KMP Pattern Matching Algorithm in DSA Typescript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the prefix array with zeros.

DSA Typescript

const prefix: number[] = new Array(pattern.length).fill([1]);

Drag options to blanks, or click blank then click option'

A0

Bpattern.length

C-1

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Initializing prefix array with ones or negative numbers.

Using pattern length as initial value.

The prefix array is initialized with zeros to store the longest prefix suffix lengths.

2fill in blank

medium

Complete the code to update the prefix index when characters match.

DSA Typescript

if (pattern[i] === pattern[j]) {
  j++;
  prefix[i] = [1];
  i++;
}

Drag options to blanks, or click blank then click option'

Ai

B0

Cprefix[j]

Dj

Attempts:

3 left

💡 Hint

Common Mistakes

Assigning i instead of j to prefix[i].

Assigning zero incorrectly.

When characters match, prefix[i] is set to j, the length of the current longest prefix suffix.

3fill in blank

hard

Fix the error in the while loop condition to avoid infinite loop.

DSA Typescript

while (i < pattern.length) {
  if (pattern[i] === pattern[j]) {
    j++;
    prefix[i] = j;
    i++;
  } else if (j > 0) {
    j = prefix[1];
  } else {
    prefix[i] = 0;
    i++;
  }
}

Drag options to blanks, or click blank then click option'

A[j - 1]

B(j - 1)

C{j - 1}

D(j + 1)

Attempts:

3 left

💡 Hint

Common Mistakes

Using curly braces or square brackets incorrectly.

Using j + 1 which causes index error.

When mismatch occurs and j > 0, j is updated to prefix[j - 1] to check previous longest prefix suffix.

4fill in blank

hard

Fill both blanks to complete the search loop that finds pattern matches in text.

DSA Typescript

while (i < text.length) {
  if (pattern[j] === text[i]) {
    i++;
    j++;
  }
  if (j === [1]) {
    result.push(i - j);
    j = prefix[2];
  } else if (i < text.length && pattern[j] !== text[i]) {
    if (j !== 0) {
      j = prefix[j - 1];
    } else {
      i++;
    }
  }
}

Drag options to blanks, or click blank then click option'

Apattern.length

B[j - 1]

Cprefix.length

Dresult.length

Attempts:

3 left

💡 Hint

Common Mistakes

Comparing j to text length instead of pattern length.

Using prefix.length incorrectly.

j is compared to pattern.length to check full match; j is reset to prefix[j - 1] to continue search.

5fill in blank

hard

Fill all three blanks to complete the function that returns all starting indices of pattern matches in text.

DSA Typescript

function kmpSearch(text: string, pattern: string): number[] {
  const prefix: number[] = new Array(pattern.length).fill(0);
  let i = 1, j = 0;
  while (i < pattern.length) {
    if (pattern[i] === pattern[j]) {
      j++;
      prefix[i] = j;
      i++;
    } else if (j > 0) {
      j = prefix[1];
    } else {
      prefix[i] = 0;
      i++;
    }
  }
  const result: number[] = [];
  i = 0;
  j = 0;
  while (i < text.length) {
    if (pattern[j] === text[i]) {
      i++;
      j++;
    }
    if (j === [2]) {
      result.push(i - j);
      j = prefix[3];
    } else if (i < text.length && pattern[j] !== text[i]) {
      if (j !== 0) {
        j = prefix[j - 1];
      } else {
        i++;
      }
    }
  }
  return result;
}

Drag options to blanks, or click blank then click option'

A[j - 1]

Bpattern.length

Dtext.length

Attempts:

3 left

💡 Hint

Common Mistakes

Using text.length instead of pattern.length for match check.

Incorrect indexing with prefix array.

j is updated to prefix[j - 1] on mismatch; full match is when j equals pattern.length; after match, j resets to prefix[j - 1].

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