * (or either of the two central corners if 1st Street has an even
 * number of corners).  Karel can put down additional beepers as it
 * looks for the midpoint, but must pick them up again before it
 * stops.  The world may be of any size, but you are allowed to
 * assume that it is at least as tall as it is wide.
 */
 
import stanford.karel.*;
 
public class MidpointFindingKarel extends SuperKarel {
 
	public void run() {
		/*
		 * Karel finds the middle (-+1) of the world and drops 
		 * a beeper there. 
		 */
		checkWidth();
		goMiddle();
		putBeeper();
		paintCorner(RED);
 
		while( beepersPresent() ) { // infinite loop (dance)
			paintCorner(GREEN);
			turnLeft();
			paintCorner(RED);
			turnLeft();
		}
	}
 
	private void checkWidth() {
		/* this method lays a line of beepers to determine the width of his world
		 * then it stacks/stores the beepers at 1,1
		 * 
		 * Pre-condition:	Karel at 1,1 facing EAST
		 * 					no Beepers at all
		 * 
		 * Post-condition:	Karel at 1,1 facing EAST
		 * 					Width of World represented as a Stack of 
		 * 					Beepers at 1,1
		 */
 
		drawLine();
		collectBeepers();
	}
 
 
	private void drawLine() {
		/* this method lays a line of beepers to determine the width of his world
		 * 
		 * Pre-condition:	Karel at 1:1 facing EAST
		 * 					no Beepers at all
		 * Post-condition:	Karel infront of RIGHT WALL (x,1) facing EAST
		 * 					behind him a line of beepers 
		 */
		while( frontIsClear() ) {
			putBeeper();
			move();
		}
		putBeeper();
	}
 
	private void collectBeepers() {
		/* this method collects a line of beepers and stacks them
		 * at 1,1
		 * 
		 * Pre-condition:	Karel infront of RIGHT WALL (x,1) facing EAST
		 * 					behind him a line of beepers
		 * 
		 * Post-condition:	Karel at 1:1 facing EAST, sitting on a Stack of
		 * 					Beepers representing the WIDTH of his World
		 */
		turnAround();
		while( frontIsClear() ) {
			while( beepersPresent() ) {
				pickBeeper();
				move();
				putBeeper();
				moveBack();
			}
			move();
		}
		turnAround();
	}
 
	private void moveBack() {
		/* moves karol ONE STEP back keeping direction heading
		 * 
		 */
		turnAround();
		move();
		turnAround();
	}
 
 
	private void goMiddle() {
		/* this method moves karel (and the beepers left at his place) to the next
		 * position, taking 2 Beepers per Step. 
		 * 
		 * Pre-condition:	Karel at 1,1 facing EAST
		 * 					X Beepers at 1,1
		 * 
		 * Post-condition:	Karel at x,1 (near middle) facing EAST
		 * 					no beepers left
		 */
 
		pickBeeper(); // off by one bug: need to walk x-1 steps
 
		while( beepersPresent() ) {
			pickBeeper(); // take one beeper per Step
			pushStack();
			move();
			if( beepersPresent() ) { // Still Beepers left?
				pickBeeper(); // take one MORE beeper as charge/cost
			}
		}
	}
 
 
 
	private void pushStack() {
		/* this method moves the whole stack of beepers on karels actual
		 * position ONE STEP further keeping the direction. 
		 * 
		 * Pre-condition:	Karel at x,1 facing EAST with 
		 * 					X Beepers at his position.
		 * 
		 * Post-condition:	Karel at x+1,1 facing EAST with 
		 * 					X-1 Beepers at his position.
		 */
 
		while( beepersPresent() ) {
			pickBeeper(); // take one beeper as charge/cost
			move();
			putBeeper();
			moveBack();
		}
	}
}

— Axel Werner 2011-02-05 17:40