[数据结构与算法]算法基础——排序算法

排序是什么？

排序是对随机一组数字进行从大到小（或从小到大）的排列。

排序算法的稳定性

常见的排序算法

算法工具类介绍

public class SortUtil {
    
    public static int[] a = new int[10];

    public static int[] create() {
        for (int i = 0; i < 10; i++) {
            Random random = new Random();
            a[i] = random.nextInt(10);
        }
        return a;
    }

    public static void show(int[] a) {
        for (int i : a) {
            System.out.print(i + " ");
        }
        System.out.println();
    }

    public static void exchange(int[] a, int i, int j) {
        int temp = a[i];
        a[i] = a[j];
        a[j] = temp;
    }

    public static boolean less(int i, int j) {
        return i < j;
    }
}

选择排序

public class Selection {
    public static void main(String[] args) {

        int[] a = SortUtil.create();
        SortUtil.show(a);

        int N = a.length;
        for (int i = 0; i < N; i++) {
            int min = i;
            for (int j = i + 1; j < N; j++) {
                if (SortUtil.less(a[j], a[min])) {
                    min = j;
                }
            }
            SortUtil.exchange(a, i, min);
        }

        SortUtil.show(a);
    }
}

插入排序

public class Insertion {
    public static void main(String[] args) {
        
        int[] a = SortUtil.create();
        SortUtil.show(a);

        int N = a.length;
        for (int i = 0; i < N; i++) {
            for (int j = i; j > 0 && SortUtil.less(a[j], a[j - 1]); j--) {
                SortUtil.exchange(a, j, j - 1);
            }
        }

        SortUtil.show(a);
    }
}

希尔排序

public class Shell {

    public static void main(String[] args) {
        
        int[] a = SortUtil.create();
        SortUtil.show(a);

        int N = a.length;
        int h = 1;
        while (h < N / 3) {
            h = 3 * h + 1;
        }
        while (h >= 1) {
            for (int i = 0; i < N; i++) {
                for (int j = i; j >= h && SortUtil.less(a[j], a[j - 1]); j -= h) {
                    SortUtil.exchange(a, j, j - 1);
                }
            }
            h /= 3;
        }

        SortUtil.show(a);
    }
}

归并排序

public class Merge {

    private static int[] aux = new int[SortUtil.a.length];

    public static void main(String[] args) {
        int[] a = SortUtil.create();
        SortUtil.show(a);
        sort(a, 0, SortUtil.a.length - 1);
        SortUtil.show(a);
    }

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

    public static void merge(int[] a, int lo, int mid, int hi) {
        int i = lo, j = mid + 1;
        for (int k = lo; k <= hi; k++) {
            aux[k] = a[k];
        }
        for (int k = lo; k <= hi; k++) {
            if (i > mid)
                a[k] = aux[j++];
            else if (j > hi)
                a[k] = aux[i++];
            else if (SortUtil.less(aux[j], aux[i]))
                a[k] = aux[j++];
            else
                a[k] = aux[i++];
        }
    }
}

快速排序