/******************************************************************************
 *  Compilation:  javac LSD.java
 *  Execution:    java LSD < input.txt
 *  Dependencies: StdIn.java StdOut.java 
 *  Data files:   http://algs4.cs.princeton.edu/51radix/words3.txt
 *
 *  LSD radix sort
 *
 *    - Sort a String[] array of n extended ASCII strings (R = 256), each of length w.
 *
 *    - Sort an int[] array of n 32-bit integers, treating each integer as 
 *      a sequence of w = 4 bytes (R = 256).
 *
 *  Uses extra space proportional to n + R.
 *
 *
 *  % java LSD < words3.txt
 *  all
 *  bad
 *  bed
 *  bug
 *  dad
 *  ...
 *  yes
 *  yet
 *  zoo
 *
 ******************************************************************************/

package edu.princeton.cs.algs4;

/**
 *  The {@code LSD} class provides static methods for sorting an
 *  array of <em>w</em>-character strings or 32-bit integers using LSD radix sort.
 *  <p>
 *  For additional documentation,
 *  see <a href="http://algs4.cs.princeton.edu/51radix">Section 5.1</a> of
 *  <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
 *
 *  @author Robert Sedgewick
 *  @author Kevin Wayne
 */
public class LSD {
    private static final int BITS_PER_BYTE = 8;

    // do not instantiate
    private LSD() { }

   /**  
     * Rearranges the array of W-character strings in ascending order.
     *
     * @param a the array to be sorted
     * @param w the number of characters per string
     */
    public static void sort(String[] a, int w) {
        int n = a.length;
        int R = 256;   // extend ASCII alphabet size
        String[] aux = new String[n];

        for (int d = w-1; d >= 0; d--) {
            // sort by key-indexed counting on dth character

            // compute frequency counts
            int[] count = new int[R+1];
            for (int i = 0; i < n; i++)
                count[a[i].charAt(d) + 1]++;

            // compute cumulates
            for (int r = 0; r < R; r++)
                count[r+1] += count[r];

            // move data
            for (int i = 0; i < n; i++)
                aux[count[a[i].charAt(d)]++] = a[i];

            // copy back
            for (int i = 0; i < n; i++)
                a[i] = aux[i];
        }
    }

   /**
     * Rearranges the array of 32-bit integers in ascending order.
     * This is about 2-3x faster than Arrays.sort().
     *
     * @param a the array to be sorted
     */
    public static void sort(int[] a) {
        final int BITS = 32;                 // each int is 32 bits 
        final int R = 1 << BITS_PER_BYTE;    // each bytes is between 0 and 255
        final int MASK = R - 1;              // 0xFF
        final int w = BITS / BITS_PER_BYTE;  // each int is 4 bytes

        int n = a.length;
        int[] aux = new int[n];

        for (int d = 0; d < w; d++) {         

            // compute frequency counts
            int[] count = new int[R+1];
            for (int i = 0; i < n; i++) {           
                int c = (a[i] >> BITS_PER_BYTE*d) & MASK;
                count[c + 1]++;
            }

            // compute cumulates
            for (int r = 0; r < R; r++)
                count[r+1] += count[r];

            // for most significant byte, 0x80-0xFF comes before 0x00-0x7F
            if (d == w-1) {
                int shift1 = count[R] - count[R/2];
                int shift2 = count[R/2];
                for (int r = 0; r < R/2; r++)
                    count[r] += shift1;
                for (int r = R/2; r < R; r++)
                    count[r] -= shift2;
            }

            // move data
            for (int i = 0; i < n; i++) {
                int c = (a[i] >> BITS_PER_BYTE*d) & MASK;
                aux[count[c]++] = a[i];
            }

            // copy back
            for (int i = 0; i < n; i++)
                a[i] = aux[i];
        }
    }

    /**
     * Reads in a sequence of fixed-length strings from standard input;
     * LSD radix sorts them;
     * and prints them to standard output in ascending order.
     *
     * @param args the command-line arguments
     */
    public static void main(String[] args) {
        String[] a = StdIn.readAllStrings();
        int n = a.length;

        // check that strings have fixed length
        int w = a[0].length();
        for (int i = 0; i < n; i++)
            assert a[i].length() == w : "Strings must have fixed length";

        // sort the strings
        sort(a, w);

        // print results
        for (int i = 0; i < n; i++)
            StdOut.println(a[i]);
    }
}

/******************************************************************************
 *  Copyright 2002-2016, Robert Sedgewick and Kevin Wayne.
 *
 *  This file is part of algs4.jar, which accompanies the textbook
 *
 *      Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
 *      Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
 *      http://algs4.cs.princeton.edu
 *
 *
 *  algs4.jar is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation, either version 3 of the License, or
 *  (at your option) any later version.
 *
 *  algs4.jar is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with algs4.jar.  If not, see http://www.gnu.org/licenses.
 ******************************************************************************/