Algorithms Analysis and Design Chapter 7

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Questions and Answers

What is the primary method used to resolve collisions in open hashing?

Storing keys in a separate table

Rehashing the keys

Using a binary tree

Storing keys in linked lists (correct)

How is the hash function for a key determined in this system?

By sorting the key alphabetically

By summing the positions of the key's letters in the alphabet and taking the result modulo 13 (correct)

By counting the number of vowels in the key

By multiplying the key's length by a prime number

In closed hashing (open addressing), where are keys stored?

In a separate database

On external storage devices

In linked lists outside the table

Inside a hash table (correct)

Which of the following describes a situation where open hashing is preferable?

When there is a large number of collisions expected Signup and view all the answers

What is a primary benefit of using hashing for implementing a dictionary?

It allows efficient operations for finding, inserting, and deleting. Signup and view all the answers

Which characteristic is important for a good hash function?

It should be easy to compute and distribute keys evenly. Signup and view all the answers

What happens during a collision in hashing?

Two different keys are hashed to the same location in the table. Signup and view all the answers

Which method is used in open hashing to resolve collisions?

Store all keys in a linked list at the colliding cell. Signup and view all the answers

What is linear probing in closed hashing?

Finding the next free bucket to resolve a collision. Signup and view all the answers

Why is it important for hash functions to minimize collisions?

Collisions can lead to slower performance and inefficient data retrieval. Signup and view all the answers

What term describes the scheme where one key is stored per cell in a hash table?

Closed hashing Signup and view all the answers

If the hash function is defined as $h(K) = K \text{ mod } m$, how would you retrieve the record with key K=314159265 for m=1000?

It would be stored at index 265. Signup and view all the answers

What is the significance of treating the table as a circular array?

It simplifies the handling of overflow conditions. Signup and view all the answers

What does the hash function described in the example likely convert?

Characters into their ASCII values. Signup and view all the answers

Which of these elements is part of the circular array representation?

ALL Signup and view all the answers

What would the result be if the hash function encountered a collision?

Probing methods may be applied. Signup and view all the answers

What is the primary purpose of hashing as shown in the example?

To efficiently retrieve records indexed by keys. Signup and view all the answers

How does the ASCII value differentiation between upper and lower case letters affect hashing?

It introduces more collision possibilities. Signup and view all the answers

In the context provided, what does 'HASH' refer to?

A function for assigning keys to data elements. Signup and view all the answers

What is input enhancement in the context of space-for-time algorithms?

Preprocessing the input to store information for later problem-solving. Signup and view all the answers

Which of the following is a method of prestructuring in algorithms?

Binary search trees Signup and view all the answers

In the brute force string searching algorithm, what happens when a mismatch is detected?

The pattern is realigned one position to the right. Signup and view all the answers

What is the primary goal of space-for-time trade-offs in algorithms?

To increase the speed of the algorithm by using more memory. Signup and view all the answers

Which indicates a successful search in the brute force algorithm for string searching?

All characters of the pattern match with the text. Signup and view all the answers

What is an example of an input enhancement algorithm?

Counting sort Signup and view all the answers

What is the characteristic of indexing schemes in the context of algorithms?

They allow efficient data retrieval through preprocessing. Signup and view all the answers

Which step is NOT part of the brute force string searching algorithm?

Sort the characters of the pattern. Signup and view all the answers

What is the purpose of the shift table in pattern matching algorithms?

To precompute shift sizes based on character occurrences. Signup and view all the answers

How is the shift value calculated for a character in the pattern?

By determining the distance from the character's rightmost occurrence among its first m-1 characters to its right end. Signup and view all the answers

In the example of the Horspool's algorithm with text 'BARD LOVED BANANAS' and pattern 'BAOBAB', what was the shift value when the character 'L' was encountered?

6 Signup and view all the answers

Which of the following symbols represents a character that is not matched in the pattern during the search?

_ Signup and view all the answers

What happens when a character from the text does not match any character from the pattern?

The algorithm shifts based on the precomputed shift value for that character. Signup and view all the answers

What is indicated by shift[‘A’]=1 in the shift table example?

The next position to compare after a mismatch is the first character of the pattern. Signup and view all the answers

What is the maximum shift value in the given shift table for any character not present in the pattern?

6 Signup and view all the answers

What does a shift value of 6 imply for characters that frequently do not match?

It indicates that more characters will need to be shifted before matching can be attempted. Signup and view all the answers

Study Notes

Space-for-Time Trade-offs

Space-for-time algorithms enhance efficiency at the cost of additional space.
Input Enhancement: Preprocesses part of the input to store useful information for problem-solving, e.g., counting sorts and string searching algorithms.
Prestructuring: Prepares input for easier element access, e.g., hashing and indexing schemes like B-trees.

String Searching and Brute Force

Pattern: A sequence of 'm' characters to locate.
Text: A longer sequence of 'n' characters to search within.
Brute Force Algorithm Steps:
- Align the pattern with the start of the text.
- Compare each character sequentially; either match all or detect a mismatch.
- Realign the pattern to the right by one position and repeat as necessary until the text is exhausted.

Shift Table

Compute shift sizes using the rightmost occurrence of characters in the pattern for efficiency in matching.
Maintain a shift table for quick access during searches, indexed by text and pattern alphabets (e.g., for pattern "BAOBAB", shift['A'] = 1).

Horspool’s Algorithm

Uses a precomputed shift table to determine the next position of the pattern during a search.
Efficient search examples can result in unsuccessful searches with various text alignments.

Hashing

A method for efficient dictionary implementation with operations such as find, insert, and delete.
Utilizes space-for-time trade-offs and representation changes for optimized performance.
Important applications include symbol tables and databases (e.g., extendible hashing).

Hash Tables and Functions

Hashing maps keys from a dataset of size 'n' into a hash table of size 'm'.
A hash function is defined as h: K -> location in hash table.
An effective hash function must be easy to compute and evenly distribute keys.

Collisions

Occur when different keys result in the same hash table location.
Good hash functions minimize collisions, but they can still occur as per the birthday paradox.
Collision handling methods:
- Open Hashing: Each cell leads to a linked list of keys.
- Closed Hashing: Each cell holds one key; collisions handled by:
  - Linear probing: Locates the next free bucket.
  - Double hashing: Uses a secondary hash function for increments.

Open vs. Closed Hashing

Open Hashing (Separate Chaining): Linked lists outside the hash table store colliding keys.
Closed Hashing (Open Addressing): Keys stored within the hash table, using a circular array approach for collision resolution.

Practical Example

Hash example: For a key representation and its hash function, keys get computed values stored as per defined functions (e.g., using alphabetical positions and modulo).

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Description

This quiz focuses on Chapter 7 of A. Levitin's book, which explores space and time trade-offs in algorithm design. It covers key concepts of space-for-time algorithms and specific examples such as counting sorts and string searching. Test your understanding of these essential principles in algorithm analysis.