归并排序

算法思想

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• 归并思想：将两个有序的数组归并成一个更大的有序的数组
• 归并过程
  • 现有两个有序的数组
  • 申请第三个、大于等于已有的两个数组长度之和的大叔组
  • 循环将两个小数组有序的存放在大叔组里面

Java

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• 源码（自顶向下）

public class Merge {
    
    private static Comparable[] aux;// 归并所需的辅助数组

    public static void sort(Comparable[] a) {
        aux = new Comparable[a.length];// 一次性分配空间
        sort(a, 0, a.length - 1);
    }

    // 将数组a[lo..hi]排序
    private static void sort(Comparable[] a, int lo, int hi) {
        if (hi <= lo) return;
        int mid = lo + (hi - lo) / 2;
        sort(a, lo, mid);// 将左半边排序
        sort(a, mid + 1, hi);// 将右半边排序
        merge(a, lo, mid, hi);// 归并结果
    }

    // 将a[lo..mid]和a[mid+1..hi]归并
    public static void merge(Comparable[] a, int lo, int mid, int hi) {
        int i = lo, j = mid + 1;

        for (int k = lo; k <= hi; k++)// 将a[lo..hi]复制到aux[lo..hi]
            aux[k] = a[k];

        for (int k = lo; k <= hi; k++)// 归并回到a[lo..hi]
            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++];
    }

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

    // 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;
    }

    // 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();
    }
}

• 源码（自底向上）

public class Merge {

    private static Comparable[] aux;// 归并所需的辅助数组

    // 进行lgN次两两归并
    public static void sort(Comparable[] a) {
        int N = a.length;
        aux = new Comparable[N];
        for (int sz = 1; sz < N; sz = sz + sz)// sz子数组大小
            for (int lo = 0; lo < N - sz; lo += sz + sz)// lo：子数组索引
                merge(a, lo, lo + sz - 1, Math.min(lo + sz + sz - 1, N - 1));
    }

    // 将a[lo..mid]和a[mid+1..hi]归并
    public static void merge(Comparable[] a, int lo, int mid, int hi) {
        int i = lo, j = mid + 1;

        for (int k = lo; k <= hi; k++)// 将a[lo..hi]复制到aux[lo..hi]
            aux[k] = a[k];

        for (int k = lo; k <= hi; k++)// 归并回到a[lo..hi]
            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++];
    }

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

    // 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;
    }

    // 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();
    }
}

• 测试用例

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

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

• 测试结果

A E E L M O P R S T X