Hash Table Concept and Hash Functions in DSA C - Time & Space Complexity

Time Complexity: Hash Table Concept and Hash Functions

O(n)

Understanding Time Complexity

We want to understand how fast a hash table can find or store data.

The question is: how does the time to do these actions change as the data grows?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

// Simple hash function example
unsigned int hash(char *str, unsigned int table_size) {
    unsigned int hash_value = 0;
    for (int i = 0; str[i] != '\0'; i++) {
        hash_value = (hash_value * 31 + (unsigned char)str[i]) % table_size;
    }
    return hash_value;
}
    

This code calculates a hash value for a string to find its place in a hash table.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Loop over each character in the input string.
• How many times: Once for every character in the string (length n).

How Execution Grows With Input

As the string gets longer, the time to compute the hash grows in a straight line.

Input Size (n)	Approx. Operations
10	About 10 steps
100	About 100 steps
1000	About 1000 steps

Pattern observation: The work grows directly with the string length.

Final Time Complexity

Time Complexity: O(n)

This means the time to compute the hash grows linearly with the input size.

Common Mistake

[X] Wrong: "Hash functions always run in constant time no matter the input size."

[OK] Correct: The hash function must look at every character in the input, so time grows with input length.

Interview Connect

Understanding how hash functions work and their time cost helps you explain why hash tables are fast and when they might slow down.

Self-Check

"What if the hash function only looked at the first few characters of the string? How would the time complexity change?"

Practice

1. What is the main purpose of a hash function in a hash table?

easy

A. To encrypt the data before storing

B. To convert a key into an index for storing data

C. To sort the data stored in the hash table

D. To count the number of elements in the table

Solution

1. Step 1: Understand the role of a hash function

   A hash function takes a key and converts it into a number called an index.

2. Step 2: Connect index to data storage

   This index tells where to store or find the data in the hash table.

3. Final Answer:

   To convert a key into an index for storing data -> Option B

4. Quick Check:

   Hash function = key to index [OK]

Hint: Hash function maps keys to storage positions [OK]

Common Mistakes:

• Thinking hash function sorts data
• Confusing hash function with encryption
• Believing hash function counts elements

2. Which of the following is the correct way to declare a hash function in C that takes an integer key and returns an integer index?

easy

A. int hashFunction(void key);

B. void hashFunction(int key);

C. int hashFunction(int key);

D. hashFunction int(int key);

Solution

1. Step 1: Check function return type and parameters

   The function should return an int and take an int parameter.

2. Step 2: Verify syntax correctness

   int hashFunction(int key); matches C syntax: return type first, then function name, then parameter list.

3. Final Answer:

   int hashFunction(int key); -> Option C

4. Quick Check:

   Correct C function declaration = int hashFunction(int key); [OK]

Hint: Function syntax: return_type name(parameter_type parameter) [OK]

Common Mistakes:

• Using void return type when int is needed
• Incorrect parameter type syntax
• Wrong order of function declaration parts

3. Consider the following C code snippet for a simple hash function and hash table insertion:

#include <stdio.h>

int hashFunction(int key) {
    return key % 5;
}

int main() {
    int hashTable[5] = {-1, -1, -1, -1, -1};
    int keys[] = {12, 22, 32};
    for (int i = 0; i < 3; i++) {
        int index = hashFunction(keys[i]);
        hashTable[index] = keys[i];
    }
    for (int i = 0; i < 5; i++) {
        printf("%d ", hashTable[i]);
    }
    return 0;
}

What is the output of this program?

medium

A. -1 -1 32 -1 -1

B. 12 22 32 -1 -1

C. -1 22 32 -1 12

D. 12 -1 -1 22 32

Solution

1. Step 1: Calculate hash indices for each key

   12 % 5 = 2, 22 % 5 = 2, 32 % 5 = 2.

2. Step 2: Insert keys into hashTable at calculated indices

   All keys map to index 2, so last key 32 overwrites previous ones. hashTable = {-1, -1, 32, -1, -1}.

3. Final Answer:

   -1 -1 32 -1 -1 -> Option A

4. Quick Check:

   Collision overwrites at index 2 = -1 -1 32 -1 -1 [OK]

Hint: Check modulo results and overwrites in array [OK]

Common Mistakes:

• Assuming keys store at different indices
• Ignoring collisions overwrite
• Miscomputing modulo operation

4. The following C code tries to insert keys into a hash table but has a bug:

int hashFunction(int key) {
    return key % 10;
}

int main() {
    int hashTable[10];
    int keys[] = {5, 15, 25};
    for (int i = 0; i < 3; i++) {
        int index = hashFunction(keys[i]);
        if (hashTable[index] == -1) {
            hashTable[index] = keys[i];
        }
    }
    return 0;
}

What is the bug in this code?

medium

A. Keys array is not declared correctly

B. hashFunction returns wrong index

C. Loop condition should be i <= 3

D. hashTable array is not initialized to -1

Solution

1. Step 1: Check initialization of hashTable

   hashTable is declared but not initialized, so values are garbage, not -1.

2. Step 2: Understand impact on insertion condition

   Condition 'hashTable[index] == -1' may never be true, so keys won't insert properly.

3. Final Answer:

   hashTable array is not initialized to -1 -> Option D

4. Quick Check:

   Uninitialized array causes insertion failure [OK]

Hint: Always initialize hash table slots before use [OK]

Common Mistakes:

• Assuming default zero initialization
• Changing loop bounds incorrectly
• Misunderstanding hash function correctness

5. You want to design a hash function for strings in C that maps each string to an index in a hash table of size 10. Which approach below is the best to reduce collisions?

hard

A. Multiply each character's ASCII by its position, sum all, then modulo 10

B. Use only the ASCII value of the first character modulo 10

C. Return a fixed index like 0 for all strings

D. Sum ASCII values of all characters and take modulo 10

Solution

1. Step 1: Evaluate simple sum method

   Summing ASCII values (Sum ASCII values of all characters and take modulo 10) can cause many collisions for anagrams.

2. Step 2: Consider position-weighted sum

   Multiplying each character by its position (Multiply each character's ASCII by its position, sum all, then modulo 10) creates more unique values, reducing collisions.

3. Step 3: Reject poor methods

   Using only first character (Use only the ASCII value of the first character modulo 10) or fixed index (Return a fixed index like 0 for all strings) causes many collisions.

4. Final Answer:

   Multiply each character's ASCII by its position, sum all, then modulo 10 -> Option A

5. Quick Check:

   Position-weighted sum reduces collisions best [OK]

Hint: Use character positions to spread hash values [OK]

Common Mistakes:

• Using only first character causes collisions
• Ignoring character positions
• Using fixed index for all keys