自顶向下的归并排序

归并排序，要将一个数组排序，可以先将它分成两半分别排序，然后将结构归并起来。
具体实现如下

public class Merge{
    private Comparable[] aux;//辅助数组
    public static void sort(Comparable[] a){
        aux = new Comparable[a.length];
        sort(a,0,a.length-1);
    }
    //排序
    private static void sort(Comparable [] a,int lo,int hi){
        if(lo>=hi) return;
        int mid = lo+ (hi-lo)/2;
        sort(a,lo,mid);                                  //对左边排序
        sort(a,mid+1,hi);                                //对右边排序
        merge(a,lo,mid,hi);                             //归并两个数组

    }
    //归并两个数组
    private static void merge(Comparable [] a,int lo,int mid,int hi){
        for(int i=lo;i<=hi;i++)
            aux[i] = a[i];
        int j=lo;
        int k = mid+1;
        for(int i = lo;i<=hi;i++){
            if(j>mid)    a[i] = aux[k++];          //左边的归并完了归并右边
            else if(k>hi) a[i] = aux[j++];         //右边的归并完了归并左边
            else if(less(a[j],a[k])) a[i] = aux[j++];  //先归并值小的
            else a[i] = aux[k++];
        }
    }
    //判断q是否小于p
    private static boolean less(Comparable q,Comparable p) {
        return q.compareTo(p)<0;
    }
    //展示数组
    public static void show(Comparable[] a) {
        for(int i=0;i<a.length;i++) {
            System.out.print(a[i]+" ");
        }
        System.out.println();
    }
    //判断数组是否排序
    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
    public static void main(String[] args) {
        Integer[] a = {5,2,9,8,6,3,0,15,25,46,10,1,9,4,7};
        sort(a);
        assert isSorted(a);
        show(a);
    }
}