在一组随机排列的数中找出第k小元素

在一组随机排列的数中找出第k小的，这个元素称为k-th Order Statistic。能想到的最直观的算法肯定是先把这些数排序然后取第k个，时间复杂度和排序算法相同，可以是Θ(nlgn)，但它也有平均情况下时间复杂度是Θ(n)的算法，将快速排序算法稍加修改就可以解决这个问题：

/*
**Find out the K-th small number of a set of random numbers with O(n)
**2011.10.25
**By LYLtim
*/

#include<stdio.h>
#include<stdlib.h>
#include<time.h>

#define LEN 6
int a[LEN], k;

void creat()
{
     register int *pa;
     srand(time(NULL));
     for (pa = a; pa < &a[LEN]; )
         printf("%d ", *pa++ = rand() % LEN);
     printf("\n");
}

void swap(int *a, int *b)
{
    int t = *a;
    *a = *b;
    *b = t; 
}

int Find (int left, int right)
{
    if (left >= right) return; //do nothing if array contains fewer than 2 elemants
    swap(&a[left], &a[(left + right) >> 1]); //move partition elem to left
    unsigned p, last = left;
    for (p = left + 1; p <= right; p++) //partiton
        if (a[p] < a[left])
            swap(&a[p], &a[++last]);
    swap(&a[left], &a[last]); //restore partiton elem
    if (last > k - 1) return Find(left, last - 1);
    if (last < k - 1) return Find(last + 1, right);
    return a[last];
}

int main(void)
{
    creat();
    printf("Inupt k to find out the K-th small number:");
    scanf("%d", &k);
    printf("The %dth small number is: %d\n", k, Find(0, LEN - 1));
}