Hash Table Exploration: Understanding Big-O Analysis and Hash Table Delete Operations in Python


Learning how different delete functions operate with different algorithms can show software engineers that the way they write their code can influence the performance of their program. For example, focusing on developing an efficient hash table improves the performance of the program; however, a software engineer must know which algorithm to focus on by studying them. Focusing on the delete functions will not improve this program; however, focusing on an efficient hashing algorithm will. As a software engineer, you must learn where to spend your time because time is money.

Because there are different ways of removing an item from an array in Python, we would need to look at each one to understand how Python deletes an item from a list. It’s important to know that the delete function does not affect the time complexity of the hash table, except for in one rare circumstance. When the hash table has only one bucket, the delete function determines the time complexity. This is not the case when we have multiple buckets, as we usually will with a hash table. 

Four Common Ways of Deleting An Item From A List In Python

Using del arraylist[index], when removing a single item every element after the removed item is shifted one position to the left, leading to O(N) time complexity.

list.remove(value), similar to del, deletes the first occurrence of a specified value. The method searches for the value and shifts all elements after it to the left with O(N) as the worst case. 

areaylist.pop() removes and returns an item at a specific index. Removing the last item is O(1) as no shifting is needed. For any other index, it's O(N) due to the shifting of elements.

Slicing replaces a specified portion of the list with another list. To delete an item, you can slice an item in the list and replace it with an empty list. This requires shifting the elements to accommodate the new size, which results in a time complexity that depends on the size of the slice and the overall list. In this case, it would produce an O(N) time complexity to shift every element in the list to delete an item.

Analyzing the Time Complexity of Delete Operations on a Hash Table

When you consider deleting an item from a hash table, the bucket selection process will never be determined by iterating over N (which is the entire data input). Instead, it will be determined by identifying the bucket by its index, which will return a linked list that represents a subset of input N. Even though we are using a delete function with O(N) complexity, the delete function is only looping over a subset of N: the linked list of one bucket. The delete function will never loop over the entire hash table. Instead, we will only be iterating over one linked list of one bucket. This means that the time complexity will likely be a constant O(1). The actual complexity is dependent upon the hashing algorithm itself as it determines the spread of the buckets. If the hashing algorithm only creates one bucket regardless of the input, the program will require looping over all of N to delete an item. This would be O(N) time complexity. If the hashing algorithm results in at least two buckets regardless of input (highly likely),  the time complexity of a delete function would be a constant O(1). This allows large datasets to reduce the complexity from the entire O(N) list that considers all input to a solution that only cycles through one bucket and one linked list as you delete an item by giving the bucket number as input.

If the hash table is poorly designed to only have one bucket, the complexity can approach O(N), but it is highly unlikely that your hash algorithm will create only one bucket. It is VERY LIKELY that this program would create an O(1) time complexity. 

Software Development as a Driver for Continuous Learning

A software engineer can benefit from learning about hash tables, because it suggests that even though your function has an O(N) time complexity, by implementing a hash table, the time complexity of your application may be reduced to O(1). Effective software engineers must be continuous learners for life.

References

Various Methods of Delete from a Python List:

https://stackoverflow.com/questions/627435/how-to-remove-an-element-from-a-list-by-indexLinks to an external site.

Hashing with chaining O(N) time complexity: 

https://www.geeksforgeeks.org/c-program-hashing-chaining/Links to an external site.

Direct hashing O(1) time complexity: 

https://www.geeksforgeeks.org/direct-address-table/Links to an external site.

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