Collision Handling Using Chaining in DSA Python - Execution Trace

Concept Flow - Collision Handling Using Chaining

Insert key-value pair

↓

Compute hash index

↓

Check bucket at index

↓

Empty

↓

Done

When inserting a key, compute its hash index. If the bucket is empty, create a new list. If collision occurs, add the new node at the start of the linked list in that bucket.

Execution Sample

DSA Python

hash_table = [[] for _ in range(3)]

# Insert keys 5, 8, 11
for key in [5, 8, 11]:
    index = key % 3
    hash_table[index].insert(0, key)

print(hash_table)

Insert keys 5, 8, and 11 into a hash table of size 3 using chaining to handle collisions.

Execution Table

Step	Operation	Key	Computed Index	Bucket State Before	Bucket State After	Visual State of Hash Table
1	Insert	5	5 % 3 = 2	[]	[5]	[[], [], [5]]
2	Insert	8	8 % 3 = 2	[5]	[8, 5]	[[], [], [8 -> 5]]
3	Insert	11	11 % 3 = 2	[8, 5]	[11, 8, 5]	[[], [], [11 -> 8 -> 5]]
4	End	-	-	-	-	Insertion complete, all keys stored with chaining at index 2

💡 All keys inserted; collisions handled by adding nodes at the head of the linked list in the bucket.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	Final
hash_table	[[], [], []]	[[], [], [5]]	[[], [], [8, 5]]	[[], [], [11, 8, 5]]	[[], [], [11, 8, 5]]
key	-	5	8	11	-
index	-	2	2	2	-

Key Moments - 3 Insights

Why do we insert new keys at the head of the list instead of the tail?

Inserting at the head is faster because it avoids traversing the entire list. As shown in steps 2 and 3 of the execution_table, new keys are added at the start, making insertion O(1).

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

If the bucket is empty (step 1), a new list is created and the key is inserted directly. This is shown by the empty list [] changing to [5] in the bucket.

How does chaining handle collisions?

When multiple keys hash to the same index (steps 2 and 3), chaining stores them in a linked list at that bucket. The visual state shows multiple keys linked together at index 2.

Visual Quiz - 3 Questions

Look at the execution_table, what is the bucket state after inserting key 8?

A [5]

B [5, 8]

C [8, 5]

D []

💡 Hint

Check row 2 in execution_table under 'Bucket State After'

At which step does the first collision occur?

A Step 1

B Step 2

C Step 3

D No collision occurs

💡 Hint

Look at the 'Computed Index' column; keys 5 and 8 both map to index 2

If the hash table size changed to 5, what would be the index for key 11?

A 1

B 2

C 3

D 0

💡 Hint

Calculate 11 % 5 and compare with 'Computed Index' column logic

Concept Snapshot

Collision Handling Using Chaining:
- Use a list (bucket) at each hash index
- On collision, add new key at head of linked list
- Insertion is O(1) by prepending
- Hash index = key % table_size
- Buckets store multiple keys linked
- Handles collisions by chaining keys together

Full Transcript

Collision handling using chaining means when two keys hash to the same index, we store them in a linked list at that index. We compute the hash index by taking the key modulo the table size. If the bucket is empty, we create a new list and insert the key. If not, we add the new key at the start of the list to keep insertion fast. This way, collisions are handled by chaining keys together in the same bucket. The example inserts keys 5, 8, and 11 into a hash table of size 3. All keys map to index 2, so they form a linked list there. This method keeps insertion simple and efficient.