Collision Handling Using Open Addressing Linear Probing in DSA Typescript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is open addressing in hash tables?

Open addressing is a collision handling method where, if a collision occurs, the algorithm searches for the next empty slot in the hash table to store the item instead of using linked lists.

beginner

Explain linear probing in open addressing.

Linear probing handles collisions by checking the next slot in the table sequentially (one by one) until an empty slot is found to insert the new item.

intermediate

What problem can occur with linear probing and how is it called?

Linear probing can cause primary clustering, where groups of filled slots form clusters, increasing the search time for empty slots.

beginner

In linear probing, how do you find the next index after a collision at index i in a table of size n?

The next index is calculated as (i + 1) mod n, moving sequentially through the table and wrapping around to the start if needed.

intermediate

Why is it important to keep the hash table size a prime number when using linear probing?

Using a prime number for the table size helps ensure that the probing sequence visits every slot, reducing the chance of infinite loops and improving distribution.

What does linear probing do when a collision happens?

A Checks the next slot sequentially until an empty one is found

B Creates a linked list at the collided slot

C Rehashes the entire table

D Deletes the collided item

Linear probing searches the next slots one by one until it finds an empty slot.

Which problem is common with linear probing?

A Stack overflow

B Primary clustering

C Memory leak

D Deadlock

Primary clustering happens when many items cluster together, slowing down insertion and search.

How is the next index calculated in linear probing for a table of size n?

A (current_index * 2) mod n

B Random index

C (current_index - 1) mod n

D (current_index + 1) mod n

Linear probing moves to the next slot by adding 1 and wrapping around using modulo.

Why use a prime number for the hash table size in linear probing?

A To ensure all slots can be probed

B To reduce memory usage

C To speed up multiplication

D To avoid collisions completely

Prime table size helps the probe sequence cover all slots, avoiding infinite loops.

What happens if the hash table is full during linear probing?

A The oldest item is removed

B The table automatically resizes

C Insertion fails because no empty slot is found

D The item is inserted anyway

If no empty slot is found after probing all slots, insertion fails.

Describe how collision handling works using open addressing with linear probing.

Think about how you find a free parking spot when your first choice is taken.

Explain why choosing a prime number for the hash table size is important in linear probing.

Consider how prime numbers help in cycling through all positions evenly.

Practice

1. What is the main idea behind linear probing in collision handling for hash tables?

easy

A. Double the size of the hash table when a collision happens.

B. Use a linked list to store multiple values at the same index.

C. If a collision occurs, check the next slot sequentially until an empty slot is found.

D. Replace the existing value at the collided slot with the new value.

Solution

1. Step 1: Understand collision handling

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

2. Step 2: Explain linear probing method

   Linear probing resolves collisions by checking the next slot in order until an empty slot is found.

3. Final Answer:

   If a collision occurs, check the next slot sequentially until an empty slot is found. -> Option C

4. Quick Check:

   Linear probing = sequential slot check [OK]

Hint: Linear probing means try next slot one by one [OK]

Common Mistakes:

• Confusing linear probing with chaining
• Thinking collision means resizing immediately
• Replacing existing values on collision

2. Which of the following TypeScript code snippets correctly implements the linear probing step to find the next index after a collision in a hash table of size size?

easy

A. let nextIndex = currentIndex % size;

B. let nextIndex = (currentIndex * 2) % size;

C. let nextIndex = (currentIndex - 1) % size;

D. let nextIndex = (currentIndex + 1) % size;

Solution

1. Step 1: Understand linear probing index calculation

   Linear probing moves to the next slot by adding 1 to the current index and wrapping around using modulo.

2. Step 2: Check code correctness

   let nextIndex = (currentIndex + 1) % size; correctly calculates nextIndex as (currentIndex + 1) % size, ensuring wrap-around.

3. Final Answer:

   let nextIndex = (currentIndex + 1) % size; -> Option D

4. Quick Check:

   Next index = (current + 1) mod size [OK]

Hint: Add 1 and mod by size for next slot [OK]

Common Mistakes:

• Multiplying index instead of adding
• Subtracting index causing negative values
• Not using modulo for wrap-around

3. Consider a hash table of size 5 using linear probing. The hash function is h(key) = key % 5. Insert keys in this order: 7, 12, 17. What is the final state of the hash table (index: value)?

medium

A. {0: null, 1: null, 2: 7, 3: 12, 4: 17}

B. {0: 17, 1: 7, 2: 12, 3: null, 4: null}

C. {0: 12, 1: 17, 2: 7, 3: null, 4: null}

D. {0: null, 1: 7, 2: null, 3: 12, 4: 17}

Solution

1. Step 1: Calculate initial hash indices

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

2. Step 2: Insert keys using linear probing

   Insert 7 at index 2. For 12, index 2 is occupied, try 3 (empty), insert 12. For 17, indices 2 and 3 occupied, try 4 (empty), insert 17.

3. Final Answer:

   {0: null, 1: null, 2: 7, 3: 12, 4: 17} -> Option A

4. Quick Check:

   All keys start at 2, linear probe fills next slots [OK]

Hint: All keys hash same, fill next slots sequentially [OK]

Common Mistakes:

• Placing all keys at index 2 ignoring collisions
• Not wrapping around the table
• Misplacing keys at wrong indices

4. The following TypeScript code tries to insert keys into a hash table using linear probing. What is the bug that causes an infinite loop?

const size = 5;
const table = new Array(size).fill(null);
function hash(key: number) { return key % size; }
function insert(key: number) {
  let index = hash(key);
  while (table[index] !== null) {
    index = (index + 1) % size;
  }
  table[index] = key;
}
insert(5);
insert(10);
insert(15);
insert(20);
insert(25);
insert(30);

medium

A. No check for full table causing infinite loop when table is full.

B. Hash function is incorrect and returns negative indices.

C. Array initialization with null is wrong; should use undefined.

D. Insert function does not update index inside the loop.

Solution

1. Step 1: Analyze insert loop behavior

   The while loop keeps moving index until an empty slot is found.

2. Step 2: Identify missing full table check

   If the table is full, the loop cycles endlessly without exit condition.

3. Final Answer:

   No check for full table causing infinite loop when table is full. -> Option A

4. Quick Check:

   Full table without exit causes infinite loop [OK]

Hint: Add full table check to avoid infinite loop [OK]

Common Mistakes:

• Assuming hash function returns negative
• Thinking null vs undefined causes loop
• Forgetting to update index inside loop

5. You have a hash table of size 7 using linear probing. The hash function is h(key) = key % 7. You insert keys: 14, 21, 28, 35, 42. Then you delete key 21. What is the correct way to handle deletion to avoid search errors in linear probing?

hard

A. Set the slot to null immediately to free it for new insertions.

B. Mark the slot as a special 'deleted' marker instead of null to continue probing.

C. Rehash the entire table after deletion to fix collisions.

D. Do nothing; deletion is not needed in linear probing.

Solution

1. Step 1: Understand deletion problem in linear probing

   Setting slot to null breaks the probe chain, causing search failures for keys after deleted slot.

2. Step 2: Use special 'deleted' marker

   Marking slot as 'deleted' allows probing to continue while allowing new insertions.

3. Final Answer:

   Mark the slot as a special 'deleted' marker instead of null to continue probing. -> Option B

4. Quick Check:

   Deleted marker keeps probe chain intact [OK]

Hint: Use 'deleted' marker slot, not null, after deletion [OK]

Common Mistakes:

• Setting slot to null breaks search chain
• Rehashing entire table unnecessarily
• Ignoring deletion impact on probing