Problem A resolution - http://icpc.baylor.edu/xwiki/wiki/public/download/worldfinals/problems/icpc2014.pdf

Ipc2014ProblemA.java

public class Ipc2014ProblemA {

	private static class BaggageBin {
		int space;
		char destination;
		
		public BaggageBin(int space) {
			if (space > 0) { 
				if (space % 2 == 0) {
					this.destination = 'A';
				}
				else {
					this.destination = 'B';
				}
			}
			this.space = space;
		}
		
		@Override
		public String toString() {
			return (this.space < 0 ? this.space : " " + this.space) + "/" + this.destination;
		}
		
	}
	
	private static BaggageBin[] mountBinMatrix(int baggageBins) {
		// right = baggageBins
		// left = baggageBins
		// totalSpace = 2 * baggageBins
		int totalSpace = 2 * baggageBins;
		int mostLeftSpace = - baggageBins + 1;
		BaggageBin[] internalBaggageBin = new BaggageBin[totalSpace];
		for (int i = 0; i < totalSpace; i++) {
			internalBaggageBin[i] = new BaggageBin(mostLeftSpace++);
		}
		return internalBaggageBin;
	}
	
	private static void printLine(int num) {
		for (int i = 0; i <= num - 1; i++) {
			System.out.print("+------");
		}
		System.out.println("+");
	}
	
	private static void printMatrix(BaggageBin[] baggageBinMatrix) {
		int length = baggageBinMatrix.length;
		int i = 0;
		printLine(length);
		for (BaggageBin baggageBin: baggageBinMatrix) {
			System.out.print("| " + baggageBin.toString() + " ");
		}
		System.out.println("|");
		printLine(length);
	}
	
	public static void main(String[] args) {
		// Assign values
		int baggageCounter = 4;
		int baggageBins = baggageCounter * 2;
		int motorizedCarts = baggageCounter;

		// Mounting baggage matrix
		BaggageBin[] binMatrix = mountBinMatrix(baggageBins);
		printMatrix(binMatrix);
		
		// Sorting
		BaggageBin[] sortedMatrix = sortBinMatrix(binMatrix);

	}

	private static BaggageBin[] sortBinMatrix(BaggageBin[] binMatrix) {
		BaggageBin[] cartMove1Matrix = sortBinMove1(binMatrix);
		printMatrix(cartMove1Matrix);
		BaggageBin[] cartMove2Matrix = sortBinMove2(cartMove1Matrix);
		printMatrix(cartMove2Matrix);
		return cartMove2Matrix;
	}

	private static BaggageBin[] sortBinMove2(BaggageBin[] binMatrix) {
		BaggageBin oldBin, newBin;
		int newMatrixPosition, oldMatrixPosition;
		int firstPosition = binMatrix.length / 2;
		int lastPosition = binMatrix.length;
		int numberMoves = (lastPosition - firstPosition) / 2;
		// Move starts from 2 (1st already is B)
		for (int move = 2; move <= numberMoves; move++) {
			// Old bin
			oldMatrixPosition = ((move * 2) - 2) + firstPosition;
			oldBin = binMatrix[oldMatrixPosition];
			newMatrixPosition = firstPosition + move - 1;
			newBin = binMatrix[newMatrixPosition];
			newBin.destination = oldBin.destination;
			oldBin.destination = ' ';
		}
		return binMatrix;
	}
	
	private static BaggageBin[] sortBinMove1(BaggageBin[] binMatrix) {
		BaggageBin oldBin, newBin;
		int newMatrixPosition, oldMatrixPosition;
		int firstPosition = binMatrix.length / 2;
		int lastPosition = binMatrix.length;
		int numberMoves = (lastPosition - firstPosition) / 2;
		for (int move = 1; move <= numberMoves; move++) {
			// Old bin
			oldMatrixPosition = (move == 1 ? move : 2 * move - 1) + firstPosition;
			oldBin = binMatrix[oldMatrixPosition];
			// New bin
			newMatrixPosition = firstPosition - 1 - (move - 1);
			newBin = binMatrix[newMatrixPosition];
			//
			newBin.destination = oldBin.destination;
			oldBin.destination = ' ';
			
		}
		return binMatrix;
	}
	
}