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Questions and Answers
What is the purpose of ignoring the last carry when calculating the hash value?
What is the purpose of ignoring the last carry when calculating the hash value?
In the context of hashing, what does the variable 'M' represent?
In the context of hashing, what does the variable 'M' represent?
Which of the following is a property of a good hash function?
Which of the following is a property of a good hash function?
What is one disadvantage of the multiplication method for hashing?
What is one disadvantage of the multiplication method for hashing?
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Which collision resolution technique involves using linked lists in each cell of the hash table?
Which collision resolution technique involves using linked lists in each cell of the hash table?
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What does the formula $h(K) = floor(M (kA , mod , 1))$ help to compute?
What does the formula $h(K) = floor(M (kA , mod , 1))$ help to compute?
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Why is it important for a hash function to have a low load factor?
Why is it important for a hash function to have a low load factor?
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What is the result of the hash function for the key 70 when the table size is 5?
What is the result of the hash function for the key 70 when the table size is 5?
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In the process of quadratic probing, which of the following represents the first probe after an initial collision?
In the process of quadratic probing, which of the following represents the first probe after an initial collision?
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What next slot will be checked if the initial hash index for key 50 (using a table size of 7) is occupied?
What next slot will be checked if the initial hash index for key 50 (using a table size of 7) is occupied?
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Which statement accurately describes quadratic probing?
Which statement accurately describes quadratic probing?
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What happens when a slot is found occupied during the insertion of key 30?
What happens when a slot is found occupied during the insertion of key 30?
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How many probes are needed to successfully insert key 50 after the hashes for the previous keys have resulted in collisions?
How many probes are needed to successfully insert key 50 after the hashes for the previous keys have resulted in collisions?
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Given the hash function and quadratic probing mechanism, which slot would key 76 occupy?
Given the hash function and quadratic probing mechanism, which slot would key 76 occupy?
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What is the main purpose of quadratic probing in hash tables?
What is the main purpose of quadratic probing in hash tables?
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What is the purpose of the load factor in a hash table?
What is the purpose of the load factor in a hash table?
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What happens when the load factor of a hash table exceeds the predefined value?
What happens when the load factor of a hash table exceeds the predefined value?
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Which of the following is NOT an application of hash data structures?
Which of the following is NOT an application of hash data structures?
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What is a significant disadvantage of using hash data structures?
What is a significant disadvantage of using hash data structures?
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In what instance is hashing particularly effective?
In what instance is hashing particularly effective?
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What is the primary goal of hashing?
What is the primary goal of hashing?
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What does rehashing in a hash table commonly involve?
What does rehashing in a hash table commonly involve?
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Which of the following statements about hash tables is incorrect?
Which of the following statements about hash tables is incorrect?
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What is the primary mathematical operation used in the Division Method of generating a hash value?
What is the primary mathematical operation used in the Division Method of generating a hash value?
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Which of the following is an advantage of the Mid Square Method?
Which of the following is an advantage of the Mid Square Method?
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What is a disadvantage of the Division Method?
What is a disadvantage of the Division Method?
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In the Mid Square Method, what is the first step to compute the hash value?
In the Mid Square Method, what is the first step to compute the hash value?
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What limits the effectiveness of the Mid Square Method when using large key sizes?
What limits the effectiveness of the Mid Square Method when using large key sizes?
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What is the procedure for the Digit Folding Method?
What is the procedure for the Digit Folding Method?
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Which of the following statements about the Division Method is true?
Which of the following statements about the Division Method is true?
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What should be considered when selecting the value of M in the Division Method?
What should be considered when selecting the value of M in the Division Method?
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What is the primary purpose of double hashing in a hash table?
What is the primary purpose of double hashing in a hash table?
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In the formula h(k, i) = (h1(k) + i * h2(k)) % n, what does 'i' represent?
In the formula h(k, i) = (h1(k) + i * h2(k)) % n, what does 'i' represent?
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What is the time complexity of the double hashing algorithm?
What is the time complexity of the double hashing algorithm?
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What will be the slot number for inserting key 72 after resolving the collision?
What will be the slot number for inserting key 72 after resolving the collision?
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If the hash table size is 7, what would be the output of h1(692)?
If the hash table size is 7, what would be the output of h1(692)?
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How is the secondary hash function h2(k) defined?
How is the secondary hash function h2(k) defined?
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Which of the following keys will cause a collision when inserting into the hash table of size 7?
Which of the following keys will cause a collision when inserting into the hash table of size 7?
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What must occur if a collision happens during key insertion in double hashing?
What must occur if a collision happens during key insertion in double hashing?
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Study Notes
Hash Functions Overview
- Hash functions transform input data (keys) into a fixed-size string of characters, which is typically a numerical value.
- Common methods of generating hash values include Division, Mid Square, Folding, and Multiplication.
Division Method
- Simple and efficient, calculates hash using remainder from dividing key k by table size M: h(K) = k mod M.
- Best performance when M is a prime number to ensure uniform key distribution.
- Example: For k = 12345 and M = 95, h(12345) = 90; for k = 1276 and M = 11, h(1276) = 0.
- Pros: Quick computation; works for any M.
- Cons: Poor performance with consecutive keys; requires careful selection of M.
Mid Square Method
- Involves squaring the key and extracting the middle digits as the hash value: h(K) = h(k²).
- Example: For k = 60; 60 x 60 = 3600, extract middle digits yields h(60) = 60.
- Pros: Utilizes all digits of the key for a better hash value; less affected by the original key’s digit distribution.
- Cons: Limited by key size; potential for collisions.
Folding Method
- Divides key k into parts, sums them to generate the hash: h(K) = s = k1 + k2 + ... + kn.
- Example: For k = 12345, split into k1 = 12, k2 = 34, k3 = 5; s = 12 + 34 + 5 = 51.
- Allows for different sized parts based on table size.
Multiplication Method
- Uses a constant A (0 < A < 1) to compute the hash: h(K) = floor(M * (kA mod 1)).
- Example: For k = 12345, A = 0.357840, and M = 100; results in h(12345) = 53.
- Pros: Suitable for various values of A; quick with powers of two for M.
- Cons: Requires careful selection of A for optimal results.
Properties of a Good Hash Function
- Efficient computation.
- Uniform key distribution to reduce collisions.
- Low load factor to maintain performance.
Collision Handling Methods
- Separate Chaining: Each cell in the hash table points to a linked list of records sharing the same hash value, requires extra memory.
- Open Addressing: Alternative slots are sought within the table for keys colliding at the same hash index.
Open Addressing Techniques
- Quadratic Probing: Uses a quadratic formula to find next slot upon collision: H + 12, H + 22, H + 32, etc..
- Double Hashing: Employs two hash functions to resolve collisions, using the form h(k, i) = (h1(k) + i * h2(k)) % n.
Load Factor
- Defined as Total elements in hash table / Size of hash table.
- A high load factor indicates the need for rehashing to maintain efficiency.
Rehashing
- Involves expanding the hash table (commonly doubling its size) when the load factor exceeds a threshold (default 0.75), redistributing keys to maintain performance.
Applications of Hash Structures
- Hashes are utilized for indexing in databases, disk data structures, and implementation of objects in programming languages.
- Real-time uses include cache mapping, password verification, cryptographic processes, and pattern matching algorithms.
Advantages and Disadvantages
- Advantages: Efficient synchronization, constant time complexity for average operations (search, insert, delete).
- Disadvantages: Inefficiency due to collisions, unmanageable colliding scenarios for large key sets, and lack of support for null values.
Conclusion
- Hashing enhances efficiency in data retrieval, providing a structured way to quickly locate items in large datasets without linear searches.
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Description
Explore different hash functions in this quiz, including the Division Method, Mid Square Method, Folding Method, and Multiplication Method. Understand the basic principles, advantages, and applications of each method to enhance your knowledge in computer science and data structures.
