Static hashing is a technique used in computer science and database systems to organize and manage large amounts of data efficiently. It is a type of hash table that uses a fixed number of buckets or slots to store data items.

In static hashing, the hash table is typically divided into a fixed number of equally sized buckets, which are identified by unique integer values or addresses. The hash function maps data items to specific buckets based on their key values. The key value is transformed using the hash function, and the resulting hash value determines the bucket in which the data item will be stored.

When inserting a new data item into a static hash table, the hash function is applied to the item’s key to determine the target bucket. If the bucket is empty, the item is placed directly into that bucket. However, if the bucket is already occupied by another item, a collision occurs.

Collision resolution strategies are employed to handle collisions in static hashing. One common method is to use overflow buckets. If a collision occurs, the data item is placed in an overflow bucket associated with the original bucket. This creates a linked list of items in the overflow bucket, allowing multiple items with the same hash value to coexist.

Static hashing offers efficient retrieval of data items since the bucket of a specific key can be determined in constant time using the hash function. However, it may suffer from poor performance in the presence of frequent collisions, which can lead to longer search times as the length of overflow lists grows.

One drawback of static hashing is the fixed number of buckets, which can limit the scalability of the hash table. If the number of items increases significantly, causing frequent collisions, the performance may degrade. To mitigate this, dynamic hashing techniques, such as extendible hashing and linear hashing, can be used to dynamically adjust the number of buckets based on the data load.

Overall, static hashing provides a simple and efficient approach to hash-based data storage, but its performance characteristics depend on the quality of the hash function, the number of buckets, and the distribution of data items.

### Operations of Static Hashing:

Static hashing supports several fundamental operations to manage data efficiently. These operations include:

- Insertion: To insert a new data item into a static hash table, the following steps are typically followed: a. Compute the hash value of the item’s key using the hash function. b. Determine the target bucket based on the hash value. c. If the bucket is empty, place the item directly into that bucket. d. If the bucket is occupied, handle the collision using a collision resolution strategy (such as using overflow buckets or chaining). e. Update any necessary metadata or indices associated with the hash table.
- Search: Searching for a data item in a static hash table involves the following steps: a. Compute the hash value of the target item’s key using the hash function. b. Determine the bucket associated with the hash value. c. If the bucket is empty, the item is not present in the hash table. d. If the bucket is occupied, search for the item either within the bucket or in associated overflow buckets based on the collision resolution strategy. e. Return the item if found, or indicate that it is not present.
- Deletion: To remove a data item from a static hash table: a. Search for the item using the search operation to ensure it exists in the hash table. b. Once found, remove the item from the appropriate bucket. c. Update any necessary metadata or indices associated with the hash table.
- Update: Updating a data item in a static hash table involves searching for the item using the search operation and modifying the desired attributes or fields of the item once found.
- Load Factor Management: The load factor is the ratio of the number of items stored in the hash table to the total number of buckets. To maintain efficiency, it is important to manage the load factor. If the load factor exceeds a certain threshold, the hash table may need to be resized or rehashed to accommodate additional items and reduce the chances of collisions. Resizing typically involves creating a new hash table with a larger number of buckets and rehashing the existing items into the new structure.

These are the primary operations involved in static hashing. Depending on the specific implementation and requirements, additional operations or variations may exist, but these operations form the core functionality of static hash tables.

### 1. Open Hashing:

Open hashing, also known as separate chaining, is a collision resolution technique used in hash tables. Unlike static hashing, which uses overflow buckets or chaining within the same bucket, open hashing allows each bucket to contain a linked list or another data structure to handle collisions.

In open hashing, each bucket in the hash table can store multiple items. When a collision occurs during insertion, the colliding item is appended to the linked list associated with the corresponding bucket. This way, multiple items with the same hash value can coexist within the same bucket by forming a chain of elements.

Here are the primary operations involved in open hashing:

- Insertion: To insert a new data item into a hash table using open hashing: a. Compute the hash value of the item’s key using the hash function. b. Determine the target bucket based on the hash value. c. If the bucket is empty, create a new linked list node containing the item and make it the head of the list for that bucket. d. If the bucket is occupied, traverse the linked list until the end and append a new node with the item to the list.
- Search: Searching for a data item in a hash table with open hashing involves: a. Compute the hash value of the target item’s key using the hash function. b. Determine the bucket associated with the hash value. c. Traverse the linked list in the bucket, comparing the search key with the keys of items in the list until a match is found or the end of the list is reached.
- Deletion: To remove a data item from a hash table with open hashing: a. Search for the item using the search operation to locate the item in the appropriate bucket. b. Once found, remove the item from the linked list by updating the pointers of the neighboring nodes.

Open hashing allows efficient insertion and search operations, especially when the load factor is low and the linked lists are short. However, as the load factor increases and the number of collisions grows, the performance can degrade as the linked lists become longer, resulting in slower search operations.

It’s worth noting that there are variations of open hashing, such as using other data structures like balanced binary search trees instead of linked lists for collision resolution. These variations aim to provide better worst-case performance by maintaining a balanced structure within each bucket.

### 2. Close Hashing:

Close hashing, also known as open addressing or linear probing, is another collision resolution technique used in hash tables. Unlike open hashing, which allows multiple items to be stored in separate data structures within the same bucket, close hashing aims to store all items directly within the hash table itself, utilizing the available buckets more densely.

In close hashing, each bucket in the hash table can hold only one item. When a collision occurs during insertion, instead of chaining or using overflow buckets, the algorithm probes for the next available bucket in a predefined sequence until an empty bucket is found.

Here are the primary operations involved in close hashing:

- Insertion: To insert a new data item into a hash table using close hashing: a. Compute the hash value of the item’s key using the hash function. b. Determine the target bucket based on the hash value. c. If the bucket is empty, place the item directly into that bucket. d. If the bucket is occupied, probe to the next bucket according to a defined sequence (e.g., linear probing) until an empty bucket is found, and then place the item there.
- Search: Searching for a data item in a hash table with close hashing involves: a. Compute the hash value of the target item’s key using the hash function. b. Determine the initial bucket associated with the hash value. c. Start at the initial bucket and probe through the buckets in the predefined sequence until either the item is found or an empty bucket is encountered.
- Deletion: To remove a data item from a hash table with close hashing: a. Search for the item using the search operation to locate the item in the appropriate bucket. b. Once found, mark the item as deleted or flag the bucket as empty.

Close hashing provides good cache performance due to the contiguous storage of items and avoids the overhead of linked lists or additional data structures. However, as the load factor increases and collisions become more frequent, the performance can degrade due to longer probe sequences, resulting in increased search times and reduced efficiency.

There are various probing strategies used in close hashing, including linear probing (sequential checking of consecutive buckets), quadratic probing (probing with quadratic increments), and double hashing (using a secondary hash function to determine the probe sequence). These strategies aim to distribute the items more evenly and reduce clustering effects that can lead to long probe sequences.

Overall, close hashing offers a compact and straightforward approach for collision resolution, but it requires careful selection of hash functions and probing strategies to ensure good performance under various load conditions.