Hash function concept in Data Structures Theory - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a hash function?

A hash function is a process that takes input data and converts it into a fixed-size number or code, called a hash value, which represents the original data.

beginner

Why do we use hash functions in data structures?

We use hash functions to quickly find, store, or check data by turning keys into indexes, making data access faster and more efficient.

beginner

What is a hash value or hash code?

A hash value is the fixed-size output produced by a hash function, which acts like a unique identifier for the original input data.

intermediate

What is a collision in hashing?

A collision happens when two different inputs produce the same hash value. Good hash functions try to minimize collisions.

beginner

Give a real-life example to explain a hash function.

Think of a library system where each book has a unique code based on its title. The code helps find the book quickly without checking every book. This code is like a hash value.

What does a hash function produce from input data?

A A larger copy of the input

B A fixed-size hash value

C A random number unrelated to input

D The original data unchanged

A hash function always produces a fixed-size hash value that represents the input data.

Why are hash functions useful in data storage?

A They delete duplicate data automatically

B They slow down data access

C They help find data quickly using hash values

D They encrypt data for security

Hash functions help find data quickly by converting keys into indexes for fast access.

What is a collision in the context of hash functions?

A When two inputs produce different hash values

B When the hash value is larger than the input

C When a hash function fails to produce a value

D When two different inputs produce the same hash value

A collision occurs when two different inputs produce the same hash value.

Which of the following is NOT a characteristic of a good hash function?

A Is easy to reverse to get original data

B Minimizes collisions

C Produces fixed-size output

D Distributes hash values evenly

Good hash functions are hard to reverse; they do not allow easy retrieval of original data from the hash.

In a library example, what does the unique code for each book represent?

A The book's hash value

B The author's name

C The book's price

D The number of pages

The unique code acts like a hash value that helps quickly identify and find the book.

Explain what a hash function is and why it is important in data structures.

Think about how turning data into a code helps find it faster.

Describe what a collision is in hashing and why it can be a problem.

Consider what happens if two different keys point to the same place.

Practice

1. What is the main purpose of a hash function in data structures?

easy

A. To encrypt data for security

B. To sort data in alphabetical order

C. To compress data into smaller files

D. To convert data into a fixed-size number for quick access

Solution

1. Step 1: Understand the role of a hash function

   A hash function takes input data and produces a fixed-size number called a hash code.

2. Step 2: Identify the purpose in data structures

   This fixed-size number helps quickly find or organize data, improving access speed.

3. Final Answer:

   To convert data into a fixed-size number for quick access -> Option D

4. Quick Check:

   Hash function = fixed-size number for quick access [OK]

Hint: Hash functions create quick lookup numbers [OK]

Common Mistakes:

• Confusing hashing with sorting
• Thinking hash functions compress data
• Assuming hash functions encrypt data

2. Which of the following is a correct property of a good hash function?

easy

A. It always produces the same output for the same input

B. It changes output randomly each time for the same input

C. It produces outputs larger than the input size

D. It sorts the input data before hashing

Solution

1. Step 1: Recall the determinism property of hash functions

   A good hash function must always produce the same output for the same input to be reliable.

2. Step 2: Evaluate other options

   Random outputs or sorting inputs are not properties of hash functions; output size is fixed, not necessarily larger.

3. Final Answer:

   It always produces the same output for the same input -> Option A

4. Quick Check:

   Deterministic output = same input same output [OK]

Hint: Good hash functions are consistent, not random [OK]

Common Mistakes:

• Thinking hash outputs change each time
• Believing hash functions sort data
• Assuming output size varies unpredictably

3. Consider a hash function that sums the ASCII values of characters in a string and then takes modulo 10. What is the hash value of "abc"?

medium

A. 4

B. 3

C. 5

D. 6

Solution

1. Step 1: Calculate ASCII values of each character

   'a' = 97, 'b' = 98, 'c' = 99; sum = 97 + 98 + 99 = 294.

2. Step 2: Apply modulo 10 to the sum

   294 % 10 = 4.

3. Final Answer:

   4 -> Option A

4. Quick Check:

   (97+98+99) mod 10 = 4 [OK]

Hint: Sum ASCII codes then mod 10 for hash [OK]

Common Mistakes:

• Adding character positions instead of ASCII
• Forgetting to apply modulo operation
• Calculating modulo with wrong divisor

4. A hash function is defined as hash(x) = (3 * x + 7) % 5. What is the error if the function returns values outside 0 to 4?

medium

A. The multiplication factor should be negative

B. The function should add 5 instead of 7

C. The modulo operation is missing or incorrect

D. The input x must be a string, not a number

Solution

1. Step 1: Understand modulo operation range

   Modulo 5 should limit output to 0 through 4 only.

2. Step 2: Identify cause of out-of-range values

   If outputs are outside 0-4, the modulo operation is either missing or applied incorrectly.

3. Final Answer:

   The modulo operation is missing or incorrect -> Option C

4. Quick Check:

   Modulo ensures output range 0-4 [OK]

Hint: Modulo keeps hash values in range [OK]

Common Mistakes:

• Ignoring modulo effect on output range
• Changing constants without reason
• Confusing input type requirements

5. You want to design a hash function for a phone book that minimizes collisions. Which approach is best?

hard

A. Use the length of the phone number as the hash value

B. Use the sum of digits in the phone number modulo a prime number

C. Use only the first digit of the phone number as the hash

D. Use the phone number reversed without modulo

Solution

1. Step 1: Understand collision minimization

   Minimizing collisions means spreading hash values evenly across possible outputs.

2. Step 2: Evaluate each option's effectiveness

   Using sum of digits modulo a prime number distributes values better than using only first digit, length, or reversed number without modulo.

3. Final Answer:

   Use the sum of digits in the phone number modulo a prime number -> Option B

4. Quick Check:

   Sum digits mod prime reduces collisions [OK]

Hint: Sum digits mod prime spreads hash values well [OK]

Common Mistakes:

• Using only part of input causing many collisions
• Ignoring modulo operation
• Choosing non-prime modulo numbers