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

Concept Flow - Collision handling (open addressing)

Start Insert

↓

Compute Hash Index

↓

Is Slot Empty?

No→Probe Next Slot

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Wrap Around if Needed

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Insert Key Here

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End Insert

When inserting, compute the hash index. If the slot is taken, check the next slot until an empty one is found, wrapping around if needed.

Execution Sample

Data Structures Theory

hash_table = [None]*5
keys = [12, 22, 32]
for key in keys:
  index = key % 5
  while hash_table[index] is not None:
    index = (index + 1) % 5
  hash_table[index] = key

Insert keys 12, 22, 32 into a hash table of size 5 using linear probing to handle collisions.

Analysis Table

Step	Key	Computed Index	Slot Empty?	Action	Hash Table State
1	12	2	Yes	Insert 12 at index 2	[None, None, 12, None, None]
2	22	2	No	Probe next index 3	[None, None, 12, None, None]
3	22	3	Yes	Insert 22 at index 3	[None, None, 12, 22, None]
4	32	2	No	Probe next index 3	[None, None, 12, 22, None]
5	32	3	No	Probe next index 4	[None, None, 12, 22, None]
6	32	4	Yes	Insert 32 at index 4	[None, None, 12, 22, 32]
7	-	-	-	All keys inserted	[None, None, 12, 22, 32]

💡 All keys inserted; no empty slots needed beyond index 4.

State 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, 12, None, None]	[None, None, 12, None, None]	[None, None, 12, 22, None]	[None, None, 12, 22, None]	[None, None, 12, 22, None]	[None, None, 12, 22, 32]	[None, None, 12, 22, 32]
index	-	2	3	3	3	4	4	-

Key Insights - 3 Insights

Why do we check the next slot when the computed index is already occupied?

Because in open addressing, if the slot is taken, we must find the next available slot by probing, as shown in steps 2 and 4 in the execution_table.

What happens if we reach the end of the table while probing?

We wrap around to the start of the table and continue probing, as indicated by the modulo operation in the code and the wrap-around step in the concept_flow.

Why do we stop probing once we find an empty slot?

Because the empty slot is where we can safely insert the new key without overwriting existing data, as shown in steps 1, 3, and 6.

Visual Quiz - 3 Questions

Look at the execution_table, what is the hash_table state after inserting key 22?

A [None, None, 22, None, None]

B [None, None, 12, None, None]

C [None, None, 12, 22, None]

D [None, None, 12, None, 22]

💡 Hint

Check the hash_table state in row 3 of the execution_table after step 3.

At which step does the condition 'Slot Empty?' become false for the first time?

A Step 1

B Step 2

C Step 4

D Step 5

💡 Hint

Look at the 'Slot Empty?' column in the execution_table to find the first 'No'.

If the table size was 3 instead of 5, what would happen when inserting key 32?

A It would insert at index 0 after probing.

B It would cause an infinite loop probing slots.

C It would insert at index 2 without probing.

D It would overwrite an existing key.

💡 Hint

Consider modulo operation with table size 3 and how probing wraps around.

Concept Snapshot

Open addressing handles collisions by probing for the next empty slot.
Compute hash index: index = key % table_size.
If slot occupied, check next slot (linear probing).
Wrap around to start if end reached.
Insert key at first empty slot found.
No extra memory needed for chaining.

Full Transcript

Collision handling with open addressing means when two keys hash to the same index, we look for the next empty slot to place the new key. We start by computing the hash index using modulo operation. If the slot is empty, we insert the key there. If not, we move to the next slot, wrapping around to the start if we reach the end of the table. This process continues until an empty slot is found. The example shows inserting keys 12, 22, and 32 into a table of size 5. Key 12 goes to index 2 directly. Key 22 also hashes to 2 but finds it occupied, so it moves to index 3. Key 32 probes indexes 2 and 3, both occupied, and inserts at index 4. This method avoids linked lists and keeps all keys in the table itself.