算法学堂

C语言中可以用bsearch()实现二分查找。同qsort()一样，bsearch()也包含在glibc库中，且同样要自定义比较函数。其原型如下：

void *bsearch(const void *key, const void *base,

                     size_t nmemb, size_t size,

                     int (*compar)(const void *, const void *));

key指向所要查找的元素，base指向进行查找的数组，nmemb为查找长度，一般为数组长度，size为每个元素所占的字节数，一般用sizeof(...)表示，compar指向比较函数，它定义比较的规则。需要注意的是，数据必须是经过预先排序的，而排序的规则要和compar所指向比较函数的规则相同。如果查找成功则返回数组中匹配元素的地址，反之则返回空。对于有多于一个的元素匹配成功的情况，bsearch()未定义返回哪一个。

bsearch实现（glibc）

从glibc的代码可以看到，bsearch的实现是很简洁的：

/* Perform a binary search for KEY in BASE which has NMEMB elements
   of SIZE bytes each.  The comparisons are done by (*COMPAR)().  */
void *
bsearch (const void *key, const void *base, size_t nmemb, size_t size,
          int (*compar) (const void *, const void *))
{
  size_t l, u, idx;
  const void *p;
  int comparison;

  l = 0;
  u = nmemb;
  while (l < u)
  {
      idx = (l + u) / 2;
      p = (void *) (((const char *) base) + (idx * size));
      comparison = (*compar) (key, p);
      if (comparison < 0)
          u = idx;
      else if (comparison > 0)
          l = idx + 1;
      else
          return (void *) p;
  }
  
  return NULL;
}

bsearch_less的实现

参考bsearch的实现，我们可以实现bsearch的变形，来找到不大于key的最接近的那个数：

void *
bsearch_less (const void *key, const void *base, size_t nmemb, size_t size,
     int (*compar) (const void *, const void *))
{
  int l, u, idx;
  const void *p;
  int comparison;

  l = 0;
  u = nmemb - 1;
  while (l <= u)
  {
      idx = (l + u) / 2;
      p = (void *) (((const char *) base) + (idx * size));
      comparison = (*compar) (key, p);
      if (comparison < 0)
         u = idx - 1;
      else if (comparison > 0)
         l = idx + 1;
      else
         return (idx == 0) ? NULL : (void *) (((const char *) p) - size);
  }

  return (u < 0) ? NULL : (void *) (((const char *) base) + (u * size));
}

bsearch_more的实现

参考bsearch的实现，我们可以实现bsearch的变形，来找到不小于key的最接近的那个数：

void *
bsearch_more(const void *key, const void *base, size_t nmemb, size_t size,
         int (*compar) (const void *, const void *))
{
  int l, u, idx;
  const void *p;
  int comparison;

  l = 0;
  u = nmemb - 1;
  while (l <= u)
  {
      idx = (l + u) / 2;
      p = (void *) (((const char *) base) + (idx * size));
      comparison = (*compar) (key, p);
      if (comparison < 0)
         u = idx - 1;
      else if (comparison > 0)
         l = idx + 1;
      else
         return (idx == u) ? NULL : (void *) (((const char *) p) + size);
  }

  return (l > nmemb - 1) ? NULL : (void *) (((const char *) base) + (l * size));
}

示例：

/* bsearch example */
#include <stdio.h>      /* printf */
#include <stdlib.h>     /* qsort, bsearch, NULL */

void *
bsearch_less (const void *key, const void *base, size_t nmemb, size_t size,
     int (*compar) (const void *, const void *))
{
  int l, u, idx;
  const void *p;
  int comparison;

  l = 0;
  u = nmemb - 1;
  while (l <= u)
  {
      idx = (l + u) / 2;
      p = (void *) (((const char *) base) + (idx * size));
      comparison = (*compar) (key, p);
      if (comparison < 0)
         u = idx - 1;
      else if (comparison > 0)
         l = idx + 1;
      else
         return (idx == 0) ? NULL : (void *) (((const char *) p) - size);
  }

  return (u < 0) ? NULL : (void *) (((const char *) base) + (u * size));
}

void *
bsearch_more(const void *key, const void *base, size_t nmemb, size_t size,
         int (*compar) (const void *, const void *))
{
  int l, u, idx;
  const void *p;
  int comparison;

  l = 0;
  u = nmemb - 1;
  while (l <= u)
  {
      idx = (l + u) / 2;
      p = (void *) (((const char *) base) + (idx * size));
      comparison = (*compar) (key, p);
      if (comparison < 0)
         u = idx - 1;
      else if (comparison > 0)
         l = idx + 1;
      else
         return (idx == u) ? NULL : (void *) (((const char *) p) + size);
  }

  return (l > nmemb - 1) ? NULL : (void *) (((const char *) base) + (l * size));
}


int compareints (const void * a, const void * b)
{
  return ( *(int*)a - *(int*)b );
}

//int values[] = { 50, 20, 60, 40, 10, 30 };
int values[] = { 50, 20, 60, 30, 10, 30 };

void test_bsearch_less(int key)
{
  int* pItem = (int*) bsearch_less (&key, values, 6, sizeof (int), compareints);
  if (pItem!=NULL)
    printf ("%d is nearest less than %d int the array.
",*pItem, key);
  else
    printf ("no key is less than %d in the array.
",key);
}

void test_bsearch(int key)
{
  int* pItem = (int*) bsearch (&key, values, 6, sizeof (int), compareints);
  if (pItem!=NULL)
    printf ("%d is in the array.
",*pItem);
  else
    printf ("%d is not in the array.
",key);

}

void test_bsearch_more(int key)
{
  int* pItem = (int*) bsearch_more(&key, values, 6, sizeof (int), compareints);
  if (pItem!=NULL)
    printf ("%d is nearest more than %d int the array.
",*pItem, key);
  else
    printf ("no key is more than %d in the array.
",key);
}

void print_values(int* base, size_t nmemb)
{
  printf("values: ");
  for (size_t i = 0; i < nmemb; ++i)
  {
    printf("%d ", *(base+i));
  }
  printf("
");
}

int main(int argc, char** argv)
{
  if (argc < 2)
  {
    printf("usage: ./bsearch_example num
");
    return -1;
  }

  int key = atoi(argv[1]);
  qsort (values, 6, sizeof (int), compareints);
  
  print_values(values,6);  

  test_bsearch(key); 
  test_bsearch_less(key); 
  test_bsearch_more(key); 
  return 0;
}

运行结果：

[root@VM_174_171_centos algorithm]# ./bsearch_example 1

values: 10 20 30 30 50 60

1 is not in the array.

no key is less than 1 in the array.

10 is nearest more than 1 int the array.

[root@VM_174_171_centos algorithm]# ./bsearch_example 10

values: 10 20 30 30 50 60

10 is in the array.

no key is less than 10 in the array.

20 is nearest more than 10 int the array.

[root@VM_174_171_centos algorithm]# ./bsearch_example 30

values: 10 20 30 30 50 60

30 is in the array.

20 is nearest less than 30 int the array.

30 is nearest more than 30 int the array.

[root@VM_174_171_centos algorithm]# ./bsearch_example 55

values: 10 20 30 30 50 60

55 is not in the array.

50 is nearest less than 55 int the array.

60 is nearest more than 55 int the array.

[root@VM_174_171_centos algorithm]# ./bsearch_example 60

values: 10 20 30 30 50 60

60 is in the array.

50 is nearest less than 60 int the array.

no key is more than 60 in the array.

[root@VM_174_171_centos algorithm]# ./bsearch_example 61

values: 10 20 30 30 50 60

61 is not in the array.

60 is nearest less than 61 int the array.

no key is more than 61 in the array.