Hash Table Concept and Hash Functions in DSA C++ - Build from Scratch

Hash Table Concept and Hash Functions

📖 Scenario: Imagine you are organizing a small library. You want to quickly find books by their unique ID numbers. To do this, you decide to use a hash table, which helps you store and find books fast using a special function called a hash function.

🎯 Goal: You will create a simple hash table using an array and a hash function. You will store book IDs and then find the position where each book should be placed in the array.

📋 What You'll Learn

Create an array to represent the hash table with a fixed size

Create a hash function that calculates the index for a given book ID

Use the hash function to find the index for each book ID

Print the calculated index for each book ID

💡 Why This Matters

🌍 Real World

Hash tables are used in many real-world applications like databases, caches, and indexing systems to quickly find data using keys.

💼 Career

Understanding hash tables and hash functions is essential for software developers, especially those working with data storage, retrieval, and optimization.

1

Create the hash table array

Create an integer array called hashTable with size 10 and initialize all elements to -1.

DSA C++

int hashTable[10] = {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1};
// Your code here

Hint

Use an array of size 10 and set all values to -1 to show empty slots.

2

Create the hash function

Create a function called hashFunction that takes an integer key and returns key % 10.

DSA C++

int hashFunction(int key) {
    // Your code here
}

Hint

The hash function returns the remainder when the key is divided by 10.

3

Calculate hash indexes for book IDs

Create an integer array called bookIDs with values {15, 25, 35, 45}. Then, use a for loop with variable i to iterate over bookIDs and calculate the hash index for each book ID using hashFunction(bookIDs[i]). Store the result in an integer array called indexes of size 4.

DSA C++

int bookIDs[4] = {15, 25, 35, 45};
int indexes[4];
// Your code here

Hint

Use a loop from 0 to 3 to calculate each index and store it in indexes.

4

Print the hash indexes

Use a for loop with variable i to print each element of the indexes array on a new line.

DSA C++

for (int i = 0; i < 4; i++) {
    // Your code here
}

Hint

Print each index on its own line using std::cout.

Practice

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

easy

A. To convert a key into an index for storing values

B. To sort the keys in ascending order

C. To encrypt the data stored in the 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 an index number that points to a position in the hash table.

2. Step 2: Identify the purpose in context

   This index helps quickly find or store the value associated with the key without searching the entire table.

3. Final Answer:

   To convert a key into an index for storing values -> Option A

4. Quick Check:

   Hash function = key to index [OK]

Hint: Hash function maps keys to indexes fast [OK]

Common Mistakes:

• Thinking hash functions sort keys
• Confusing hashing with encryption
• Assuming hash function counts elements

2. Which of the following is the correct syntax to declare a hash table using unordered_map in C++?

easy

A. hash_map table;

B. unordered_map table;

C. map table;

D. unordered table;

Solution

1. Step 1: Recall C++ hash table declaration

   The standard C++ hash table is declared using unordered_map from the STL.

2. Step 2: Check each option

   unordered_map table; uses unordered_map which is correct syntax. hash_map table; uses hash_map which is non-standard. map table; uses map which is a balanced tree, not a hash table. unordered table; uses unordered which is invalid.

3. Final Answer:

   unordered_map<int, string> table; -> Option B

4. Quick Check:

   unordered_map syntax = correct [OK]

Hint: Use unordered_map for hash tables in C++ [OK]

Common Mistakes:

• Using map instead of unordered_map
• Using non-standard hash_map
• Incorrect container names

3. What will be the output of the following C++ code snippet?

#include <iostream>
#include <unordered_map>
using namespace std;

int main() {
    unordered_map table;
    table[1] = "apple";
    table[2] = "banana";
    table[3] = "cherry";
    cout << table[2] << endl;
    return 0;
}

medium

A. Compilation error

B. apple

C. cherry

D. banana

Solution

1. Step 1: Understand the unordered_map insertions

   Keys 1, 2, 3 are assigned values "apple", "banana", and "cherry" respectively.

2. Step 2: Check the output statement

   The code prints the value stored at key 2, which is "banana".

3. Final Answer:

   banana -> Option D

4. Quick Check:

   table[2] = banana [OK]

Hint: Access value by key directly with table[key] [OK]

Common Mistakes:

• Confusing keys and values
• Assuming order matters in unordered_map
• Expecting compilation error due to syntax

4. Identify the error in the following C++ code that uses a hash table:

#include <iostream>
#include <unordered_map>
using namespace std;

int main() {
    unordered_map table;
    table.insert("key1", 100);
    cout << table["key1"] << endl;
    return 0;
}

medium

A. insert() requires a pair, not two separate arguments

B. unordered_map keys cannot be strings

C. table["key1"] is invalid syntax

D. Missing #include <map> header

Solution

1. Step 1: Check insert() method usage

   The insert() method expects a single argument of type pair, not two separate arguments.

2. Step 2: Identify correct usage

   Correct usage: table.insert(make_pair("key1", 100)); or table["key1"] = 100;

3. Final Answer:

   insert() requires a pair, not two separate arguments -> Option A

4. Quick Check:

   insert() needs pair argument [OK]

Hint: insert() needs pair, not separate key and value [OK]

Common Mistakes:

• Passing key and value as separate arguments to insert()
• Thinking string keys are invalid
• Confusing table[key] syntax

5. You want to design a hash function for strings that minimizes collisions for English words. Which approach is best?

hard

A. Sum ASCII values of all characters modulo table size

B. Use the length of the string modulo table size

C. Use polynomial rolling hash combining character codes and powers

D. Use the first character's ASCII value only

Solution

1. Step 1: Evaluate simple hash methods

   Summing ASCII values or using string length often causes many collisions because different strings can have same sums or lengths.

2. Step 2: Understand polynomial rolling hash

   This method combines character codes with powers of a base number, spreading keys more evenly and reducing collisions.

3. Step 3: Compare options

   Use polynomial rolling hash combining character codes and powers is the best because it balances speed and collision reduction for strings.

4. Final Answer:

   Use polynomial rolling hash combining character codes and powers -> Option C

5. Quick Check:

   Polynomial rolling hash = fewer collisions [OK]

Hint: Polynomial rolling hash reduces collisions best [OK]

Common Mistakes:

• Using simple sums causing many collisions
• Ignoring string content beyond length or first char
• Choosing inefficient or weak hash functions