希尔排序

定义

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希尔排序是一种基于插入排序的快速的排序算法

算法思想

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• 将整个数组分成间隔为h的小段
• 在每个间隔为h的小段中使用插入排序
• 排序之初，各个子数组都很短，排序之后，各个子数组都是部分有序的，这两种情况都很适合插入排序

Java

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• 源码

public class Shell {
    //将a[]按升序排序
    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) {
            // 将数组变为h有序
            for (int i = h; i < N; i++) {
                // 将a[i]插入到a[i-h]，a[i-2*h]，a[i-3*h]...之中
                for (int j = i; j >= h && less(a[j], a[j - h]); j -= h)
                    exch(a, j, j - h);
            }
            h = h / 3;
        }
    }

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

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

    // 在单行中打印数组
    public static void show(Comparable[] a) {
        for (int i = 0; i < a.length; i++)
            System.out.print(a[i] + " ");
        System.out.println();
    }

    // 测试数组元素是否有序
    public static boolean isSorted(Comparable[] a) {
        for (int i = 1; i < a.length; i++)
            if (less(a[i], a[i - 1])) return false;
        return true;
    }
}

• 测试用例

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

        String[] test = {"S", "O", "R", "T", "E", "X", "A", "M", "P", "L", "E"};
        Shell.sort(test);
        assert Shell.isSorted(test);
        Shell.show(test);
    }
}

• 测试结果

A E E L M O P R S T X