散列表（四）：冲突处理的方法之开地址法（二次探测再散列的实现）

前面的文章分析了开地址法的其中一种：线性探测再散列，这篇文章来讲开地址法的第二种：二次探测再散列

（二）、二次探测再散列

为改善“堆积”问题，减少为完成搜索所需的平均探查次数，可使用二次探测法。

通过某一个散列函数对表项的关键码 x 进行计算，得到桶号，它是一个非负整数。



若设表的长度为TableSize = 23，则在线性探测再散列 举的例子中利用二次探查法所得到的散列结果如图所示。



比如轮到放置Blum 的时候，本来应该是位置1，已经被Burke 占据，接着探测 H0 + 1 = 2,，发现被Broad 占据，接着探测 H0 - 1 =

0，发现空位于是放进去，探测次数为3。

下面来看具体代码实现，跟前面讲过的线性探测再散列 差不多，只是探测的方法不同，但使用的数据结构也有点不一样，此外还实

现了开裂，如果装载因子 a > 1/2； 则建立新表，将旧表内容拷贝过去，所以hash_t 结构体需要再保存一个size 成员，同样的原因，

为了将旧表内容拷贝过去，hash_node_t 结构体需要再保存 *key 和 *value 的size。



common.h：

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#ifndef _COMMON_H_ #define _COMMON_H_ #include <unistd.h> #include <sys/types.h> #include <stdlib.h> #include <stdio.h> #include <string.h> #define ERR_EXIT(m) \ do \ { \ perror(m); \ exit(EXIT_FAILURE); \ } \ while (0) #endif

hash.h：

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#ifndef _HASH_H_ #define _HASH_H_ typedef struct hash hash_t; typedef unsigned int (*hashfunc_t)(unsigned int, void *); hash_t *hash_alloc(unsigned int buckets, hashfunc_t hash_func); void hash_free(hash_t *hash); void *hash_lookup_entry(hash_t *hash, void *key, unsigned int key_size); void hash_add_entry(hash_t *hash, void *key, unsigned int key_size, void *value, unsigned int value_size); void hash_free_entry(hash_t *hash, void *key, unsigned int key_size); #endif /* _HASH_H_ */

hash.c：

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#include "hash.h" #include "common.h" #include <assert.h> typedef enum entry_status { EMPTY, ACTIVE, DELETED } entry_status_t; typedef struct hash_node { enum entry_status status; void *key; unsigned int key_size; //在拷贝进新的哈希表时有用 void *value; unsigned int value_size; //在拷贝进新的哈希表时有用 } hash_node_t; struct hash { unsigned int buckets; unsigned int size; //累加，如果size > buckets / 2 ,则需要开裂建立新表 hashfunc_t hash_func; hash_node_t *nodes; }; unsigned int next_prime(unsigned int n); int is_prime(unsigned int n); unsigned int hash_get_bucket(hash_t *hash, void *key); hash_node_t *hash_get_node_by_key(hash_t *hash, void *key, unsigned int key_size); hash_t *hash_alloc(unsigned int buckets, hashfunc_t hash_func) { hash_t *hash = (hash_t *)malloc(sizeof(hash_t)); //assert(hash != NULL); hash->buckets = buckets; hash->hash_func = hash_func; int size = buckets * sizeof(hash_node_t); hash->nodes = (hash_node_t *)malloc(size); memset(hash->nodes, 0, size); printf("The hash table has allocate.\n"); return hash; } void hash_free(hash_t *hash) { unsigned int buckets = hash->buckets; int i; for (i = 0; i < buckets; i++) { if (hash->nodes[i].status != EMPTY) { free(hash->nodes[i].key); free(hash->nodes[i].value); } } free(hash->nodes); printf("The hash table has free.\n"); } void *hash_lookup_entry(hash_t *hash, void *key, unsigned int key_size) { hash_node_t *node = hash_get_node_by_key(hash, key, key_size); if (node == NULL) { return NULL; } return node->value; } void hash_add_entry(hash_t *hash, void *key, unsigned int key_size, void *value, unsigned int value_size) { if (hash_lookup_entry(hash, key, key_size)) { fprintf(stderr, "duplicate hash key\n"); return; } unsigned int bucket = hash_get_bucket(hash, key); unsigned int i = bucket; unsigned int j = i; int k = 1; int odd = 1; while (hash->nodes[i].status == ACTIVE) { if (odd) { i = j + k * k; odd = 0; // i % hash->buckets; while (i >= hash->buckets) { i -= hash->buckets; } } else { i = j - k * k; odd = 1; while (i < 0) { i += hash->buckets; } ++k; } } hash->nodes[i].status = ACTIVE; if (hash->nodes[i].key) ////释放原来被逻辑删除的项的内存 { free(hash->nodes[i].key); } hash->nodes[i].key = malloc(key_size); hash->nodes[i].key_size = key_size; //保存key_size; memcpy(hash->nodes[i].key, key, key_size); if (hash->nodes[i].value) //释放原来被逻辑删除的项的内存 { free(hash->nodes[i].value); } hash->nodes[i].value = malloc(value_size); hash->nodes[i].value_size = value_size; //保存value_size; memcpy(hash->nodes[i].value, value, value_size); if (++(hash->size) < hash->buckets / 2) return; //在搜索时可以不考虑表装满的情况； //但在插入时必须确保表的装填因子不超过0.5。 //如果超出，必须将表长度扩充一倍，进行表的分裂。 unsigned int old_buckets = hash->buckets; hash->buckets = next_prime(2 * old_buckets); hash_node_t *p = hash->nodes; unsigned int size; hash->size = 0; //从0 开始计算 size = sizeof(hash_node_t) * hash->buckets; hash->nodes = (hash_node_t *)malloc(size); memset(hash->nodes, 0, size); for (i = 0; i < old_buckets; i++) { if (p[i].status == ACTIVE) { hash_add_entry(hash, p[i].key, p[i].key_size, p[i].value, p[i].value_size); } } for (i = 0; i < old_buckets; i++) { // active or deleted if (p[i].key) { free(p[i].key); } if (p[i].value) { free(p[i].value); } } free(p); //释放旧表 } void hash_free_entry(hash_t *hash, void *key, unsigned int key_size) { hash_node_t *node = hash_get_node_by_key(hash, key, key_size); if (node == NULL) return; // 逻辑删除 node->status = DELETED; } unsigned int hash_get_bucket(hash_t *hash, void *key) { unsigned int bucket = hash->hash_func(hash->buckets, key); if (bucket >= hash->buckets) { fprintf(stderr, "bad bucket lookup\n"); exit(EXIT_FAILURE); } return bucket; } hash_node_t *hash_get_node_by_key(hash_t *hash, void *key, unsigned int key_size) { unsigned int bucket = hash_get_bucket(hash, key); unsigned int i = 1; unsigned int pos = bucket; int odd = 1; unsigned int tmp = pos; while (hash->nodes[pos].status != EMPTY && memcmp(key, hash->nodes[pos].key, key_size) != 0) { if (odd) { pos = tmp + i * i; odd = 0; // pos % hash->buckets; while (pos >= hash->buckets) { pos -= hash->buckets; } } else { pos = tmp - i * i; odd = 1; while (pos < 0) { pos += hash->buckets; } i++; } } if (hash->nodes[pos].status == ACTIVE) { return &(hash->nodes[pos]); } // 如果运行到这里，说明pos为空位或者被逻辑删除 // 可以证明，当表的长度hash->buckets为质数且表的装填因子不超过0.5时， // 新的表项 x 一定能够插入，而且任何一个位置不会被探查两次。 // 因此，只要表中至少有一半空的，就不会有表满问题。 return NULL; } unsigned int next_prime(unsigned int n) { // 偶数不是质数 if (n % 2 == 0) { n++; } for (; !is_prime(n); n += 2); // 不是质数，继续求 return n; } int is_prime(unsigned int n) { unsigned int i; for (i = 3; i * i <= n; i += 2) { if (n % i == 0) { // 不是，返回0 return 0; } } // 是，返回1 return 1; }

main.c：

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#include "hash.h" #include "common.h" typedef struct stu { char sno[5]; char name[32]; int age; } stu_t; typedef struct stu2 { int sno; char name[32]; int age; } stu2_t; unsigned int hash_str(unsigned int buckets, void *key) { char *sno = (char *)key; unsigned int index = 0; while (*sno) { index = *sno + 4 * index; sno++; } return index % buckets; } unsigned int hash_int(unsigned int buckets, void *key) { int *sno = (int *)key; return (*sno) % buckets; } int main(void) { stu2_t stu_arr[] = { { 1234, "AAAA", 20 }, { 4568, "BBBB", 23 }, { 6729, "AAAA", 19 } }; hash_t *hash = hash_alloc(256, hash_int); int size = sizeof(stu_arr) / sizeof(stu_arr[0]); int i; for (i = 0; i < size; i++) { hash_add_entry(hash, &(stu_arr[i].sno), sizeof(stu_arr[i].sno), &stu_arr[i], sizeof(stu_arr[i])); } int sno = 4568; stu2_t *s = (stu2_t *)hash_lookup_entry(hash, &sno, sizeof(sno)); if (s) { printf("%d %s %d\n", s->sno, s->name, s->age); } else { printf("not found\n"); } sno = 1234; hash_free_entry(hash, &sno, sizeof(sno)); s = (stu2_t *)hash_lookup_entry(hash, &sno, sizeof(sno)); if (s) { printf("%d %s %d\n", s->sno, s->name, s->age); } else { printf("not found\n"); } hash_free(hash); return 0; }

simba@ubuntu:~/Documents/code/struct_algorithm/search/hash_table/quardratic_probing$ ./main

The hash table has allocate.

4568 BBBB 23

not found

The hash table has free.