🔷 LINEAR PROBING VISUALIZER

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🔷 LINEAR PROBING VISUALIZER

Hashing • Collision Resolution • Step-by-Step Animation

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📥 Hash Table Configuration

Table Size Value

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🗂️ Hash Table

🔵 Current Probe

🟡 Collision

🟢 Found

🔴 Deleted

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📈 Live Statistics

Operation -

Hash Index -

Current Index -

Collisions 0

Probes 0

Enter a value and choose an operation.

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📝 Step-by-Step Explanation

1

Linear Probing resolves a collision by checking the next available position sequentially.

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🧮 Mathematical Concept

Hash Function:
h(k) = k mod m

If collision occurs:
h<sub>i</sub>(k) = (h(k) + i) mod m

where:
k = key
m = hash table size
i = probe number

``` Example: Key = 25 Table Size = 10
h(25) = 25 mod 10     = 5

First position = Index 5

If Index 5 is occupied:
Probe 1: (5 + 1) mod 10 = 6
Probe 2: (5 + 2) mod 10 = 7
Probe 3: (5 + 3) mod 10 = 8 ```

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💡 How Linear Probing Works

1

Calculate the hash index using key mod table size.

2

Check the calculated position.

3

If the position is empty, insert the value.

4

If the position is occupied, a collision occurs.

5

Move to the next position: (index + 1) mod table size.

6

Continue until an appropriate position is found.

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🔢 Worked Example

Table Size = 10

Insert 25:
25 mod 10 = 5
Store 25 at Index 5.

Insert 35:
35 mod 10 = 5
Index 5 is occupied → Collision!

Next index:
(5 + 1) mod 10 = 6
Store 35 at Index 6.

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⚖️ Advantages & Disadvantages

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Advantages:
Simple to implement, requires no linked lists, and provides good cache performance because elements are stored in consecutive locations.

−

Disadvantages:
Clustering can occur. As the table becomes full, the number of probes can increase significantly.

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⏱️ Complexity

Average Search O(1)

Average Insert O(1)

Worst Case O(n)

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B.K. PAUL

Bhairab Ganguly College

Data Structures • Hashing • Linear Probing

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