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：

 1 /*
 2 **Find out the K-th small number of a set of random numbers with O(n)
 3 **2011.10.25
 4 **By LYLtim
 5 */
 6 
 7 #include<stdio.h>
 8 #include<stdlib.h>
 9 #include<time.h>
10 
11 #define LEN 6
12 int a[LEN], k;
13 
14 void creat()
15 {
16      register int *pa;
17      srand(time(NULL));
18      for (pa = a; pa < &a[LEN]; )
19          printf("%d ", *pa++ = rand() % LEN);
20      printf("\n");
21 }
22 
23 void swap(int *a, int *b)
24 {
25     int t = *a;
26     *a = *b;
27     *b = t; 
28 }
29 
30 int Find (int left, int right)
31 {
32     if (left >= right) return; //do nothing if array contains fewer than 2 elemants
33     swap(&a[left], &a[(left + right) >> 1]); //move partition elem to left
34     unsigned p, last = left;
35     for (p = left + 1; p <= right; p++) //partiton
36         if (a[p] < a[left])
37             swap(&a[p], &a[++last]);
38     swap(&a[left], &a[last]); //restore partiton elem
39     if (last > k - 1) return Find(left, last - 1);
40     if (last < k - 1) return Find(last + 1, right);
41     return a[last];
42 }
43 
44 int main(void)
45 {
46     creat();
47     printf("Inupt k to find out the K-th small number:");
48     scanf("%d", &k);
49     printf("The %dth small number is: %d\n", k, Find(0, LEN - 1));
50 }