Collision problems are a common issue when working with hash tables. A collision occurs when two or more keys are mapped to the same index in the hash table, leading to an overlap in the data stored at that index. This can cause the hash table to become inefficient and slow, as it takes longer to retrieve data from the table.
One way to solve collision problems in hash tables is to use a technique called chaining. In chaining, each index in the hash table is a linked list, and when a collision occurs, the new key-value pair is added to the end of the list. This allows for multiple key-value pairs to be stored at the same index without causing any overlap.
Another solution is to use open addressing, where the hash table does not use linked lists to store data. Instead, when a collision occurs, the hash table will search for the next available empty index to store the key-value pair. This can be done using a linear probing or a quadratic probing approach.
In linear probing, the hash table will search for the next empty index by incrementing the index by 1 until it finds an empty slot. This can lead to clustering, where a group of occupied indices are stored together, which can decrease the efficiency of the hash table.
Quadratic probing is similar to linear probing, but instead of incrementing the index by 1, it increments it by a fixed number, such as 2 or 3. This helps to avoid clustering and can be more efficient than linear probing.
Swift offers several options for implementing hash tables. The Dictionary and Set types in Swift use a hash table implementation under the hood and handle collisions automatically. However, if you want to implement your own hash table, you can use an array and handle collisions using chaining or open addressing.
Let's take a look at examples of these techniques:
One way to solve collision problems in hash tables is to use a technique called chaining. In chaining, each index in the hash table is a linked list, and when a collision occurs, the new key-value pair is added to the end of the list. This allows for multiple key-value pairs to be stored at the same index without causing any overlap.
Another solution is to use open addressing, where the hash table does not use linked lists to store data. Instead, when a collision occurs, the hash table will search for the next available empty index to store the key-value pair. This can be done using a linear probing or a quadratic probing approach.
In linear probing, the hash table will search for the next empty index by incrementing the index by 1 until it finds an empty slot. This can lead to clustering, where a group of occupied indices are stored together, which can decrease the efficiency of the hash table.
Quadratic probing is similar to linear probing, but instead of incrementing the index by 1, it increments it by a fixed number, such as 2 or 3. This helps to avoid clustering and can be more efficient than linear probing.
Swift offers several options for implementing hash tables. The Dictionary and Set types in Swift use a hash table implementation under the hood and handle collisions automatically. However, if you want to implement your own hash table, you can use an array and handle collisions using chaining or open addressing.
Let's take a look at examples of these techniques:
Chaining Solution
In this example, we have a Node structure that represents a node in the linked list, and a HashTable class that uses an array to store the nodes. The hash(key:) function converts a given key into an array index, and the put(key:value:) function adds a new key-value pair to the hash table. If there is a collision, the function adds the new node to the end of the linked list at the corresponding index. The get(key:) function retrieves the value for a given key by traversing the linked list and returning the value of the first node with a matching key.
Notice how both keys, 'c' and 'w', point to the identical index, 17.
Notice how both keys, 'c' and 'w', point to the identical index, 17.
Quadratic Probing Solution
In this example, we have a hash table with a fixed size of 10. The hash function takes in a key and returns the index where it should be stored in the hash table. The insert function uses quadratic probing to find a free slot in the hash table for the key. If the initial index for the key is already occupied, it will search the next index using the formula (index + i * i) % data.count, where i is the number of probes made. This continues until a free slot is found, and the key is inserted into the free slot.
