Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 8: Problem 17

Write an algorithm to delete an element from a hash table that uses linear probing as its clash resolution strategy, Analyze your algorithm, and show the results using order notation.

Short Answer

Expert verified
The algorithm starts by computing the hash of the key to be deleted. If the hashed index is empty, the key isn't in the table. If the key at the hashed index is the key to be deleted, it gets marked as a dummy node. If not, it steps linearly through the array until the key is found or an empty cell is reached. The algorithm then repeats this process until it has scanned the entire table once. The time complexity of this algorithm can be as quick as \(O(1)\) in the best case (no collisions), but can be as slow as \(O(n)\) in the worst case where n is the number of slots in the hash table.

Step by step solution

01

Understanding Hash Tables and Linear Probing

A hash table is a data structure that implements an associative array abstract data type, a structure that can map keys to values. A hash table uses a hash function to compute an index into an array of buckets or slots, from which the desired value can be found. When a collision occurs (two keys hash to the same index), Linear Probing handles it by probing, or searching through the table until it finds an empty spot where it shops the value.
02

Writing the Algorithm

Here is a primitive algorithm for deletion in a hash table using linear probing: 1. Compute the hash code of the key to be deleted, call this \(index\).2. If the hash table at index is empty, then the key we want to delete doesn't exist in the table. So, stop.3. If the key at index equals the key to be deleted, remove the key-value and mark it as deleted or a 'dummy' node. 4. If the key at index doesn't match the key to be deleted, keep moving in the array until either the key is found or an empty cell is found.5. Repeat the process until traversing the entire hash table once.
03

Analyzing the Algorithm

In the best-case scenario, the key to be deleted will be found at the initial index i.e., immediate success which gives the time complexity of \(O(1)\). This is the case where there are no collisions. However, in the worst case, there could be many collisions leading to a longer search time for an element in the hash table. Hence, in the worst case, it will go through all the cells of the hash table once which gives the time complexity of \(O(n)\), where n refers to the total number of slots in the hash table.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Show that the median of five numbers can be found by making six comparisons.

Discuss the advantages of using each of the following instead of the other: (a) A binary search tree with a balancing mechanism (b) \(A 3-2\) tree

Give at least two examples of situations in which hashing is not appropriate.

Let \(S\) and \(T\) be two arrays of \(m\) and \(n\) elements, respectively. Write an algorithm that finds all the common elements and stores them in an array \(U\) Show that this can be done in \(\Theta(n+m)\) time.

Suppose a very large sorted list is stored in external storage. Assuming that this list cannot be brought into internal memory, develop a searching algorithm that looks for a key in this list. What major factor(s) should be considered when an external search algorithm is developed? Define the major fac\(\operatorname{tor}(s),\) analyze your algorithm, and show the results using order notation.
See all solutions

Recommended explanations on Computer Science Textbooks

Computer Programming

Read Explanation

Problem Solving Techniques

Read Explanation

Functional Programming

Read Explanation

Computer Organisation and Architecture

Read Explanation

Algorithms in Computer Science

Read Explanation

Issues in Computer Science

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free