算法学堂 - 二分查找及其变形
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.\n",*pItem, key); else printf ("no key is less than %d in the array.\n",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.\n",*pItem); else printf ("%d is not in the array.\n",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.\n",*pItem, key); else printf ("no key is more than %d in the array.\n",key); } void print_values(int* base, size_t nmemb) { printf("values: "); for (size_t i = 0; i < nmemb; ++i) { printf("%d ", *(base+i)); } printf("\n"); } int main(int argc, char** argv) { if (argc < 2) { printf("usage: ./bsearch_example num\n"); 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.
