Collision Handling Using Open Addressing Linear Probing in DSA C

Mental Model

When two items want the same spot in a table, we look for the next empty spot in order until we find one.

Analogy: Imagine parking cars in a row of parking spots. If your favorite spot is taken, you move forward one spot at a time until you find an empty one.

Index: 0  1  2  3  4  5  6
Table: [ ] [ ] [ ] [ ] [ ] [ ] [ ]
          ↑
       hash(key) points here

Dry Run Walkthrough

Input: Insert keys 10, 20, 30 into a hash table of size 7 using linear probing with hash function key % 7

Goal: Show how collisions are handled by moving to the next empty slot

Step 1: Insert 10: compute hash 10 % 7 = 3, slot 3 is empty, place 10 there

Index: 0  1  2  3  4  5  6
Table: [ ] [ ] [ ] [10] [ ] [ ] [ ]

Why: First insertion, slot is free so we put 10 there

Step 2: Insert 20: compute hash 20 % 7 = 6, slot 6 is empty, place 20 there

Index: 0  1  2  3  4  5  6
Table: [ ] [ ] [ ] [10] [ ] [ ] [20]

Why: Slot 6 is free, so 20 goes there without collision

Step 3: Insert 30: compute hash 30 % 7 = 2, slot 2 is empty, place 30 there

Index: 0  1  2  3  4  5  6
Table: [ ] [ ] [30] [10] [ ] [ ] [20]

Why: Slot 2 is free, so 30 goes there without collision

Step 4: Insert 17: compute hash 17 % 7 = 3, slot 3 is occupied by 10, move to next slot 4 which is empty, place 17 there

Index: 0  1  2  3  4  5  6
Table: [ ] [ ] [30] [10] [17] [ ] [20]

Why: Collision at slot 3, so linear probing moves to next free slot 4

Result:

Index: 0  1  2  3  4  5  6
Table: [ ] [ ] [30] [10] [17] [ ] [20]

Annotated Code

DSA C

#include <stdio.h>
#define TABLE_SIZE 7

int hash(int key) {
    return key % TABLE_SIZE;
}

void insert(int table[], int key) {
    int index = hash(key);
    int start_index = index;
    while (table[index] != -1) {
        index = (index + 1) % TABLE_SIZE; // move to next slot
        if (index == start_index) {
            printf("Hash table is full, cannot insert %d\n", key);
            return;
        }
    }
    table[index] = key;
}

void print_table(int table[]) {
    printf("Hash Table:\n");
    for (int i = 0; i < TABLE_SIZE; i++) {
        if (table[i] == -1) {
            printf("[%d]: empty\n", i);
        } else {
            printf("[%d]: %d\n", i, table[i]);
        }
    }
}

int main() {
    int table[TABLE_SIZE];
    for (int i = 0; i < TABLE_SIZE; i++) {
        table[i] = -1; // initialize all slots as empty
    }

    insert(table, 10);
    insert(table, 20);
    insert(table, 30);
    insert(table, 17);

    print_table(table);
    return 0;
}

int index = hash(key);

compute initial slot using hash function

while (table[index] != -1) {

check if slot is occupied to handle collision

index = (index + 1) % TABLE_SIZE; // move to next slot

move to next slot in linear probing

if (index == start_index) {

detect full table to stop infinite loop

table[index] = key;

insert key into found empty slot

Output

Hash Table:

[0]: empty

[1]: empty

[2]: 30

[3]: 10

[4]: 17

[5]: empty

[6]: 20

Complexity Analysis

Time: O(n) in worst case because we may check every slot if many collisions occur

Space: O(n) because we store n keys in the table array

vs Alternative: Compared to chaining which uses linked lists, linear probing uses only the array but can have clustering causing slower insert/search

Edge Cases

Inserting into a full table

The code detects full table and prints an error message without infinite loop

DSA C

if (index == start_index) {

Inserting first element

Inserted directly at hashed slot since it is empty

DSA C

while (table[index] != -1) {

When to Use This Pattern

When you see a hash table with collisions and no extra lists, think of linear probing to find next free slot by moving forward.

Common Mistakes

Mistake: Not wrapping around the table when reaching the end during probing
Fix: Use modulo operation to wrap index back to start: index = (index + 1) % TABLE_SIZE

Mistake: Not checking for full table causing infinite loop
Fix: Add a check to stop when index returns to start_index

Summary

It handles collisions by moving forward to find the next empty slot in the hash table.

Use it when you want a simple way to resolve collisions without extra memory for linked lists.

The key insight is to keep trying the next slot until you find an empty one or confirm the table is full.