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Questions and Answers
What is the primary method used to resolve collisions in open hashing?
What is the primary method used to resolve collisions in open hashing?
How is the hash function for a key determined in this system?
How is the hash function for a key determined in this system?
In closed hashing (open addressing), where are keys stored?
In closed hashing (open addressing), where are keys stored?
Which of the following describes a situation where open hashing is preferable?
Which of the following describes a situation where open hashing is preferable?
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What is a primary benefit of using hashing for implementing a dictionary?
What is a primary benefit of using hashing for implementing a dictionary?
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Which characteristic is important for a good hash function?
Which characteristic is important for a good hash function?
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What happens during a collision in hashing?
What happens during a collision in hashing?
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Which method is used in open hashing to resolve collisions?
Which method is used in open hashing to resolve collisions?
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What is linear probing in closed hashing?
What is linear probing in closed hashing?
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Why is it important for hash functions to minimize collisions?
Why is it important for hash functions to minimize collisions?
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What term describes the scheme where one key is stored per cell in a hash table?
What term describes the scheme where one key is stored per cell in a hash table?
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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?
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?
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What is the significance of treating the table as a circular array?
What is the significance of treating the table as a circular array?
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What does the hash function described in the example likely convert?
What does the hash function described in the example likely convert?
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Which of these elements is part of the circular array representation?
Which of these elements is part of the circular array representation?
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What would the result be if the hash function encountered a collision?
What would the result be if the hash function encountered a collision?
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What is the primary purpose of hashing as shown in the example?
What is the primary purpose of hashing as shown in the example?
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How does the ASCII value differentiation between upper and lower case letters affect hashing?
How does the ASCII value differentiation between upper and lower case letters affect hashing?
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In the context provided, what does 'HASH' refer to?
In the context provided, what does 'HASH' refer to?
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What is input enhancement in the context of space-for-time algorithms?
What is input enhancement in the context of space-for-time algorithms?
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Which of the following is a method of prestructuring in algorithms?
Which of the following is a method of prestructuring in algorithms?
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In the brute force string searching algorithm, what happens when a mismatch is detected?
In the brute force string searching algorithm, what happens when a mismatch is detected?
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What is the primary goal of space-for-time trade-offs in algorithms?
What is the primary goal of space-for-time trade-offs in algorithms?
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Which indicates a successful search in the brute force algorithm for string searching?
Which indicates a successful search in the brute force algorithm for string searching?
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What is an example of an input enhancement algorithm?
What is an example of an input enhancement algorithm?
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What is the characteristic of indexing schemes in the context of algorithms?
What is the characteristic of indexing schemes in the context of algorithms?
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Which step is NOT part of the brute force string searching algorithm?
Which step is NOT part of the brute force string searching algorithm?
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What is the purpose of the shift table in pattern matching algorithms?
What is the purpose of the shift table in pattern matching algorithms?
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How is the shift value calculated for a character in the pattern?
How is the shift value calculated for a character in the pattern?
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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?
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?
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Which of the following symbols represents a character that is not matched in the pattern during the search?
Which of the following symbols represents a character that is not matched in the pattern during the search?
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What happens when a character from the text does not match any character from the pattern?
What happens when a character from the text does not match any character from the pattern?
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What is indicated by shift[‘A’]=1 in the shift table example?
What is indicated by shift[‘A’]=1 in the shift table example?
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What is the maximum shift value in the given shift table for any character not present in the pattern?
What is the maximum shift value in the given shift table for any character not present in the pattern?
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What does a shift value of 6 imply for characters that frequently do not match?
What does a shift value of 6 imply for characters that frequently do not match?
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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.
