Collision handling (chaining) in Data Structures Theory - Step-by-Step Execution

Concept Flow - Collision handling (chaining)

Start: Insert key

↓

Compute hash index

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Check bucket at index

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Bucket empty?

Yes→Create new chain with key

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Insert key

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Bucket not empty?

No→Add key to existing chain

↓

Insertion done

When inserting a key, compute its hash index. If the bucket is empty, create a new chain with the key. If not, add the key to the existing chain at that bucket.

Execution Sample

Data Structures Theory

hash_table = [[] for _ in range(5)]
keys = [12, 7, 17]
for key in keys:
    index = key % 5
    hash_table[index].append(key)

Insert keys 12, 7, and 17 into a hash table of size 5 using chaining to handle collisions.

Analysis Table

Step	Key	Computed Index	Bucket State Before	Action	Bucket State After
1	12	2	[]	Bucket empty, create chain and insert 12	[12]
2	7	2	[12]	Bucket not empty, append 7 to chain	[12, 7]
3	17	2	[12, 7]	Bucket not empty, append 17 to chain	[12, 7, 17]
4	-	-	All buckets processed	Insertion complete	Final state: [[], [], [12, 7, 17], [], []]

💡 All keys inserted; chaining handled collisions by storing multiple keys in the same bucket list.

State Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	Final
hash_table	[[], [], [], [], []]	[[], [], [12], [], []]	[[], [], [12, 7], [], []]	[[], [], [12, 7, 17], [], []]	[[], [], [12, 7, 17], [], []]
index	-	2	2	2	-
key	-	12	7	17	-

Key Insights - 3 Insights

Why do multiple keys end up in the same bucket?

Because their hash indexes are the same (see execution_table steps 1-3 where index is 2), chaining stores them in a list at that bucket.

What happens if the bucket is empty when inserting a key?

A new list (chain) is created to hold the key, as shown in step 1 where the bucket was empty and key 12 was inserted.

How does chaining help with collisions?

Chaining stores all keys with the same hash index in a list, so no keys are lost or overwritten (see bucket state changes in execution_table).

Visual Quiz - 3 Questions

Look at the execution_table at step 2, what is the bucket state after inserting key 7?

A [12]

B [12, 7]

C [7]

D []

💡 Hint

Check the 'Bucket State After' column at step 2 in execution_table.

At which step does the bucket first become non-empty?

A Step 1

B Step 2

C Step 3

D Step 4

💡 Hint

Look at 'Bucket State Before' column; initially empty, then filled at step 1.

If the hash table size changed to 7, how would the computed index for key 17 change?

A Index would be 2

B Index would be 5

C Index would be 3

D Index would be 0

💡 Hint

Use modulo operation: 17 % 7 = 3; check 'Computed Index' logic in execution_table.

Concept Snapshot

Collision handling with chaining:
- Compute hash index for key
- If bucket empty, create new list and insert key
- If bucket not empty, append key to existing list
- Allows multiple keys per bucket to handle collisions
- Simple and effective method for collision resolution

Full Transcript

This visual execution trace shows how collision handling with chaining works in a hash table. When inserting keys, the hash index is computed using modulo operation. If the bucket at that index is empty, a new list (chain) is created and the key is inserted. If the bucket already contains keys, the new key is appended to the existing list. This way, multiple keys with the same hash index are stored together, preventing data loss due to collisions. The example inserts keys 12, 7, and 17 into a hash table of size 5, all mapping to index 2, demonstrating how chaining stores them in the same bucket list.