算法Sedgewick第四版-第1章基础-2.1Elementary Sortss-004希尔排序法(Shell Sort)

一、介绍

1.希尔排序的思路：希尔排序是插入排序的改进。当输入的数据，顺序是很乱时，插入排序会产生大量的交换元素的操作，比如array[n]的最小的元素在最后,则要经过n-1次交换才能排到第一位，因为插入排序元素只能一位一位地交换。基于插入排序的这个缺点，希尔排序是以一个区间来的交换元素，然后不断缩小区间，直到为1。它的理论是，每次经过一个区间的排序后，元素就会更有序些，所以下一个区间排序时，要交换的元素次数会变少。

2.详细的数据排序交换过程

3.

Proposition.

The number of compares used by shellsort with the increments 1, 4, 13, 40, 121, 364, ... is O(N^3/2).

二、代码

 package algorithms.elementary21;

 import algorithms.util.StdIn;
 import algorithms.util.StdOut;

 /******************************************************************************
  *  Compilation:  javac Shell.java
  *  Execution:    java Shell < input.txt
  *  Dependencies: StdOut.java StdIn.java
  *  Data files:   http://algs4.cs.princeton.edu/21sort/tiny.txt
  *                http://algs4.cs.princeton.edu/21sort/words3.txt
  *
  *  Sorts a sequence of strings from standard input using shellsort.
  *
  *  Uses increment sequence proposed by Sedgewick and Incerpi.
  *  The nth element of the sequence is the smallest integer >= 2.5^n
  *  that is relatively prime to all previous terms in the sequence.
  *  For example, incs[4] is 41 because 2.5^4 = 39.0625 and 41 is
  *  the next integer that is relatively prime to 3, 7, and 16.
  *
  *  % more tiny.txt
  *  S O R T E X A M P L E
  *
  *  % java Shell < tiny.txt
  *  A E E L M O P R S T X                 [ one string per line ]
  *
  *  % more words3.txt
  *  bed bug dad yes zoo ... all bad yet
  *
  *  % java Shell < words3.txt
  *  all bad bed bug dad ... yes yet zoo    [ one string per line ]
  *
  *
  ******************************************************************************/

 /**
  *  The <tt>Shell</tt> class provides static methods for sorting an
  *  array using Shellsort with Knuth's increment sequence (1, 4, 13, 40, ...).
  *  <p>
  *  For additional documentation, see <a href="http://algs4.cs.princeton.edu/21elementary">Section 2.1</a> of
  *  <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
  *
  *  @author Robert Sedgewick
  *  @author Kevin Wayne
  */
 public class Shell {

     // This class should not be instantiated.
     private Shell() { }

     /**
      * Rearranges the array in ascending order, using the natural order.
      * @param a the array to be sorted
      */
     public static void sort(Comparable[] a) {
         int N = a.length;

         // 3x+1 increment sequence:  1, 4, 13, 40, 121, 364, 1093, ...
         int h = 1;
         while (h < N/3) h = 3*h + 1; 

         while (h >= 1) {
             // h-sort the array
             for (int i = h; i < N; i++) {
                 for (int j = i; j >= h && less(a[j], a[j-h]); j -= h) {
                     exch(a, j, j-h);
                 }
             }
             assert isHsorted(a, h);
             h /= 3;
         }
         assert isSorted(a);
     }

    /***************************************************************************
     *  Helper sorting functions.
     ***************************************************************************/

     // is v < w ?
     private static boolean less(Comparable v, Comparable w) {
         return v.compareTo(w) < 0;
     }

     // exchange a[i] and a[j]
     private static void exch(Object[] a, int i, int j) {
         Object swap = a[i];
         a[i] = a[j];
         a[j] = swap;
     }

    /***************************************************************************
     *  Check if array is sorted - useful for debugging.
     ***************************************************************************/
     private static boolean isSorted(Comparable[] a) {
         for (int i = 1; i < a.length; i++)
             if (less(a[i], a[i-1])) return false;
         return true;
     }

     // is the array h-sorted?
     private static boolean isHsorted(Comparable[] a, int h) {
         for (int i = h; i < a.length; i++)
             if (less(a[i], a[i-h])) return false;
         return true;
     }

     // print array to standard output
     private static void show(Comparable[] a) {
         for (int i = 0; i < a.length; i++) {
             StdOut.println(a[i]);
         }
     }

     /**
      * Reads in a sequence of strings from standard input; Shellsorts them;
      * and prints them to standard output in ascending order.
      */
     public static void main(String[] args) {
         String[] a = StdIn.readAllStrings();
         Shell.sort(a);
         show(a);
     }

 }