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

Time Complexity: Hash Table Concept and Hash Functions

O(k)

Understanding Time Complexity

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

How does the time to do these actions change as we add more items?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

function hash(key, size) {
  let hashValue = 0;
  for (let i = 0; i < key.length; i++) {
    hashValue += key.charCodeAt(i);
  }
  return hashValue % size;
}

function insert(table, key, value) {
  const index = hash(key, table.length);
  table[index] = value;
}
    

This code creates a simple hash function and inserts a value into a hash table using the hash index.

Identify Repeating Operations

• Primary operation: Loop over each character in the key string inside the hash function.
• How many times: Once per insert, the loop runs as many times as the key length.

How Execution Grows With Input

The time to compute the hash grows with the length of the key, not the number of items in the table.

Input Size (key length)	Approx. Operations
10	10 additions
100	100 additions
1000	1000 additions

Pattern observation: The work grows linearly with the key length, but inserting into the table is constant time.

Final Time Complexity

Time Complexity: O(k)

This means the time depends on the key length (k), not the number of items stored.

Common Mistake

[X] Wrong: "Hash table operations always take the same time no matter what."

[OK] Correct: The hash function time depends on the key length, so longer keys take more time to process.

Interview Connect

Understanding how hash functions affect speed helps you explain why hash tables are fast and when they might slow down.

Self-Check

"What if the hash function used a fixed number of characters from the key instead of the whole key? How would the time complexity change?"

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 data

B. To sort the keys in alphabetical 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 a number that can be used as an index in the hash table.

2. Step 2: Identify the correct purpose

   Sorting keys or encrypting data is not the job of a hash function; it only maps keys to indexes.

3. Final Answer:

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

4. Quick Check:

   Hash function = key to index [OK]

Hint: Hash functions map keys to indexes, not sort or encrypt [OK]

Common Mistakes:

• Thinking hash functions sort keys
• Confusing hash functions with encryption
• Believing hash functions count elements

2. Which of the following is the correct way to create an empty hash table (object) in JavaScript?

easy

A. const table = [];

B. const table = {};

C. const table = new Map();

D. const table = new HashTable();

Solution

1. Step 1: Recall JavaScript object syntax

   In JavaScript, an empty object is created using curly braces {} which can act as a hash table.

2. Step 2: Evaluate options

   const table = []; creates an array, not a hash table. const table = new Map(); creates a Map, which is a different structure. const table = new HashTable(); is invalid as HashTable is not a built-in class.

3. Final Answer:

   const table = {}; -> Option B

4. Quick Check:

   Empty hash table = {} [OK]

Hint: Use curly braces {} to create an empty object hash table [OK]

Common Mistakes:

• Using [] which creates an array, not a hash table
• Using Map() which is different from object
• Assuming HashTable is a built-in JavaScript class

3. What will be the output of the following code?

const hashTable = {};
hashTable['apple'] = 5;
hashTable['banana'] = 3;
hashTable['apple'] = 10;
console.log(hashTable['apple']);

medium

A. 10

B. 3

C. 5

D. undefined

Solution

1. Step 1: Understand key assignment in hash tables

   Assigning a value to an existing key updates the value stored at that key.

2. Step 2: Trace the code

   Initially, 'apple' is set to 5, then updated to 10. So, hashTable['apple'] will be 10.

3. Final Answer:

   10 -> Option A

4. Quick Check:

   Last assignment to 'apple' = 10 [OK]

Hint: Last value assigned to a key is stored [OK]

Common Mistakes:

• Thinking the first assigned value remains
• Confusing keys and values
• Expecting undefined for existing keys

4. Identify the error in the following code snippet that tries to use a hash function:

function hash(key) {
  return key.length % 10;
}
const table = {};
table[hash('cat')] = 'animal';
table[hash('dog')] = 'animal';
console.log(table['cat']);

medium

A. Using key.length causes runtime error

B. Cannot use numbers as keys in JavaScript objects

C. Accessing table['cat'] is incorrect; should use table[hash('cat')]

D. Hash function should return a string, not a number

Solution

1. Step 1: Understand how keys are stored and accessed

   The hash function returns a number used as a key in the table object.

2. Step 2: Check how the table is accessed

   The code tries to access table['cat'], but the key stored is a number from hash('cat'), so it should access table[hash('cat')].

3. Final Answer:

   Accessing table['cat'] is incorrect; should use table[hash('cat')] -> Option C

4. Quick Check:

   Access key must match stored key type [OK]

Hint: Access hash table with hashed key, not original key [OK]

Common Mistakes:

• Accessing with original key instead of hashed key
• Thinking keys must be strings only
• Assuming hash function causes error due to key.length

5. Given the hash function below, what is the best way to handle collisions when two keys produce the same hash?

function simpleHash(key) {
  let sum = 0;
  for (let char of key) {
    sum += char.charCodeAt(0);
  }
  return sum % 5;
}

Choose the best collision handling method.

hard

A. Increase the hash size to avoid collisions

B. Overwrite the existing value with the new one

C. Ignore the new key and keep the old value

D. Use chaining by storing multiple values in a list at the same index

Solution

1. Step 1: Understand collision in hash tables

   When two keys produce the same hash index, a collision occurs and must be handled to store both values.

2. Step 2: Evaluate collision handling methods

   Overwriting loses data, ignoring new keys is incorrect, increasing hash size alone doesn't solve collisions. Chaining stores multiple values in a list at the same index, preserving all data.

3. Final Answer:

   Use chaining by storing multiple values in a list at the same index -> Option D

4. Quick Check:

   Chaining handles collisions by lists [OK]

Hint: Use lists (chaining) to store multiple values at one index [OK]

Common Mistakes:

• Overwriting values causing data loss
• Ignoring new keys on collision
• Thinking increasing hash size removes all collisions