Problem:
Problem F: Gap

Let’s play a card game called Gap.

You have 28 cards labeled with two-digit numbers. The first digit (from 1 to 4) represents the
suit of the card, and the second digit (from 1 to 7) represents the value of the card.

First, you shuffle the cards and lay them face up on the table in four rows of seven cards, leaving
a space of one card at the extreme left of each row. The following shows an example of initial
layout.

Next, you remove all cards of value 1, and put them in the open space at the left end of the
rows: “11” to the top row, “21” to the next, and so on.

Now you have 28 cards and four spaces, called gaps, in four rows and eight columns. You start
moving cards from this layout.

At each move, you choose one of the four gaps and fill it with the successor of the left neighbor
of the gap. The successor of a card is the next card in the same suit, when it exists. For instance
the successor of “42” is “43”, and “27” has no successor.

In the above layout, you can move “43” to the gap at the right of “42”, or “36” to the gap at
the right of “35”. If you move “43”, a new gap is generated to the right of “16”. You cannot
move any card to the right of a card of value 7, nor to the right of a gap.

The goal of the game is, by choosing clever moves, to make four ascending sequences of the same
suit, as follows.

Your task is to find the minimum number of moves to reach the goal layout.

Input

The input starts with a line containing the number of initial layouts that follow.

Each layout consists of five lines - a blank line and four lines which represent initial layouts of
four rows. Each row has seven two-digit numbers which correspond to the cards.

Output

For each initial layout, produce a line with the minimum number of moves to reach the goal
layout. Note that this number should not include the initial four moves of the cards of value 1.
If there is no move sequence from the initial layout to the goal layout, produce “-1”.

Sample Input

4

12 13 14 15 16 17 21
22 23 24 25 26 27 31
32 33 34 35 36 37 41
42 43 44 45 46 47 11

26 31 13 44 21 24 42
17 45 23 25 41 36 11
46 34 14 12 37 32 47
16 43 27 35 22 33 15

17 12 16 13 15 14 11
27 22 26 23 25 24 21
37 32 36 33 35 34 31
47 42 46 43 45 44 41

27 14 22 35 32 46 33
13 17 36 24 44 21 15
43 16 45 47 23 11 26
25 37 41 34 42 12 31

Output for the Sample Input

0
33
60
-1

Solution in JAVA (judge verdict: Memory Limit Exceeded)


import java.awt.Point;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.LinkedList;
import java.util.Queue;
import java.util.SortedMap;

public class Main {
	InputStream is;

	int __t__ = 1;
	int __f__ = 0;
	int __FILE_DEBUG_FLAG__ = __f__;
	String __DEBUG_FILE_NAME__ = "src/T";

	FastScanner in;
	PrintWriter out;
	
	int[][] IDEAL = {
			{11, 12, 13, 14, 15, 16, 17, 0},
			{21, 22, 23, 24, 25, 26, 27, 0},
			{31, 32, 33, 34, 35, 36, 37, 0},
			{41, 42, 43, 44, 45, 46, 47, 0}			
	};
	
	boolean isSolved(int[][] target) {
		for (int i = 0; i < target.length; i++) {
			for (int j = 0; j < target[0].length; j++) {
				if (target[i][j] != IDEAL[i][j]) return false;
			}
		}		
		return true;
	}
	
	String getKey(int[][] a) {
		StringBuilder res = new StringBuilder();
		for (int i = 0; i < a.length; i++) {
			for (int j = 0; j < a[i].length; j++) {
				res.append(a[i][j] + " ");
			}
		}
		return res.toString();
	}
	
	int[][] copy(int[][] a) {
		if (X.isEmpty()) throw new RuntimeException();
		
		int[][] res = X.poll();
		for (int i = 0; i < H; i++) {
			for (int j = 0; j < W; j++) {
				res[i][j] = a[i][j];
			}
		}
		return res;
	}
	
	int H = 4, W = 8;
	HashMap<String, Integer> hash = new HashMap<String, Integer>();	
	Queue<int[][]> q = new LinkedList<int[][]>();

	Queue<int[][]> X = new LinkedList<int[][]>();
	
	public void solve() {
		int T = in.nextInt();
		
		for (int i = 0; i < 4000; i++) {
			X.add(new int[H][W]);
		}
		
		main : 
		for (int times = 0; times < T; times++) {

			int[][] map = X.poll();
			for (int i = 0; i < H; i++) {
				Arrays.fill(map[i], 0);
			}
			for (int i = 0; i < H; i++) {
				for (int j = 0; j < W - 1; j++) {
					int next = in.nextInt();
					if (next % 10 == 1) {
						map[(next / 10) - 1][0] = next;
					} else {
						map[i][j+1] = next;
					}
				}
			}
			hash.clear();
			q.clear();
			
			q.add(map);			
			hash.put(getKey(map), 0);
			
			Queue<Point> cand = new LinkedList<Point>();
			while (!q.isEmpty()) {
				int[][] next = q.poll();
				int val = hash.get(getKey(next));

				if (isSolved(next)) {
					System.out.println(val);
					hash.clear();
					X.add(next);
					while (!q.isEmpty()) {
						X.add(q.poll());
					}
					continue main;
				}
				
				cand.clear();
				for (int i = 0; i < H; i++) {
					for (int j = 0; j < W; j++) {
						if (next[i][j] == 0) cand.add(new Point(j, i));
					}
				}
				
				while (!cand.isEmpty()) {
					Point p = cand.poll();
					int[][] nmap = copy(next);
					int nx = -1, ny = -1;
					for (int i = 0; i < H; i++) {
						for (int j = 0; j < W; j++) {
							if (next[i][j] == next[p.y][p.x - 1] + 1) {
								nx = j;
								ny = i;
							}
						}
					}
					if (nx != -1 && ny != -1) {
						nmap[p.y][p.x] = nmap[ny][nx];
						nmap[ny][nx] = 0;
						
						String key = getKey(nmap);
						if (!hash.containsKey(key)) {
							hash.put(key, val + 1);
							q.add(nmap);
						} else {
							X.add(nmap);
						}
					} else {
						X.add(nmap);
					}
				}
				
				X.add(next);
			}
			System.out.println(-1);
			hash.clear();
		}
	}
	
	public void run() {
		if (__FILE_DEBUG_FLAG__ == __t__) {
			try {
				is = new FileInputStream(__DEBUG_FILE_NAME__);
			} catch (FileNotFoundException e) {
				// TODO ????????????????????? catch ????????????
				e.printStackTrace();
			}
			System.out.println("FILE_INPUT!");
		} else {
			is = System.in;
		}
		in = new FastScanner(is);
		out = new PrintWriter(System.out);

		solve();
	}

	public static void main(String[] args) {
		new Main().run();
	}

	public void mapDebug(int[][] a) {
		System.out.println("--------map display---------");

		for (int i = 0; i < a.length; i++) {
			for (int j = 0; j < a[i].length; j++) {
				System.out.printf("%3d ", a[i][j]);
			}
			System.out.println();
		}

		System.out.println("----------------------------");
		System.out.println();
	}

	public void debug(Object... obj) {
		System.out.println(Arrays.deepToString(obj));
	}

	class FastScanner {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public FastScanner(InputStream stream) {
			this.stream = stream;
			//stream = new FileInputStream(new File("dec.in"));

		}

		int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		boolean isEndline(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		int[] nextIntArray(int n) {
			int[] array = new int[n];
			for (int i = 0; i < n; i++)
				array[i] = nextInt();

			return array;
		}

		int[][] nextIntMap(int n, int m) {
			int[][] map = new int[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextIntArray(m);
			}
			return map;
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		long[] nextLongArray(int n) {
			long[] array = new long[n];
			for (int i = 0; i < n; i++)
				array[i] = nextLong();

			return array;
		}

		long[][] nextLongMap(int n, int m) {
			long[][] map = new long[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextLongArray(m);
			}
			return map;
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		double[] nextDoubleArray(int n) {
			double[] array = new double[n];
			for (int i = 0; i < n; i++)
				array[i] = nextDouble();

			return array;
		}

		double[][] nextDoubleMap(int n, int m) {
			double[][] map = new double[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextDoubleArray(m);
			}
			return map;
		}

		String next() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		String[] nextStringArray(int n) {
			String[] array = new String[n];
			for (int i = 0; i < n; i++)
				array[i] = next();

			return array;
		}

		String nextLine() {
			int c = read();
			while (isEndline(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndline(c));
			return res.toString();
		}
	}
}