Collision handling (chaining) in Data Structures Theory - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding the purpose of chaining in hash tables

Why is chaining used in hash tables to handle collisions?

A To increase the size of the hash table dynamically when collisions occur

B To store multiple elements at the same index using linked lists or similar structures

C To prevent any collisions by using a perfect hash function

D To sort the elements in the hash table for faster searching

💡 Hint

Think about how multiple items can share the same position in a hash table.

Chaining allows multiple elements to be stored at the same index by linking them together, usually with a linked list. This way, collisions do not overwrite existing data.

📋 Factual

intermediate

Identifying the data structure used in chaining

Which data structure is most commonly used to implement chaining in hash tables?

A Linked list

B Stack

C Binary search tree

D Array

💡 Hint

Consider a structure that allows easy insertion and traversal of multiple elements.

Linked lists are commonly used in chaining because they allow efficient insertion and traversal of elements that share the same hash index.

🔍 Analysis

advanced

Analyzing performance impact of chaining

What happens to the average search time in a hash table using chaining when the number of elements greatly exceeds the number of buckets?

A Search time increases linearly because chains become longer

B Search time remains constant because chaining handles collisions efficiently

C Search time decreases because more elements improve hashing distribution

D Search time becomes zero because all elements are stored in one place

💡 Hint

Think about what happens when many elements share the same bucket.

When many elements hash to the same bucket, the linked list (chain) grows longer, making search time proportional to the chain length, which increases linearly.

❓ Comparison

advanced

Comparing chaining with open addressing

Which of the following is a key advantage of chaining over open addressing for collision handling?

A Chaining eliminates the need for a hash function

B Chaining requires less memory because it uses only the array

C Chaining guarantees constant time search regardless of load factor

D Chaining avoids clustering by storing collided elements outside the main array

💡 Hint

Consider how elements are stored when collisions happen in both methods.

Chaining stores collided elements in separate linked lists, avoiding clustering issues common in open addressing where elements are stored within the array itself.

❓ Reasoning

expert

Determining the number of items in a chained hash table bucket

Given a hash table with 10 buckets using chaining, and 35 elements inserted, what is the minimum number of elements that must be in at least one bucket?

A 5

B 6

C 4

D 3

💡 Hint

Use the pigeonhole principle to reason about distribution.

By the pigeonhole principle, with 35 elements and 10 buckets, at least one bucket must contain at least ceil(35/10) = 4 elements. If all buckets had 3 or fewer, the maximum total would be 30, which is less than 35.

Practice

1. What is the main idea behind collision handling by chaining in hash tables?

easy

A. Use a second hash function to find a new index

B. Overwrite the existing item when a collision occurs

C. Resize the hash table immediately after a collision

D. Store collided items in a linked list at the same index

Solution

1. Step 1: Understand collision in hash tables

   When two keys hash to the same index, a collision occurs.

2. Step 2: Explain chaining method

   Chaining stores all collided items in a linked list at that index, preserving all entries.

3. Final Answer:

   Store collided items in a linked list at the same index -> Option D

4. Quick Check:

   Chaining = linked list at index [OK]

Hint: Chaining means linked lists hold collisions at one spot [OK]

Common Mistakes:

• Thinking collisions overwrite existing data
• Confusing chaining with open addressing
• Assuming resizing happens immediately on collision

2. Which of the following is the correct way to represent chaining in a hash table?

easy

A. Each index holds a single value only

B. Each index holds a linked list of values

C. Each index holds a separate hash table

D. Each index holds a fixed-size array of values

Solution

1. Step 1: Recall chaining structure

   Chaining uses linked lists to store multiple items at one index.

2. Step 2: Match options to chaining

   Only Each index holds a linked list of values describes linked lists at each index, which is chaining.

3. Final Answer:

   Each index holds a linked list of values -> Option B

4. Quick Check:

   Chaining = linked list per index [OK]

Hint: Chaining means linked lists at each hash index [OK]

Common Mistakes:

• Choosing single value per index (no chaining)
• Confusing chaining with nested hash tables
• Thinking arrays are used instead of lists

3. Consider a hash table using chaining with 5 buckets. The hash function is h(key) = key % 5. Insert keys 7, 12, 17, 22. What does the bucket at index 2 contain?

medium

A. [7, 12, 17, 22]

B. [7, 17]

C. [12, 22]

D. [2]

Solution

1. Step 1: Calculate hash for each key

   7 % 5 = 2, 12 % 5 = 2, 17 % 5 = 2, 22 % 5 = 2. All keys map to index 2.

2. Step 2: List keys in bucket 2

   Bucket 2 contains keys 7, 12, 17, 22.

3. Step 3: Verify which keys actually hash to 2

   7 % 5 = 2, 12 % 5 = 2, 17 % 5 = 2, 22 % 5 = 2. All keys map to index 2.

4. Step 4: Check options carefully

   [7, 17] lists [7, 17], but keys 12 and 22 also hash to 2, so [7, 17] is incomplete. [7, 12, 17, 22] lists all keys, which is correct.

5. Final Answer:

   [7, 12, 17, 22] -> Option A

6. Quick Check:

   All keys mod 5 = 2 [OK]

Hint: Apply mod function to keys to find bucket [OK]

Common Mistakes:

• Miscomputing modulo operation
• Assuming keys distribute to different buckets
• Confusing bucket index with key values

4. A hash table uses chaining but the linked list at one index is not updated correctly after insertion. What is the likely error?

medium

A. The new node is not linked to the existing list

B. The hash function returns different values for same key

C. The table size is too small

D. The keys are not unique

Solution

1. Step 1: Understand chaining insertion

   When inserting, the new node must link to the existing list at that index.

2. Step 2: Identify error from symptoms

   If the list is not updated, likely the new node was not linked properly.

3. Final Answer:

   The new node is not linked to the existing list -> Option A

4. Quick Check:

   Missing link causes list update failure [OK]

Hint: Check if new node links to list head [OK]

Common Mistakes:

• Blaming hash function for insertion errors
• Thinking table size causes linking issues
• Confusing key uniqueness with chaining errors

5. You have a hash table with chaining. If many keys hash to the same index, what is the best way to improve performance?

hard

A. Ignore collisions and overwrite old keys

B. Use a linked list with more nodes at that index

C. Increase the table size and rehash all keys

D. Store all keys in a single bucket

Solution

1. Step 1: Understand impact of many collisions

   Many keys in one bucket slow down search because linked list grows long.

2. Step 2: Improve performance by resizing

   Increasing table size reduces collisions by spreading keys across more buckets.

3. Step 3: Rehash keys after resizing

   Rehashing redistributes keys according to new table size for better balance.

4. Final Answer:

   Increase the table size and rehash all keys -> Option C

5. Quick Check:

   Resize + rehash reduces collisions [OK]

Hint: Resize table and rehash keys to reduce collisions [OK]

Common Mistakes:

• Adding more nodes without resizing
• Overwriting keys loses data
• Putting all keys in one bucket defeats hashing