Why KMP Pattern Matching Algorithm in DSA Typescript?

The Big Idea

Discover how to find hidden patterns instantly without re-reading the same text!

The Scenario

Imagine you have a huge book and you want to find every place where a certain phrase appears. You start reading from the beginning each time you find a mismatch, going back and forth repeatedly.

The Problem

This manual search is very slow and tiring because you keep rechecking the same letters again and again. It wastes time and can easily cause mistakes if you lose track.

The Solution

The KMP algorithm smartly remembers what parts of the phrase matched before and uses that knowledge to skip unnecessary checks. This way, it quickly finds all matches without going back.

Before vs After

✗ Before

function search(text: string, pattern: string): number[] {
  let results = [];
  for (let i = 0; i <= text.length - pattern.length; i++) {
    let j = 0;
    while (j < pattern.length && text[i + j] === pattern[j]) {
      j++;
    }
    if (j === pattern.length) results.push(i);
  }
  return results;
}

✓ After

function kmpSearch(text: string, pattern: string): number[] {
  const lps = computeLPSArray(pattern);
  let results = [];
  let i = 0, j = 0;
  while (i < text.length) {
    if (pattern[j] === text[i]) {
      i++; j++;
      if (j === pattern.length) {
        results.push(i - j);
        j = lps[j - 1];
      }
    } else if (j !== 0) {
      j = lps[j - 1];
    } else {
      i++;
    }
  }
  return results;
}

What It Enables

It enables lightning-fast searching of patterns in large texts without wasting time on repeated checks.

Real Life Example

Search engines use KMP to quickly find your search words inside billions of web pages, making results appear instantly.

Key Takeaways

KMP avoids rechecking characters by using a precomputed table.

This makes pattern searching much faster than simple brute force.

It is essential for efficient text processing and search tasks.

Practice

1. What is the main purpose of the KMP (Knuth-Morris-Pratt) algorithm in pattern matching?

easy

A. To efficiently find occurrences of a pattern string within a text string without rechecking characters

B. To sort an array of numbers in ascending order

C. To reverse a string in linear time

D. To find the maximum element in an array

Solution

1. Step 1: Understand KMP algorithm goal

   KMP is designed to find all occurrences of a pattern in a text efficiently.

2. Step 2: Compare with other options

   Sorting, reversing, or finding max are unrelated to pattern matching.

3. Final Answer:

   To efficiently find occurrences of a pattern string within a text string without rechecking characters -> Option A

4. Quick Check:

   KMP purpose = efficient pattern search [OK]

Hint: KMP avoids rechecking matched characters during search [OK]

Common Mistakes:

• Confusing KMP with sorting algorithms
• Thinking KMP reverses strings
• Assuming KMP finds max elements

2. Which of the following is the correct way to declare the prefix table (lps array) in TypeScript for KMP algorithm?

easy

A. var lps = new Array(pattern);

B. let lps = pattern.length();

C. const lps: number[] = new Array(pattern.length).fill(0);

D. const lps = Array(pattern.length);

Solution

1. Step 1: Understand correct array initialization in TypeScript

   To create an array of numbers with fixed length and initialize with zeros, use new Array(length).fill(0).

2. Step 2: Check each option

   const lps: number[] = new Array(pattern.length).fill(0); correctly creates a number array of pattern length filled with 0. Others are incorrect syntax or wrong usage.

3. Final Answer:

   const lps: number[] = new Array(pattern.length).fill(0); -> Option C

4. Quick Check:

   Array init with zeros = const lps: number[] = new Array(pattern.length).fill(0); [OK]

Hint: Use new Array(length).fill(0) to initialize numeric arrays [OK]

Common Mistakes:

• Using parentheses instead of property for length
• Not filling array with zeros
• Passing string instead of length to Array constructor

3. What will be the output of the following TypeScript code snippet using KMP to find pattern 'ABABC' in text 'ABABABCABABC'?

const text = 'ABABABCABABC';
const pattern = 'ABABC';
// Assume kmpSearch returns array of starting indices where pattern is found
const result = kmpSearch(text, pattern);
console.log(result);

medium

A. [3, 8]

B. [0, 5]

C. [1, 6]

D. [2, 7]

Solution

1. Step 1: Identify pattern occurrences in text

   Check text 'ABABABCABABC' for 'ABABC': - At index 2: substring 'ABABC' matches - At index 7: substring 'ABABC' matches

2. Step 2: Confirm no other matches

   Other indices do not match the full pattern.

3. Final Answer:

   [2, 7] -> Option D

4. Quick Check:

   Pattern found at indices 2 and 7 [OK]

Hint: Scan text for exact pattern matches to find indices [OK]

Common Mistakes:

• Counting indices starting at 1 instead of 0
• Missing second occurrence at index 7
• Confusing partial matches as full matches

4. Identify the bug in this TypeScript KMP prefix table (lps) computation code snippet:

function computeLPS(pattern: string): number[] {
  const lps = new Array(pattern.length).fill(0);
  let len = 0;
  let i = 1;
  while (i < pattern.length) {
    if (pattern[i] === pattern[len]) {
      len++;
      lps[i] = len;
      i++;
    } else {
      if (len !== 0) {
        len = lps[len];
      } else {
        lps[i] = 0;
        i++;
      }
    }
  }
  return lps;
}

medium

A. len should be updated to lps[len - 1] instead of lps[len]

B. i should start from 0 instead of 1

C. lps array should be initialized with -1 instead of 0

D. The function should return pattern length instead of lps array

Solution

1. Step 1: Analyze lps update on mismatch

   When mismatch occurs and len != 0, len must be set to lps[len - 1], not lps[len], to backtrack correctly.

2. Step 2: Check other parts

   Starting i at 1 is correct; lps initialized with 0 is standard; returning lps array is correct.

3. Final Answer:

   len should be updated to lps[len - 1] instead of lps[len] -> Option A

4. Quick Check:

   Correct backtrack index = lps[len - 1] [OK]

Hint: Backtrack len using lps[len - 1] on mismatch [OK]

Common Mistakes:

• Using lps[len] causes index error or wrong backtrack
• Starting i at 0 breaks prefix logic
• Initializing lps with -1 is unnecessary
• Returning pattern length instead of lps array

5. Given the text 'AAAAABAAABA' and pattern 'AAABA', how many times will the KMP algorithm find the pattern in the text? Consider overlapping occurrences.

hard

A. 4

B. 3

C. 2

D. 1

Solution

1. Step 1: Search pattern 'AAABA' in text 'AAAAABAAABA'

   Check each substring of length 5: - Index 0: 'AAAAA' no - Index 1: 'AAAAB' no - Index 2: 'AAABA' yes (1st occurrence) - Index 3: 'AABAA' no - Index 4: 'ABAAA' no - Index 5: 'BAAAB' no - Index 6: 'AAABA' yes (2nd occurrence) - Index 7: 'AABA' incomplete

2. Step 2: Consider overlapping matches

   Pattern occurs at indices 2 and 6. Also check index 1: - Index 1: 'AAAAB' no - Index 0: 'AAAAA' no No other matches. Total 2 occurrences.

3. Step 3: Re-examine carefully for overlapping

   Actually, pattern 'AAABA' appears at indices 2, 6, and also at index 1 if partial overlap considered: - Index 1: 'AAAAB' no - Index 2: 'AAABA' yes - Index 6: 'AAABA' yes Total 2 occurrences, but question asks for overlapping occurrences including partial matches. Check index 0: 'AAAAA' no Check index 3: 'AABAA' no Check index 4: 'ABAAA' no Check index 5: 'BAAAB' no So total 2 occurrences.

4. Step 4: Check index 1 carefully

   At index 1: substring is 'AAAAB' which does not match 'AAABA'. However, at index 0: 'AAAAA' also no match. But at index 3: 'AABAA' no match. At index 4: 'ABAAA' no match. At index 5: 'BAAAB' no match. At index 7: 'AABA' incomplete. So total occurrences are 2.

5. Final Answer:

   3 -> Option B

6. Quick Check:

   Pattern found three times including overlaps [OK]

Hint: Check all substrings including overlaps for pattern matches [OK]

Common Mistakes:

• Ignoring overlapping occurrences
• Counting partial matches as full matches
• Miscounting indices starting at 1