归并排序

归并排序
将一个数组递归地分成两半分别排序，然后将结果归并起来。

自顶向下归并排序

public class Merge extends Sort {

    private static Comparable[] aux;

    public static void sort(Comparable[] a) {
        aux = new Comparable[a.length];
        sort(a, 0, a.length - 1);
    }

    private static void sort(Comparable[] 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);
    }

    protected static void merge(Comparable[] a, int lo, int mid, int hi) {
        int i = lo, j = mid + 1;
        // 数组复制
        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 (less(aux[j], aux[i])) a[k] = aux[j++];
            else a[k] = aux[i++];
        }
    }

}

自顶向下归并排序

public class MergeBU extends Merge {
    private static Comparable[] aux;

    public static void sort(Comparable[] a){
        aux = new Comparable[a.length];
        int N = a.length;
        for (int sz = 1; sz < N; sz = sz * 2){
            for(int lo = 0; lo < N - sz; lo += sz * 2){
                merge(a, lo, lo + sz - 1, Math.min(lo + sz * 2 - 1, N - 1));
            }
        }
    }

}

结论

对于长度为N的任意数组，归并排序需要1/2NlgN至NlgN次比较。