Collision Handling Using Open Addressing Linear Probing in DSA Python - Execution Trace

Concept Flow - Collision Handling Using Open Addressing Linear Probing

Start: Insert key

↓

Compute hash index

↓

Check slot at index

↓

Slot empty?

Yes→Insert key here

No↓

Move to next index (linear probing)

↓

Index wraps around?

Yes→Start from 0

↓

Repeat check slot

↓

If full table, insertion fails

Insert key by hashing to index; if occupied, move step-by-step to next slot until empty found or table full.

Execution Sample

DSA Python

hash_table = [None]*5
keys = [7, 12, 17]
for key in keys:
    index = key % 5
    while hash_table[index] is not None:
        index = (index + 1) % 5
    hash_table[index] = key
print(hash_table)

Insert keys 7, 12, 17 into a size 5 hash table using linear probing for collisions.

Execution Table

Step	Operation	Key	Computed Index	Slot Status	Action	Hash Table State
1	Insert	7	7 % 5 = 2	Empty	Insert at index 2	[None, None, 7, None, None]
2	Insert	12	12 % 5 = 2	Occupied (7)	Probe next index 3	[None, None, 7, None, None]
3	Check	12	3	Empty	Insert at index 3	[None, None, 7, 12, None]
4	Insert	17	17 % 5 = 2	Occupied (7)	Probe next index 3	[None, None, 7, 12, None]
5	Check	17	3	Occupied (12)	Probe next index 4	[None, None, 7, 12, None]
6	Check	17	4	Empty	Insert at index 4	[None, None, 7, 12, 17]
7	End	-	-	-	-	[None, None, 7, 12, 17]

💡 All keys inserted; linear probing resolved collisions by moving to next empty slots.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	After Step 5	After Step 6	Final
hash_table	[None, None, None, None, None]	[None, None, 7, None, None]	[None, None, 7, None, None]	[None, None, 7, 12, None]	[None, None, 7, 12, None]	[None, None, 7, 12, None]	[None, None, 7, 12, 17]	[None, None, 7, 12, 17]
index	N/A	2	2 then 3	3	2 then 3 then 4	4	N/A	N/A
key	N/A	7	12	12	17	17	N/A	N/A

Key Moments - 3 Insights

Why do we move to the next index when the computed slot is occupied?

Because the slot at the computed index already holds a key (see steps 2 and 4 in execution_table), linear probing moves sequentially to the next slot to find an empty place.

What happens if the index reaches the end of the table during probing?

The index wraps around to 0 (start of the table) as shown in the concept_flow, ensuring all slots are checked circularly.

Why does the insertion stop after finding an empty slot?

Because the key is successfully placed there, no need to continue probing (see steps 1, 3, and 6 where insertion happens).

Visual Quiz - 3 Questions

Look at the execution_table at step 4, what is the slot status at computed index?

A Empty

B Occupied by 12

C Occupied by 7

D Occupied by 17

💡 Hint

Check the 'Slot Status' column at step 4 in execution_table.

At which step does the key 12 get inserted into the hash table?

A Step 2

B Step 3

C Step 5

D Step 6

💡 Hint

Look for the 'Action' column mentioning insertion for key 12 in execution_table.

If the hash table size was 3 instead of 5, what would happen when inserting key 17?

A Insertion would fail due to full table

B Inserted at index 2 without probing

C Probing would wrap around and find an empty slot

D Inserted at index 1 directly

💡 Hint

Consider the table size and probing steps in variable_tracker and concept_flow.

Concept Snapshot

Collision Handling Using Open Addressing Linear Probing:
- Compute index = key % table_size
- If slot occupied, move to next index (index + 1) % table_size
- Repeat until empty slot found or table full
- Insert key at empty slot
- Wrap around to start if end reached
- Ensures all slots checked sequentially
- Stops when key inserted or table full

Full Transcript

This concept shows how to handle collisions in a hash table using open addressing with linear probing. When inserting a key, we compute its index by taking the key modulo the table size. If the slot at that index is empty, we insert the key there. If it is occupied, we move step-by-step to the next slot, wrapping around to the start if needed, until we find an empty slot. This process is called linear probing. The execution table traces inserting keys 7, 12, and 17 into a size 5 table, showing how collisions at index 2 are resolved by moving to the next free slots. The variable tracker shows how the hash table and index change after each step. Key moments clarify why we probe next slots and how wrap-around works. The visual quiz tests understanding of slot status, insertion steps, and behavior with smaller table sizes. The snapshot summarizes the key rules for linear probing collision handling.