几种排序算法学习总结

  1 package sort;
  2 
  3 import edu.princeton.cs.algs4.StdIn;
  4 import edu.princeton.cs.algs4.StdOut;
  5 
  6 import java.util.Comparator;
  7 
  8 /**
  9  *  The {@code Selection} class provides static methods for sorting an
 10  *  array using <em>selection sort</em>.
 11  *  This implementation makes ~ &frac12; <em>n</em><sup>2</sup> compares to sort
 12  *  any array of length <em>n</em>, so it is not suitable for sorting large arrays.
 13  *  It performs exactly <em>n</em> exchanges.
 14  *  <p>
 15  *  This sorting algorithm is not stable. It uses &Theta;(1) extra memory
 16  *  (not including the input array).
 17  *  <p>
 18  *  For additional documentation, see
 19  *  <a href="https://algs4.cs.princeton.edu/21elementary">Section 2.1</a>
 20  *  of <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
 21  *
 22  *  @author Robert Sedgewick
 23  *  @author Kevin Wayne
 24  */
 25 public class Selection {
 26 
 27     // This class should not be instantiated.
 28     private Selection() { }
 29 
 30     /**
 31      * Rearranges the array in ascending order, using the natural order.
 32      * @param a the array to be sorted
 33      */
 34     public static void sort(Comparable[] a) {
 35         int n = a.length;
 36         for (int i = 0; i < n; i++) {
 37             int min = i;
 38             for (int j = i+1; j < n; j++) {
 39                 if (less(a[j], a[min])) min = j;
 40             }
 41             exch(a, i, min);
 42             assert isSorted(a, 0, i);
 43         }
 44         assert isSorted(a);
 45     }
 46 
 47     /**
 48      * Rearranges the array in ascending order, using a comparator.
 49      * @param a the array
 50      * @param comparator the comparator specifying the order
 51      */
 52     public static void sort(Object[] a, Comparator comparator) {
 53         int n = a.length;
 54         for (int i = 0; i < n; i++) {
 55             int min = i;
 56             for (int j = i+1; j < n; j++) {
 57                 if (less(comparator, a[j], a[min])) min = j;
 58             }
 59             exch(a, i, min);
 60             assert isSorted(a, comparator, 0, i);
 61         }
 62         assert isSorted(a, comparator);
 63     }
 64 
 65 
 66     /***************************************************************************
 67      *  Helper sorting functions.
 68      ***************************************************************************/
 69 
 70     // is v < w ?
 71     private static boolean less(Comparable v, Comparable w) {
 72         return v.compareTo(w) < 0;
 73     }
 74 
 75     // is v < w ?
 76     private static boolean less(Comparator comparator, Object v, Object w) {
 77         return comparator.compare(v, w) < 0;
 78     }
 79 
 80 
 81     // exchange a[i] and a[j]
 82     private static void exch(Object[] a, int i, int j) {
 83         Object swap = a[i];
 84         a[i] = a[j];
 85         a[j] = swap;
 86     }
 87 
 88 
 89     /***************************************************************************
 90      *  Check if array is sorted - useful for debugging.
 91      ***************************************************************************/
 92 
 93     // is the array a[] sorted?
 94     private static boolean isSorted(Comparable[] a) {
 95         return isSorted(a, 0, a.length - 1);
 96     }
 97 
 98     // is the array sorted from a[lo] to a[hi]
 99     private static boolean isSorted(Comparable[] a, int lo, int hi) {
100         for (int i = lo + 1; i <= hi; i++)
101             if (less(a[i], a[i-1])) return false;
102         return true;
103     }
104 
105     // is the array a[] sorted?
106     private static boolean isSorted(Object[] a, Comparator comparator) {
107         return isSorted(a, comparator, 0, a.length - 1);
108     }
109 
110     // is the array sorted from a[lo] to a[hi]
111     private static boolean isSorted(Object[] a, Comparator comparator, int lo, int hi) {
112         for (int i = lo + 1; i <= hi; i++)
113             if (less(comparator, a[i], a[i-1])) return false;
114         return true;
115     }
116 
117 
118 
119     // print array to standard output
120     private static void show(Comparable[] a) {
121         for (int i = 0; i < a.length; i++) {
122             StdOut.println(a[i]);
123         }
124     }
125 
126     /**
127      * Reads in a sequence of strings from standard input; selection sorts them;
128      * and prints them to standard output in ascending order.
129      *
130      * @param args the command-line arguments
131      */
132     public static void main(String[] args) {
133         String[] a = StdIn.readAllStrings();
134         Selection.sort(a);
135         show(a);
136     }
137 }

import java.util.Comparator;

/**
 *  The {@code Insertion} class provides static methods for sorting an
 *  array using insertion sort.
 *  <p>
 *  In the worst case, this implementation makes ~ &frac12; <em>n</em><sup>2</sup>
 *  compares and ~ &frac12; <em>n</em><sup>2</sup> exchanges to sort an array
 *  of length <em>n</em>. So, it is not suitable for sorting large arbitrary
 *  arrays. More precisely, the number of exchanges is exactly equal to the
 *  number of inversions. So, for example, it sorts a partially-sorted array
 *  in linear time.
 *  <p>
 *  This sorting algorithm is stable.
 *  It uses &Theta;(1) extra memory (not including the input array).
 *  <p>
 *  See <a href="https://algs4.cs.princeton.edu/21elementary/InsertionPedantic.java.html">InsertionPedantic.java</a>
 *  for a version that eliminates the compiler warning.
 *  <p>
 *  For additional documentation, see <a href="https://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 Insertion {

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

    /**
     * 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;
        for (int i = 1; i < n; i++) {
            for (int j = i; j > 0 && less(a[j], a[j-1]); j--) {
                exch(a, j, j-1);
            }
            assert isSorted(a, 0, i);
        }
        assert isSorted(a);
    }

    /**
     * Rearranges the subarray a[lo..hi) in ascending order, using the natural order.
     * @param a the array to be sorted
     * @param lo left endpoint (inclusive)
     * @param hi right endpoint (exclusive)
     */
    public static void sort(Comparable[] a, int lo, int hi) {
        for (int i = lo + 1; i < hi; i++) {
            for (int j = i; j > lo && less(a[j], a[j-1]); j--) {
                exch(a, j, j-1);
            }
        }
        assert isSorted(a, lo, hi);
    }

    /**
     * Rearranges the array in ascending order, using a comparator.
     * @param a the array
     * @param comparator the comparator specifying the order
     */
    public static void sort(Object[] a, Comparator comparator) {
        int n = a.length;
        for (int i = 1; i < n; i++) {
            for (int j = i; j > 0 && less(a[j], a[j-1], comparator); j--) {
                exch(a, j, j-1);
            }
            assert isSorted(a, 0, i, comparator);
        }
        assert isSorted(a, comparator);
    }

    /**
     * Rearranges the subarray a[lo..hi) in ascending order, using a comparator.
     * @param a the array
     * @param lo left endpoint (inclusive)
     * @param hi right endpoint (exclusive)
     * @param comparator the comparator specifying the order
     */
    public static void sort(Object[] a, int lo, int hi, Comparator comparator) {
        for (int i = lo + 1; i < hi; i++) {
            for (int j = i; j > lo && less(a[j], a[j-1], comparator); j--) {
                exch(a, j, j-1);
            }
        }
        assert isSorted(a, lo, hi, comparator);
    }


    // return a permutation that gives the elements in a[] in ascending order
    // do not change the original array a[]
    /**
     * Returns a permutation that gives the elements in the array in ascending order.
     * @param a the array
     * @return a permutation {@code p[]} such that {@code a[p[0]]}, {@code a[p[1]]},
     *    ..., {@code a[p[n-1]]} are in ascending order
     */
    public static int[] indexSort(Comparable[] a) {
        int n = a.length;
        int[] index = new int[n];
        for (int i = 0; i < n; i++)
            index[i] = i;

        for (int i = 1; i < n; i++)
            for (int j = i; j > 0 && less(a[index[j]], a[index[j-1]]); j--)
                exch(index, j, j-1);

        return index;
    }

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

    // is v < w ?
    private static boolean less(Object v, Object w, Comparator comparator) {
        return comparator.compare(v, 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;
    }

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

   /***************************************************************************
    *  Check if array is sorted - useful for debugging.
    ***************************************************************************/
    private static boolean isSorted(Comparable[] a) {
        return isSorted(a, 0, a.length);
    }

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

    private static boolean isSorted(Object[] a, Comparator comparator) {
        return isSorted(a, 0, a.length, comparator);
    }

    // is the array a[lo..hi) sorted
    private static boolean isSorted(Object[] a, int lo, int hi, Comparator comparator) {
        for (int i = lo + 1; i < hi; i++)
            if (less(a[i], a[i-1], comparator)) 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; insertion 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();
        Insertion.sort(a);
        show(a);
    }
}

/**
 *  The {@code Shell} class provides static methods for sorting an
 *  array using <em>Shellsort</em> with
 *  <a href = "https://oeis.org/A003462"> Knuth‘s increment sequence</a>
 *  (1, 4, 13, 40, ...). In the worst case, this implementation makes
 *  &Theta;(<em>n</em><sup>3/2</sup>) compares and exchanges to sort
 *  an array of length <em>n</em>.
 *  <p>
 *  This sorting algorithm is not stable.
 *  It uses &Theta;(1) extra memory (not including the input array).
 *  <p>
 *  For additional documentation, see
 *  <a href="https://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. 
     *
     * @param args the command-line arguments
     */
    public static void main(String[] args) {
        String[] a = StdIn.readAllStrings();
        Shell.sort(a);
        show(a);
    }

}

import java.io.IOException;
 
public class Bubble{
 public static void main(String []args) {
     //冒泡排序
        int[] a = new int[] {1,5,8,2,3,9,4};
        int i ,j;
        for (i = 0; i < a.length - 1; i++) {    
            for (j = 0; j < a.length - 1 - i; j++) {
                if (a[j] > a[j+1]) {
                    int temp = a[j];
                    a[j] = a[j+1];
                    a[j+1] = temp;    
                }
            }
        }
        for (i = 0; i < a.length; i++) {
            System.out.print(a[i]+ " ");
        }
    }
}

/**
 *  The {@code Quick} class provides static methods for sorting an
 *  array and selecting the ith smallest element in an array using quicksort.
 *  <p>
 *  For additional documentation, see
 *  <a href="https://algs4.cs.princeton.edu/23quicksort">Section 2.3</a>   
 *  of <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
 *
 *  @author Robert Sedgewick
 *  @author Kevin Wayne
 */
public class Quick {

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

    /**
     * Rearranges the array in ascending order, using the natural order.
     * @param a the array to be sorted
     */
    public static void sort(Comparable[] a) {
        StdRandom.shuffle(a);
        sort(a, 0, a.length - 1);
        assert isSorted(a);
    }

    // quicksort the subarray from a[lo] to a[hi]
    private static void sort(Comparable[] a, int lo, int hi) { 
        if (hi <= lo) return;
        int j = partition(a, lo, hi);
        sort(a, lo, j-1);
        sort(a, j+1, hi);
        assert isSorted(a, lo, hi);
    }

    // partition the subarray a[lo..hi] so that a[lo..j-1] <= a[j] <= a[j+1..hi]
    // and return the index j.
    private static int partition(Comparable[] a, int lo, int hi) {
        int i = lo;
        int j = hi + 1;
        Comparable v = a[lo];
        while (true) { 

            // find item on lo to swap
            while (less(a[++i], v)) {
                if (i == hi) break;
            }

            // find item on hi to swap
            while (less(v, a[--j])) {
                if (j == lo) break;      // redundant since a[lo] acts as sentinel
            }

            // check if pointers cross
            if (i >= j) break;

            exch(a, i, j);
        }

        // put partitioning item v at a[j]
        exch(a, lo, j);

        // now, a[lo .. j-1] <= a[j] <= a[j+1 .. hi]
        return j;
    }

    /**
     * Rearranges the array so that {@code a[k]} contains the kth smallest key;
     * {@code a[0]} through {@code a[k-1]} are less than (or equal to) {@code a[k]}; and
     * {@code a[k+1]} through {@code a[n-1]} are greater than (or equal to) {@code a[k]}.
     *
     * @param  a the array
     * @param  k the rank of the key
     * @return the key of rank {@code k}
     * @throws IllegalArgumentException unless {@code 0 <= k < a.length}
     */
    public static Comparable select(Comparable[] a, int k) {
        if (k < 0 || k >= a.length) {
            throw new IllegalArgumentException("index is not between 0 and " + a.length + ": " + k);
        }
        StdRandom.shuffle(a);
        int lo = 0, hi = a.length - 1;
        while (hi > lo) {
            int i = partition(a, lo, hi);
            if      (i > k) hi = i - 1;
            else if (i < k) lo = i + 1;
            else return a[i];
        }
        return a[lo];
    }



   /***************************************************************************
    *  Helper sorting functions.
    ***************************************************************************/
    
    // is v < w ?
    private static boolean less(Comparable v, Comparable w) {
        if (v == w) return false;   // optimization when reference equals
        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) {
        return isSorted(a, 0, a.length - 1);
    }

    private static boolean isSorted(Comparable[] a, int lo, int hi) {
        for (int i = lo + 1; i <= hi; i++)
            if (less(a[i], a[i-1])) 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; quicksorts them; 
     * and prints them to standard output in ascending order. 
     * Shuffles the array and then prints the strings again to
     * standard output, but this time, using the select method.
     *
     * @param args the command-line arguments
     */
    public static void main(String[] args) {
        String[] a = StdIn.readAllStrings();
        Quick.sort(a);
        show(a);
        assert isSorted(a);

        // shuffle
        StdRandom.shuffle(a);

        // display results again using select
        StdOut.println();
        for (int i = 0; i < a.length; i++) {
            String ith = (String) Quick.select(a, i);
            StdOut.println(ith);
        }
    }

}