快速排序的Hoare划分

在《算法导论》中有介绍到快排的原始划分方法——Hoare划分，在算导7.1节中给出的快排经典算法中，将主元值与围绕它划分形成的两个部分分隔开了，而Hoare-Partition划分则总是将主元值放入两个划分A[p..j]和A[j+1..r]的某一个中。算导给出的Hoare-Partition划分伪代码如下：

Hoare-Partition(A,p,r):x =  A[p]i = p-1j = r+1while true   do repeat j = j-1      until A[j] <= x   do repeat i = i+1      until A[i] >= x   if x<j      then exchange A[i],A[j]   else      return j

为了便于比较，用C++语言同时实现了经典Partiion和Hoare-Partition的代码如下：

#include<iostream>#define MAXN 10int hoare_partition(int arr[],int p,int q){    int i,j,x,t;    x=arr[p];    i=p;    j=q;    while(1){for(;i<q && arr[i] < x;i++);for(;j>p && arr[j]>=x;j--);        if(i<j){            t = arr[i];            arr[i] = arr[j];            arr[j] = t;        }else{            return j;}    }}void hoare_qsort(int arr[],int p,int q){    if(p>=q)        return;    int pivot =  hoare_partition(arr,p,q);hoare_qsort(arr,p,pivot);    hoare_qsort(arr,pivot+1,q);}int partition(int arr[],int p,int q){    int i,j,x,t;    x = arr[q];    i = p-1;    for(j=p;j<=q;j++){        if(arr[j]<x){            t = arr[++i];            arr[i] = arr[j];            arr[j] = t;        }    }    t = arr[i+1];    arr[i+1] = arr[q];    arr[q] = t;    return i+1;}void quick_sort(int arr[],int p, int q){    if(p>=q)        return;    int pivot = partition(arr,p,q);    quick_sort(arr,p,pivot-1);    quick_sort(arr,pivot,q);}int main(){    int arr[MAXN] = {6,9,11,5,1,2,4,10,8,3};    printf("Classical quick sort:");    quick_sort(arr,0,MAXN-1);    for(int i=0;i<MAXN;i++)        printf("%d ",arr[i]);    printf("\nEarliest quick sort:");    hoare_qsort(arr,0,MAXN-1);    for(int i=0;i<MAXN;i++)        printf("%d ",arr[i]);}