Linear Probing Hash Table My Thoughts 2022

Open addressing resolves hash collisions in a hash table data structure. This approach searches the hash table for an available bucket when a collision is detected & if an empty bucket is available, the space is then utilized by the new object. One open addressing approach is linear probing.

Linear probing is a common approach of open addressing that increments to check if the next bucket is empty if a collision is detected. Regarding collisions, collisions are just keys that map to the same index, and this will cause the data to be overwritten.

It is essential to understand that a hash table is a key, value pair data structure that, if implemented correctly, will allow you, on average, to access the data stored in it at a constant time O(1) regardless of the size of x (size of the table).

A critical reason why hash tables can access the data on average at constant time O(1) is that they utilize arrays or an array-like container with indices. Suppose you know the index of an item in an array. In that case, you can access the data at a constant time because the complexity needed to access the data is not dependent on the size of x since we know the exact location in memory.

Using the following formula, you can compute the index, i = hash(k) mod x. Replace k with the unique key & x with the size of the array to get the index. The modulo operator “%” returns the remainder after dividing two numbers and ensures that we stay within the array sequence.

Good hash tables contain the following:

1. A way to insert/update the table.

2. A way to search the table.

3. A way to remove keys from the table.

4. A way to extend the table.

Let’s start by listing the things that we need for linear probing to work.

For this article, I implemented linear probing using C++ & I used a vector as the container to store the “Entry” objects. Below I show the directory structure I used for the source code.

To be as brief as possible, I will show the header files and comment below the code block.

In the insert method, I initialize a variable and set it equal to the return value of the hash function method. I then used geometric resizing to double the table size if it reached a load factor of 76% or greater. Hence, If the hash table is 76% full, then I want to double the size of the table. I used the extend method to extend and recursively called the insert method to test again in the else block.

If the load factor is within a valid range, then I want to check if the bucket entry key is equal to the insert key and if so, I want to update the entry and return true. In the code, if the entry key is not equal to “None” the bucket is not available. The index will change each loop because we increment one until we reach an empty bucket to find the next available bucket. I always want to have at least one bucket open for this to work.

If nothing works in this method, I will always return false.

In the search method, I initialize a variable and set it equal to the return value of the hash function method. If the bucket key is not equal to “None” I test to see if it is equal to the search key and if it is, I return the index. if I am still in the loop I increment to the next bucket & use modulo to stay within the sequence.

If the search key is not within the table, the method will return a negative one.

If the remove key is not within the table, the method will return false.

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