Why Rabin Karp String Matching in DSA Typescript?

The Big Idea

What if you could find a phrase in a huge book almost instantly without reading every word?

The Scenario

Imagine you have a huge book and you want to find every place where a certain phrase appears. You try to read every page and check each word one by one to see if it matches your phrase.

The Problem

This manual way is very slow and tiring. Checking every word and comparing it letter by letter wastes a lot of time, especially if the book is very long or the phrase appears many times.

The Solution

Rabin Karp uses a clever trick: it turns words into numbers (called hashes) so it can quickly compare these numbers instead of letters. This way, it can skip many unnecessary checks and find matches faster.

Before vs After

✗ Before

for (let i = 0; i <= text.length - pattern.length; i++) {
  if (text.substring(i, i + pattern.length) === pattern) {
    console.log('Match at', i);
  }
}

✓ After

let patternHash = hash(pattern);
for (let i = 0; i <= text.length - pattern.length; i++) {
  let currentHash = hash(text.substring(i, i + pattern.length));
  if (currentHash === patternHash) {
    console.log('Match at', i);
  }
}

What It Enables

It enables fast searching of patterns in large texts by comparing numbers instead of letters.

Real Life Example

Search engines use this method to quickly find your search words inside billions of web pages.

Key Takeaways

Manual letter-by-letter search is slow for big texts.

Rabin Karp uses hashing to speed up pattern matching.

This method helps find matches quickly and efficiently.

Practice

1. What is the main idea behind the Rabin Karp String Matching algorithm?

easy

A. Use hashing to find pattern matches efficiently

B. Use recursion to match patterns

C. Sort the text and pattern before matching

D. Use brute force to check every substring

Solution

1. Step 1: Understand the algorithm's approach

   The Rabin Karp algorithm uses a hash function to convert strings into numbers for quick comparison.

2. Step 2: Identify the benefit of hashing

   Hashing allows checking if substrings match the pattern by comparing hash values instead of characters directly.

3. Final Answer:

   Use hashing to find pattern matches efficiently -> Option A

4. Quick Check:

   Rabin Karp = hashing for matching [OK]

Hint: Remember: Rabin Karp uses hashing to speed up matching [OK]

Common Mistakes:

• Thinking it uses recursion
• Assuming it sorts strings before matching
• Confusing it with brute force checking

2. Which of the following is the correct way to compute the initial hash of a string s of length m using a base d and a prime modulus q in TypeScript?

easy

A. let hash = 0; for(let i=0; i

B. let hash = 1; for(let i=0; i

C. let hash = 0; for(let i=0; i

D. let hash = 0; for(let i=0; i

Solution

1. Step 1: Understand the rolling hash formula

   The hash is computed as hash = (hash * d + current_char) mod q for each character.

2. Step 2: Match the code with the formula

   let hash = 0; for(let i=0; i

3. Final Answer:

   let hash = 0; for(let i=0; i -> Option A

4. Quick Check:

   Rolling hash = (prev_hash * d + char) % q [OK]

Hint: Hash = (prev_hash * base + char) mod prime [OK]

Common Mistakes:

• Mixing up base and modulus in calculation
• Starting hash from 1 instead of 0
• Incorrect order of operations in formula

3. What will be the output of the following TypeScript code snippet using Rabin Karp to find pattern "abc" in text "ababcabc"?

const text = "ababcabc";
const pattern = "abc";
const d = 256;
const q = 101;

function rabinKarp(text: string, pattern: string): number[] {
  const m = pattern.length;
  const n = text.length;
  let p = 0, t = 0, h = 1;
  const result: number[] = [];

  for (let i = 0; i < m - 1; i++) h = (h * d) % q;

  for (let i = 0; i < m; i++) {
    p = (d * p + pattern.charCodeAt(i)) % q;
    t = (d * t + text.charCodeAt(i)) % q;
  }

  for (let i = 0; i <= n - m; i++) {
    if (p === t) {
      let match = true;
      for (let j = 0; j < m; j++) {
        if (text[i + j] !== pattern[j]) {
          match = false;
          break;
        }
      }
      if (match) result.push(i);
    }
    if (i < n - m) {
      t = (d * (t - text.charCodeAt(i) * h) + text.charCodeAt(i + m)) % q;
      if (t < 0) t += q;
    }
  }
  return result;
}

console.log(rabinKarp(text, pattern));

medium

A. [2, 4, 6]

B. [0, 3, 5]

C. [1, 4]

D. [2, 5]

Solution

1. Step 1: Identify pattern occurrences in text

   The pattern "abc" appears starting at index 2 ("ababcabc") and index 5.

2. Step 2: Verify code logic for matching indices

   The code correctly finds these two positions and returns [2, 5].

3. Final Answer:

   [2, 5] -> Option D

4. Quick Check:

   Pattern found at indices 2 and 5 [OK]

Hint: Check substring start indices where pattern matches [OK]

Common Mistakes:

• Including index 0 which is partial match
• Confusing overlapping matches
• Forgetting to adjust negative hash values

4. The following Rabin Karp implementation has a bug causing incorrect matches. What is the error?

function rabinKarpBug(text: string, pattern: string): number[] {
  const m = pattern.length;
  const n = text.length;
  const d = 256;
  const q = 101;
  let p = 0, t = 0, h = 1;
  const result: number[] = [];

  for (let i = 0; i < m; i++) h = (h * d) % q;

  for (let i = 0; i < m; i++) {
    p = (d * p + pattern.charCodeAt(i)) % q;
    t = (d * t + text.charCodeAt(i)) % q;
  }

  for (let i = 0; i <= n - m; i++) {
    if (p === t) {
      let match = true;
      for (let j = 0; j < m; j++) {
        if (text[i + j] !== pattern[j]) {
          match = false;
          break;
        }
      }
      if (match) result.push(i);
    }
    if (i < n - m) {
      t = (d * (t - text.charCodeAt(i) * h) + text.charCodeAt(i + m)) % q;
      if (t < 0) t += q;
    }
  }
  return result;
}

medium

A. The hash update formula inside the loop is missing modulo operation

B. The initial value of h is computed incorrectly; it should be for (i = 0; i < m-1; i++)

C. The pattern hash p is not computed correctly

D. The loop for checking matches uses wrong indices

Solution

1. Step 1: Check computation of h

   Variable h should be (d^(m-1)) % q, but loop runs m times, making h too large.

2. Step 2: Understand impact on rolling hash

   Incorrect h causes wrong subtraction in rolling hash, leading to incorrect matches.

3. Final Answer:

   The initial value of h is computed incorrectly; it should be for (i = 0; i < m-1; i++) -> Option B

4. Quick Check:

   h loop runs m-1 times, not m [OK]

Hint: Compute h with loop to m-1, not m [OK]

Common Mistakes:

• Calculating h with wrong loop range
• Forgetting modulo in hash updates
• Misindexing pattern or text in loops

5. You want to use Rabin Karp to find all occurrences of pattern "aaa" in text "aaaaaa". What is the output of the algorithm and why is it important to verify matches after hash comparison?

hard

A. [0, 1, 2, 3, 4], because every substring is checked without hash

B. [0, 3], because only non-overlapping matches are counted

C. [0, 1, 2, 3], because overlapping matches exist and hash collisions can occur

D. [0], because Rabin Karp only finds first match

Solution

1. Step 1: Identify all pattern occurrences in text

   The pattern "aaa" appears starting at indices 0, 1, 2, and 3 in "aaaaaa" due to overlapping.

2. Step 2: Explain importance of verifying matches after hash

   Hash collisions can cause false positives, so character-by-character check confirms actual matches.

3. Final Answer:

   [0, 1, 2, 3], because overlapping matches exist and hash collisions can occur -> Option C

4. Quick Check:

   Overlapping matches + verify after hash = [0,1,2,3] [OK]

Hint: Check overlapping matches and confirm after hashing [OK]

Common Mistakes:

• Ignoring overlapping matches
• Assuming hash guarantees no false positives
• Counting only first or non-overlapping matches