幾種常見的排序算法

 

 

一.選擇排序

　　在待排序的一組數據中，選出最小(最大)的一個數與第一個位置的數交換，而後在剩下的數中，再找最小（最大）的數與第二個位置的數交換位置，依次類推，直到第N-1個元素與第N個元素交換位置，選擇排序結束。

 

 

 

import edu.princeton.cs.algs4.StdIn;
import edu.princeton.cs.algs4.StdOut;
import java.util.Comparator;

public class Selection {

    private Selection() { }

    //排序
    public static void sort(Comparable[] a) {
        int n = a.length;
        for (int i = 0; i < n; i++) {
            int min = i;
            for (int j = i+1; j < n; j++) {
                if (less(a[j], a[min])) min = j;
            }
            exch(a, i, min);
            assert isSorted(a, 0, i);
        }
        assert isSorted(a);
    }

    //使用比較器按升序從新排列數組
    public static void sort(Object[] a, Comparator comparator) {
        int n = a.length;
        for (int i = 0; i < n; i++) {
            int min = i;
            for (int j = i+1; j < n; j++) {
                if (less(comparator, a[j], a[min])) min = j;
            }
            exch(a, i, min);
            assert isSorted(a, comparator, 0, i);
        }
        assert isSorted(a, comparator);
    }


    //對元素進行比較
    private static boolean less(Comparable v, Comparable w) {
        return v.compareTo(w) < 0;
    }

    // 對元素進行比較
    private static boolean less(Comparator comparator, Object v, Object w) {
        return comparator.compare(v, w) < 0;
    }


    // 交換兩個數據
    private static void exch(Object[] a, int i, int j) {
        Object swap = a[i];
        a[i] = a[j];
        a[j] = swap;
    }

    // 檢查數組是否已排序-對調試有用。
    private static boolean isSorted(Comparable[] a) {
        return isSorted(a, 0, a.length - 1);
    }

    // 判斷從lo到hi的元素是否已經有序
    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, comparator, 0, a.length - 1);
    }

    private static boolean isSorted(Object[] a, Comparator comparator, int lo, int hi) {
        for (int i = lo + 1; i <= hi; i++)
            if (less(comparator, a[i], a[i-1])) return false;
        return true;
    }

    //輸出元素
    private static void show(Comparable[] a) {
        for (int i = 0; i < a.length; i++) {
            StdOut.println(a[i]);
        }
    }

    public static void main(String[] args) {
        String[] a = StdIn.readAllStrings();
        Selection.sort(a);
        show(a);
    }
}

 

二.插入排序

將一個記錄插入到已排好序的序列中，從而獲得一個新的有序序列（將序列的第一個數據當作是一個有序的子序列，而後從第二個記錄逐個向該有序的子序列進行有序的插入，直至整個序列有序）

package sort;

import edu.princeton.cs.algs4.StdIn;
import edu.princeton.cs.algs4.StdOut;
import java.util.Comparator;

public class Insertion {

    private Insertion() { }

    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);
    }

    //對lo到hi的元素進行排序
    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);
    }

    //使用比較器按升序從新排列數組
    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);
    }

    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);
    }

    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;
    }

    //對元素進行比較
    private static boolean less(Comparable v, Comparable w) {
        return v.compareTo(w) < 0;
    }

    private static boolean less(Object v, Object w, Comparator comparator) {
        return comparator.compare(v, w) < 0;
    }

    // 交換兩個數據
    private static void exch(Object[] a, int i, int j) {
        Object swap = a[i];
        a[i] = a[j];
        a[j] = swap;
    }

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

    // 檢查數組是否已排序-對調試有用。
    private static boolean isSorted(Comparable[] a) {
        return isSorted(a, 0, a.length);
    }

    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);
    }

    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;
    }

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

    public static void main(String[] args) {
        String[] a = StdIn.readAllStrings();
        Insertion.sort(a);
        show(a);
    }
}

 

三.希爾排序

希爾排序的思想是使數組中任意間隔爲h的元素都是有序的。這樣的數組被稱爲h有序數組。換句話說，一個h有序數組就是h個互相獨立的有序數組編制在一塊兒組成的一個數組（以下圖）。在進行排序的時候，若是h很大，咱們可以將元素移動到很遠的地方，爲了實現更小的h有序創造方便，用這種方式，對於任意以1結尾的h序列，咱們都可以將數組排序，這就是希爾排序。

package sort;

import edu.princeton.cs.algs4.StdIn;
import edu.princeton.cs.algs4.StdOut;

public class Shell {

    private Shell() { }

    public static void sort(Comparable[] a) {
        int n = a.length;

        int h = 1;
        while (h < n/3) h = 3*h + 1;    //1, 4, 13, 40, 121, 364, 1093, ...
        while (h >= 1) {
            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);
    }

    // 比較兩個元素
    private static boolean less(Comparable v, Comparable w) {
        return v.compareTo(w) < 0;
    }

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

    //判斷是否有序
    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;
    }

    // 判斷從h開始是否有序
    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;
    }

    // 輸出元素
    private static void show(Comparable[] a) {
        for (int i = 0; i < a.length; i++) {
            StdOut.println(a[i]);
        }
    }

    public static void main(String[] args) {
        String[] a = StdIn.readAllStrings();
        Shell.sort(a);
        show(a);
    }
}

 

四.歸併排序

1.自頂向下的歸併排序

package sort;

import edu.princeton.cs.algs4.StdIn;
import edu.princeton.cs.algs4.StdOut;

public class Merge {

    private Merge() { }

    //排序函數
    public static void sort(Comparable[] a) {
        Comparable[] aux = new Comparable[a.length];
        sort(a, aux, 0, a.length-1);
        assert isSorted(a);
    }

    private static void sort(Comparable[] a, Comparable[] aux, int lo, int hi) {
        if (hi <= lo) return;
        int mid = lo + (hi - lo) / 2;
        sort(a, aux, lo, mid);
        sort(a, aux, mid + 1, hi);
        merge(a, aux, lo, mid, hi);
    }

    private static void sort(Comparable[] a, int[] index, int[] aux, int lo, int hi) {
        if (hi <= lo) return;
        int mid = lo + (hi - lo) / 2;
        sort(a, index, aux, lo, mid);
        sort(a, index, aux, mid + 1, hi);
        merge(a, index, aux, lo, mid, hi);
    }

    //合併兩個有序數組
    private static void merge(Comparable[] a, Comparable[] aux, int lo, int mid, int hi) {
        // precondition: a[lo .. mid] and a[mid+1 .. hi] are sorted subarrays
        assert isSorted(a, lo, mid);
        assert isSorted(a, mid+1, hi);

        // copy to aux[]
        for (int k = lo; k <= hi; k++) {
            aux[k] = a[k];
        }

        // merge back to a[]
        int i = lo, j = mid+1;
        for (int k = lo; k <= hi; k++) {
            if      (i > mid)              a[k] = aux[j++];
            else if (j > hi)               a[k] = aux[i++];
            else if (less(aux[j], aux[i])) a[k] = aux[j++];
            else                           a[k] = aux[i++];
        }

        // postcondition: a[lo .. hi] is sorted
        assert isSorted(a, lo, hi);
    }

    private static void merge(Comparable[] a, int[] index, int[] aux, int lo, int mid, int hi) {

        // copy to aux[]
        for (int k = lo; k <= hi; k++) {
            aux[k] = index[k];
        }

        // merge back to a[]
        int i = lo, j = mid+1;
        for (int k = lo; k <= hi; k++) {
            if      (i > mid)                    index[k] = aux[j++];
            else if (j > hi)                     index[k] = aux[i++];
            else if (less(a[aux[j]], a[aux[i]])) index[k] = aux[j++];
            else                                 index[k] = aux[i++];
        }
    }

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

    //判斷數組是否有序
    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;
    }

    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;

        int[] aux = new int[n];
        sort(a, index, aux, 0, n-1);
        return index;
    }

    //輸出元素
    private static void show(Comparable[] a) {
        for (int i = 0; i < a.length; i++) {
            StdOut.println(a[i]);
        }
    }

    public static void main(String[] args) {
        String[] a = StdIn.readAllStrings();
        Merge.sort(a);
        show(a);
    }
}

 

2.自底向上的歸併排序

package sort;

import edu.princeton.cs.algs4.StdIn;
import edu.princeton.cs.algs4.StdOut;

public class MergeBU {

    private MergeBU() { }

    // stably merge a[lo..mid] with a[mid+1..hi] using aux[lo..hi]
    private static void merge(Comparable[] a, Comparable[] aux, int lo, int mid, int hi) {

        // copy to aux[]
        for (int k = lo; k <= hi; k++) {
            aux[k] = a[k];
        }

        // merge back to a[]
        int i = lo, j = mid+1;
        for (int k = lo; k <= hi; k++) {
            if      (i > mid)              a[k] = aux[j++];  // this copying is unneccessary
            else if (j > hi)               a[k] = aux[i++];
            else if (less(aux[j], aux[i])) a[k] = aux[j++];
            else                           a[k] = aux[i++];
        }

    }

    /**
     * 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;
        Comparable[] aux = new Comparable[n];
        for (int len = 1; len < n; len *= 2) {
            for (int lo = 0; lo < n-len; lo += len+len) {
                int mid  = lo+len-1;
                int hi = Math.min(lo+len+len-1, n-1);
                merge(a, aux, lo, mid, hi);
            }
        }
        assert isSorted(a);
    }

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


    /***************************************************************************
     *  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;
    }

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

    public static void main(String[] args) {
        String[] a = StdIn.readAllStrings();
        MergeBU.sort(a);
        show(a);
    }
}

 

五.快速排序

它的基本思想是： 選擇一個基準數，經過一趟排序將要排序的數據分割成獨立的兩部分；其中一部分的全部數據都比另一部分的全部數據都要小。而後，再按此方法對這兩部分數據分別進行快速排序，整個排序過程能夠遞歸進行，以此達到整個數據變成有序序列。

 

 

1.快速排序

package sort;

import edu.princeton.cs.algs4.StdIn;
import edu.princeton.cs.algs4.StdOut;
import edu.princeton.cs.algs4.StdRandom;

public class Quick {

    private Quick() { }

    //使用天然順序按升序從新排列數組。
    public static void sort(Comparable[] a) {
        StdRandom.shuffle(a);
        sort(a, 0, a.length - 1);
        assert isSorted(a);
    }

    // 排序 a[lo] 到 a[hi]的元素
    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);
    }

    // 分區子陣列a[lo..hi]，使a[lo..j-1]<=a[j]<=a[j+1..hi]
    private static int partition(Comparable[] a, int lo, int hi) {
        int i = lo;
        int j = hi + 1;
        Comparable v = a[lo];
        while (true) {
            // 查找左邊須要交換的元素
            while (less(a[++i], v)) {
                if (i == hi) break;
            }
            // 查找右邊須要交換的元素
            while (less(v, a[--j])) {
                if (j == lo) break;
            }
            if (i >= j) break;
            exch(a, i, j);
        }
        exch(a, lo, j);
        return j;
    }

    //從新排列數組，使{@code a[k]}包含第k個最小鍵；
    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];
    }

    // 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;
    }

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

    //判斷數組是否有序
    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;
    }

    //輸出數組
    private static void show(Comparable[] a) {
        for (int i = 0; i < a.length; i++) {
            StdOut.println(a[i]);
        }
    }

    public static void main(String[] args) {
        String[] a = StdIn.readAllStrings();
        Quick.sort(a);
        show(a);
        assert isSorted(a);

        StdRandom.shuffle(a);

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

}

2.三向切分的快速排序

package sort;

import edu.princeton.cs.algs4.StdIn;
import edu.princeton.cs.algs4.StdOut;
import edu.princeton.cs.algs4.StdRandom;

public class Quick3way {

    private Quick3way() { }

    public static void sort(Comparable[] a) {
        StdRandom.shuffle(a);
        sort(a, 0, a.length - 1);
        assert isSorted(a);
    }

    private static void sort(Comparable[] a, int lo, int hi) {
        if (hi <= lo) return;
        int lt = lo, gt = hi;
        Comparable v = a[lo];
        int i = lo + 1;
        while (i <= gt) {
            int cmp = a[i].compareTo(v);
            if      (cmp < 0) exch(a, lt++, i++);
            else if (cmp > 0) exch(a, i, gt--);
            else              i++;
        }

        // a[lo..lt-1] < v = a[lt..gt] < a[gt+1..hi].
        sort(a, lo, lt-1);
        sort(a, gt+1, hi);
        assert isSorted(a, lo, hi);
    }

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

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

    //判斷數組是否有序
    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;
    }



    // 輸出數組
    private static void show(Comparable[] a) {
        for (int i = 0; i < a.length; i++) {
            StdOut.println(a[i]);
        }
    }

    public static void main(String[] args) {
        String[] a = StdIn.readAllStrings();
        Quick3way.sort(a);
        show(a);
    }

}

 

六.堆排序

堆是具備如下性質的徹底二叉樹：每一個結點的值都大於或等於其左右孩子結點的值，稱爲大頂堆；或者每一個結點的值都小於或等於其左右孩子結點的值，稱爲小頂堆。

大頂堆

 

小頂堆

 

算法演示

 

 

package sort;

import edu.princeton.cs.algs4.StdIn;
import edu.princeton.cs.algs4.StdOut;

public class Heap {

    private Heap() { }

    public static void sort(Comparable[] pq) {
        int n = pq.length;
        for (int k = n/2; k >= 1; k--)
            sink(pq, k, n);
        while (n > 1) {
            exch(pq, 1, n--);
            sink(pq, 1, n);
        }
    }

    //下沉
    private static void sink(Comparable[] pq, int k, int n) {
        while (2*k <= n) {
            int j = 2*k;
            if (j < n && less(pq, j, j+1)) j++;
            if (!less(pq, k, j)) break;
            exch(pq, k, j);
            k = j;
        }
    }

    //比較
    private static boolean less(Comparable[] pq, int i, int j) {
        return pq[i-1].compareTo(pq[j-1]) < 0;
    }

    //交換
    private static void exch(Object[] pq, int i, int j) {
        Object swap = pq[i-1];
        pq[i-1] = pq[j-1];
        pq[j-1] = swap;
    }

    //輸出元素
    private static void show(Comparable[] a) {
        for (int i = 0; i < a.length; i++) {
            StdOut.println(a[i]);
        }
    }

    public static void main(String[] args) {
        String[] a = StdIn.readAllStrings();
        Heap.sort(a);
        show(a);
    }
}