Collision Handling Using Chaining in DSA Javascript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is collision in a hash table?

Collision happens when two different keys hash to the same index in the hash table.

beginner

How does chaining handle collisions in a hash table?

Chaining stores all elements that hash to the same index in a linked list or chain at that index.

beginner

What data structure is commonly used in chaining to store collided elements?

A linked list is commonly used to store collided elements at the same index.

intermediate

Why is chaining preferred over open addressing in some cases?

Chaining can handle more elements than the table size and is simpler to implement for collisions.

beginner

What happens when you search for a key in a hash table using chaining?

You go to the index from the hash function and then search through the linked list at that index to find the key.

What does chaining use to handle collisions?

A Linked lists at each index

B Rehashing the key

C Linear probing

D Double hashing

Chaining uses linked lists at each index to store multiple elements that hash to the same index.

If two keys hash to the same index, what does chaining do?

A Overwrites the old key

B Stores both keys in a linked list at that index

C Finds a new empty index

D Deletes the old key

Chaining stores both keys in a linked list at the same index to handle collisions.

Which of these is NOT true about chaining?

A It can store more elements than the table size

B It uses linked lists to handle collisions

C It requires rehashing on every collision

D It keeps all collided elements at the same index

Chaining does not require rehashing on collisions; it stores collided elements in a linked list.

What is the time complexity to search in a hash table using chaining in the worst case?

A O(1)

B O(n log n)

C O(log n)

D O(n)

In the worst case, all elements could be in one linked list, making search O(n).

Which of the following is a benefit of chaining?

A Allows storing more elements than the table size

B Handles collisions without needing extra space

C Always guarantees O(1) search time

D Avoids linked lists completely

Chaining allows storing more elements than the table size by using linked lists at each index.

Explain how collision handling using chaining works in a hash table.

Think about what happens when two keys get the same index.

Describe the advantages and disadvantages of using chaining for collision handling.

Consider both space and time aspects.

Practice

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

easy

A. Resize the hash table immediately after every insertion

B. Replace the existing element with the new one when a collision happens

C. Store multiple elements in a linked list at the same index when collisions occur

D. Use a secondary hash function to find a new index

Solution

1. Step 1: Understand collision in hash tables

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

2. Step 2: How chaining handles collisions

   Chaining stores all collided elements in a linked list at that index.

3. Final Answer:

   Store multiple elements in a linked list at the same index when collisions occur -> Option C

4. Quick Check:

   Chaining = linked list at index [OK]

Hint: Chaining means linked list at one index for collisions [OK]

Common Mistakes:

• Thinking chaining replaces old values
• Confusing chaining with open addressing
• Assuming resizing happens on every collision

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

easy

A. const table = new Array(10).fill([]);

B. const table = Array.from({ length: 10 }, () => []);

C. const table = new Array(10);

D. const table = Array(10).fill(null);

Solution

1. Step 1: Understand array initialization with unique lists

   Using fill([]) fills all indexes with the same array reference.

2. Step 2: Use Array.from with a function to create unique arrays

   Array.from({ length: 10 }, () => []) creates a new empty array at each index.

3. Final Answer:

   const table = Array.from({ length: 10 }, () => []); -> Option B

4. Quick Check:

   Unique arrays per index = const table = Array.from({ length: 10 }, () => []); [OK]

Hint: Use Array.from with function for unique arrays [OK]

Common Mistakes:

• Using fill([]) causes all indexes to share one array
• new Array(10) leaves slots undefined
• Filling with null does not create lists for chaining

3. Consider the following JavaScript code for inserting keys into a hash table with chaining:

const table = Array.from({ length: 5 }, () => []);
function hash(key) { return key % 5; }

// Insert keys
[7, 12, 17].forEach(key => {
  const index = hash(key);
  table[index].push(key);
});

console.log(table);

What is the output printed?

medium

A. [[7, 12, 17], [], [], [], []]

B. [[], [], [], [7, 12, 17], []]

C. [[], [7], [12], [17], []]

D. [[], [], [7, 12, 17], [], []]

Solution

1. Step 1: Calculate hash index for each key

   7 % 5 = 2, 12 % 5 = 2, 17 % 5 = 2.

2. Step 2: Insert keys at index 2

   All keys go into table[2], so table[2] = [7, 12, 17].

3. Final Answer:

   [[], [], [7, 12, 17], [], []] -> Option D

4. Quick Check:

   All keys at index 2 = [[], [], [7, 12, 17], [], []] [OK]

Hint: Calculate key % size to find index [OK]

Common Mistakes:

• Miscomputing modulo results
• Inserting keys at wrong indexes
• Confusing array positions in output

4. The following code attempts to insert keys into a hash table with chaining but has a bug:

const table = new Array(3).fill([]);
function hash(key) { return key % 3; }

function insert(key) {
  const index = hash(key);
  table[index].push(key);
}

insert(1);
insert(4);
insert(7);
console.log(table);

What is the bug and how to fix it?

medium

A. Bug: All indexes share the same array; Fix: Use Array.from with () => []

B. Bug: hash function is incorrect; Fix: Use key % 10 instead

C. Bug: push method is wrong; Fix: Use unshift instead

D. Bug: table size is too small; Fix: Increase size to 10

Solution

1. Step 1: Identify the bug with fill([])

   Using fill([]) assigns the same array reference to all indexes.

2. Step 2: Fix by creating unique arrays per index

   Use Array.from({ length: 3 }, () => []) to create separate arrays.

3. Final Answer:

   Bug: All indexes share the same array; Fix: Use Array.from with () => [] -> Option A

4. Quick Check:

   fill([]) shares arrays, Array.from creates unique ones [OK]

Hint: Avoid fill([]); use Array.from with function [OK]

Common Mistakes:

• Changing hash function unnecessarily
• Using wrong array methods
• Ignoring shared reference problem

5. You have a hash table of size 4 using chaining. You insert keys [3, 7, 11, 15, 19]. The hash function is key % 4. After all insertions, which index has the longest chain and what is its content?

medium

A. Index 3: [3, 7, 11, 15, 19]

B. Index 1: [3, 7, 11, 15, 19]

C. Index 3: [3, 7, 11, 15]

D. Index 3: [3, 7, 11]

Solution

1. Step 1: Compute hash index for each key

   3 % 4 = 3, 7 % 4 = 3, 11 % 4 = 3, 15 % 4 = 3, 19 % 4 = 3.

2. Step 2: Insert all keys at index 3

   All keys go into table[3], so chain is [3, 7, 11, 15, 19].

3. Final Answer:

   Index 3: [3, 7, 11, 15, 19] -> Option A

4. Quick Check:

   All keys mod 4 = 3, chain length 5 [OK]

Hint: All keys mod 4 equal 3, so chain at index 3 [OK]

Common Mistakes:

• Miscomputing modulo for some keys
• Assuming keys spread across indexes
• Forgetting all keys collide at same index