/*
 * Problem C. Recycled Numbers
 * 
 * Do you ever become frustrated with television because you keep seeing the
 * same things, recycled over and over again? Well I personally don't care about
 * television, but I do sometimes feel that way about numbers.
 * 
 * Let's say a pair of distinct positive integers (n, m) is recycled if you can
 * obtain m by moving some digits from the back of n to the front without
 * changing their order. For example, (12345, 34512) is a recycled pair since
 * you can obtain 34512 by moving 345 from the end of 12345 to the front. Note
 * that n and m must have the same number of digits in order to be a recycled
 * pair. Neither n nor m can have leading zeros.
 * 
 * Given integers A and B with the same number of digits and no leading zeros,
 * how many distinct recycled pairs (n, m) are there with A â¤ n < m â¤ B?
 * 
 * Input
 * 
 * The first line of the input gives the number of test cases, T. T test cases
 * follow. Each test case consists of a single line containing the integers A
 * and B.
 * 
 * Output
 * 
 * For each test case, output one line containing "Case #x: y", where x is the
 * case number (starting from 1), and y is the number of recycled pairs (n, m)
 * with A â¤ n < m â¤ B.
 * 
 * Limits
 * 
 * 1 â¤ T â¤ 50.
 * 
 * A and B have the same number of digits.

Small dataset

1 â¤ A â¤ B â¤ 1000.

Large dataset

1 â¤ A â¤ B â¤ 2000000.

Sample


Input 
 	
Output 
 
4
1 9
10 40
100 500
1111 2222
Case #1: 0
Case #2: 3
Case #3: 156
Case #4: 287
 */

package google.codejam.y2012.qualifications;

import google.codejam.commons.Utils;

import java.io.IOException;
import java.util.StringTokenizer;

/**
 * @author Marco Lackovic <marco.lackovic@gmail.com>
 * @version 1.0, Apr 14, 2012
 */
public class RecycledNumbers {

	private static final String INPUT_FILE_NAME = "C-large.in";
	private static final String OUTPUT_FILE_NAME = "C-large.out";

	public static void main(String[] args) throws IOException {
		String[] input = Utils.readFromFile(INPUT_FILE_NAME);
		String[] output = new String[input.length];
		int x = 0;
		for (String line : input) {
			StringTokenizer st = new StringTokenizer(line);
			int a = Integer.valueOf(st.nextToken());
			int b = Integer.valueOf(st.nextToken());
			System.out.println("Computing case #" + (x + 1));
			output[x++] = "Case #" + x + ": " + recycledNumbers(a, b);
		}
		Utils.writeToFile(output, OUTPUT_FILE_NAME);
	}

	private static int recycledNumbers(int a, int b) {
		int count = 0;
		for (int n = a; n < b; n++) {
			count += getNumGreaterRotations(n, b);
		}
		return count;
	}

	private static int getNumGreaterRotations(int n, int b) {
		int count = 0;
		char[] chars = Integer.toString(n).toCharArray();
		for (int i = 0; i < chars.length; i++) {
			chars = rotateRight(chars);
			if (chars[0] != '0') {
				int m = Integer.valueOf(new String(chars));
				if (n == m) {
					break;
				} else if (n < m && m <= b) {
					count++;
				}
			}
		}
		return count;
	}

	private static char[] rotateRight(char[] chars) {
		char last = chars[chars.length - 1];
		for (int i = chars.length - 2; i >= 0; i--) {
			chars[i + 1] = chars[i];
		}
		chars[0] = last;
		return chars;
	}

}

package fixjava;

import java.util.concurrent.Callable;
import java.util.concurrent.Future;

import fixjava.ParallelWorkQueue.CallableFactory;

public class ArrayStats {
	public final double[][] data;
	public final int n, k;

	private double[][] centered;
	private double[] mean;
	private double[][] cov;
	private double[] stddev = null;
	private double[][] corr = null;

	/** Calculate covariance matrix */
	public ArrayStats(double[][] data) {
		if (data == null || data.length < 2 || data[0].length < 2)
			throw new IllegalArgumentException("Invalid data");
		this.data = data;
		this.n = data.length;
		this.k = data[0].length;
	}

	/** Compute mean for each dimension */
	public double[] mean() {
		if (mean == null) {
			mean = new double[k];
			for (int dim = 0; dim < k; dim++) {
				double tot = 0;
				for (int pt = 0; pt < n; pt++)
					tot += data[pt][dim];
				mean[dim] = tot / n;
			}
		}
		return mean;
	}

	/** Compute stddev for each dimension */
	public double[] stddev() {
		if (stddev == null) {
			// Make sure means are computed
			mean();

			stddev = new double[k];
			for (int dim = 0; dim < k; dim++) {
				for (int pt = 0; pt < n; pt++) {
					double diff = data[pt][dim] - mean[dim];
					stddev[dim] += diff * diff;
				}
				stddev[dim] = Math.sqrt(stddev[dim] / n);
			}
		}
		return stddev;
	}

	/** Re-center data by subtracting mean from each dimension */
	public double[][] centered() {
		if (centered == null) {
			// Make sure means are computed
			mean();

			centered = new double[n][k];
			for (int pt = 0; pt < n; pt++)
				for (int dim = 0; dim < k; dim++)
					centered[pt][dim] = data[pt][dim] - mean[dim];
		}
		return centered;
	}

	/** Compute covariance matrix */
	public double[][] cov() {
		if (cov == null) {
			// Make sure centered version of data is computed
			centered();

			// Work on transposed array for cache coherence
			final double[][] centeredT = ArrayUtils.transpose(centered);

			cov = new double[k][k];

			try {
				//final DecimalFormat formatPercent1dp = new DecimalFormat("0.0%");
				for (Future<Void> res : new ParallelWorkQueue<Integer, Void>(/* numThreads = */25,
						ParallelWorkQueue.makeIntRangeIterable(k), new CallableFactory<Integer, Void>() {
							//IntegerMutable counter = new IntegerMutable();

							@Override
							public Callable<Void> newInstance(final Integer ii) {
								return new Callable<Void>() {
									int dim1 = ii.intValue();
									double[][] centeredTLocal = centeredT;
									double[][] covLocal = cov;

									@Override
									public Void call() {
										for (int dim2 = dim1; dim2 < k; dim2++) {
											double numer = 0.0;
											for (int pt = 0; pt < n; pt++)
												numer += centeredTLocal[dim1][pt] * centeredTLocal[dim2][pt];
											int denom = n - 1;
											covLocal[dim1][dim2] = covLocal[dim2][dim1] = denom == 0 ? 0 : numer / denom;
										}
										//										int count = counter.increment();
										//										if (count % 10 == 0)
										//											System.out.println(formatPercent1dp.format((count / (float) (k - 1))));
										return null;
									}
								};
							}
						}))
					// Barricade
					res.get();
			} catch (Exception e) {
				e.printStackTrace();
				System.exit(1);
			}
		}
		return cov;
	}

	/** Compute correlation matrix */
	public double[][] corr() {
		if (corr == null) {
			// Make sure per-dim stddevs and covariance matrix are computed
			stddev();
			cov();

			corr = new double[k][k];
			for (int dim1 = 0; dim1 < k; dim1++) {
				for (int dim2 = dim1; dim2 < k; dim2++) {
					double prod = stddev[dim1] * stddev[dim2];
					corr[dim1][dim2] = corr[dim2][dim1] = prod == 0.0 ? 0.0 : cov[dim1][dim2] / prod;
				}
			}
		}
		return corr;
	}
}
