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

Time Complexity: Hash Table Concept and Hash Functions

O(k + m)

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 operations change as we add more items?

Scenario Under Consideration

Analyze the time complexity of inserting and searching in a hash table using a hash function.

class HashTable {
  private buckets: Array> = [];
  private size: number;

  constructor(size: number) {
    this.size = size;
    this.buckets = Array(size).fill(null).map(() => []);
  }

  private hash(key: string): number {
    let hashValue = 0;
    for (const char of key) {
      hashValue += char.charCodeAt(0);
    }
    return hashValue % this.size;
  }

  set(key: string, value: number): void {
    const index = this.hash(key);
    // Check if key already exists and update
    for (let i = 0; i < this.buckets[index].length; i++) {
      if (this.buckets[index][i][0] === key) {
        this.buckets[index][i][1] = value;
        return;
      }
    }
    this.buckets[index].push([key, value]);
  }

  get(key: string): number | undefined {
    const index = this.hash(key);
    for (const [k, v] of this.buckets[index]) {
      if (k === key) return v;
    }
    return undefined;
  }
}
    

This code creates a hash table that stores key-value pairs using a simple hash function and handles collisions by storing multiple pairs in the same bucket.

Identify Repeating Operations

Look at what repeats when we insert or search:

• Primary operation: Loop over characters in the key to compute the hash.
• How many times: Once per operation, proportional to key length.
• Secondary operation: Loop over items in a bucket when searching for a key.
• How many times: Depends on number of items in that bucket (collision count).

How Execution Grows With Input

As we add more items, the time to compute the hash stays about the same (depends on key length, not number of items).

But searching inside a bucket can get slower if many items land in the same bucket.

Input Size (n)	Approx. Operations
10	Hash calculation + few items in bucket
100	Hash calculation + more items in bucket if collisions occur
1000	Hash calculation + possibly many items in bucket if hash is poor

Pattern observation: Hash calculation cost stays steady; bucket search cost grows with collisions.

Final Time Complexity

Time Complexity: O(k + m)

This means time grows with key length k plus the number of items m in the bucket due to collisions.

Common Mistake

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

[OK] Correct: If many keys collide, searching a bucket can take longer, so time depends on how well the hash function spreads keys.

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 we used a better hash function that spreads keys evenly? How would the time complexity change?"

Practice

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

easy

A. To sort the keys in ascending order

B. To count the number of elements in the table

C. To encrypt the stored data for security

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

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 storage in hash table

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

3. Final Answer:

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

4. Quick Check:

   Hash function = key to index [OK]

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

Common Mistakes:

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

2. Which of the following is the correct way to declare a hash table (Map) in TypeScript?

easy

A. const map = new map();

B. const map = Map;

C. const map = new Map();

D. const map = new Map(); string, number;

Solution

1. Step 1: Recall TypeScript Map syntax

   In TypeScript, a Map is created with new Map().

2. Step 2: Check each option's syntax

   const map = new Map(); uses correct syntax: new Map(). Others have syntax errors or wrong usage.

3. Final Answer:

   const map = new Map(); -> Option C

4. Quick Check:

   Map declaration = new Map<Key, Value>() [OK]

Hint: Use new Map() to declare [OK]

Common Mistakes:

• Omitting 'new' keyword
• Using lowercase 'map' instead of 'Map'
• Incorrect generic syntax

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

const map = new Map();
map.set('apple', 5);
map.set('banana', 3);
map.set('apple', 10);
console.log(map.get('apple'));

medium

A. 10

B. Error

C. undefined

D. 5

Solution

1. Step 1: Understand Map set behavior

   Setting a key that already exists updates its value.

2. Step 2: Trace the code

   First 'apple' is set to 5, then updated to 10. So map.get('apple') returns 10.

3. Final Answer:

   10 -> Option A

4. Quick Check:

   Updated value = 10 [OK]

Hint: Last set value for key is stored [OK]

Common Mistakes:

• Assuming first value stays
• Thinking get returns undefined if key repeated
• Confusing Map with object property behavior

4. Identify the error in the following TypeScript code using a hash table:

const map = new Map();
map.set(1, 'one');
map.set(2, 'two');
console.log(map.get('1'));

medium

A. Missing parentheses in map.get call

B. Using string '1' instead of number 1 as key

C. Map keys must be strings only

D. Cannot mix number and string values in Map

Solution

1. Step 1: Check Map key type

   Map is declared with number keys, so keys must be numbers.

2. Step 2: Analyze map.get argument

   map.get('1') uses string '1', which does not match number 1 key, so returns undefined.

3. Final Answer:

   Using string '1' instead of number 1 as key -> Option B

4. Quick Check:

   Key type mismatch causes undefined [OK]

Hint: Match key types exactly when using get() [OK]

Common Mistakes:

• Assuming '1' and 1 are same keys
• Thinking Map keys must be strings
• Ignoring type mismatch errors

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

hard

A. Multiply each character code by a prime number and sum, then modulo table size

B. Use the length of the string as the hash value

C. Sum the ASCII codes of all characters and take modulo table size

D. Use the first character's ASCII code only

Solution

1. Step 1: Understand collision minimization

   Good hash functions spread keys evenly to reduce collisions.

2. Step 2: Evaluate each approach

   Sum the ASCII codes of all characters and take modulo table size sums codes but can cause many collisions (e.g., 'abc' and 'cab'). Use the length of the string as the hash value uses length only, very poor. Use the first character's ASCII code only uses first char only, also poor. Multiply each character code by a prime number and sum, then modulo table size uses weighted sum with primes, better distribution.

3. Final Answer:

   Multiply each character code by a prime number and sum, then modulo table size -> Option A

4. Quick Check:

   Weighted sum with primes = better hash [OK]

Hint: Use prime multipliers for better hash spread [OK]

Common Mistakes:

• Using simple sums causing collisions
• Ignoring character positions
• Using string length as hash