Edit Distance Problem Levenshtein in DSA Javascript - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Levenshtein Distance Calculation

What is the output of the following JavaScript code that calculates the Levenshtein distance between two strings?

DSA Javascript

function levenshtein(a, b) {
  const dp = Array(a.length + 1).fill(null).map(() => Array(b.length + 1).fill(0));
  for (let i = 0; i <= a.length; i++) dp[i][0] = i;
  for (let j = 0; j <= b.length; j++) dp[0][j] = j;
  for (let i = 1; i <= a.length; i++) {
    for (let j = 1; j <= b.length; j++) {
      if (a[i - 1] === b[j - 1]) {
        dp[i][j] = dp[i - 1][j - 1];
      } else {
        dp[i][j] = Math.min(dp[i - 1][j] + 1, dp[i][j - 1] + 1, dp[i - 1][j - 1] + 1);
      }
    }
  }
  return dp[a.length][b.length];
}

console.log(levenshtein("kitten", "sitting"));

A 4

B 3

C 5

D 6

💡 Hint

Think about the minimum number of edits (insertions, deletions, substitutions) to convert 'kitten' to 'sitting'.

The Levenshtein distance between "kitten" and "sitting" is 3. The edits are: substitute 'k' with 's', substitute 'e' with 'i', insert 'g' at the end.

🧠 Conceptual

intermediate

Understanding Levenshtein Distance Operations

Which of the following operations are considered when calculating the Levenshtein distance between two strings?

A Insertion, Deletion, Transposition

B Insertion, Reversal, Substitution

C Substitution, Transposition, Reversal

D Insertion, Deletion, Substitution

💡 Hint

Levenshtein distance counts the minimum edits needed using basic operations.

Levenshtein distance counts the minimum number of insertions, deletions, and substitutions required to change one string into another. Transposition is not included.

❓ Predict Output

advanced

Result of Levenshtein Distance Matrix

What is the value of dp[3][3] after running the following code snippet for strings 'abc' and 'yabd'?

DSA Javascript

function levenshteinMatrix(a, b) {
  const dp = Array(a.length + 1).fill(null).map(() => Array(b.length + 1).fill(0));
  for (let i = 0; i <= a.length; i++) dp[i][0] = i;
  for (let j = 0; j <= b.length; j++) dp[0][j] = j;
  for (let i = 1; i <= a.length; i++) {
    for (let j = 1; j <= b.length; j++) {
      if (a[i - 1] === b[j - 1]) {
        dp[i][j] = dp[i - 1][j - 1];
      } else {
        dp[i][j] = Math.min(dp[i - 1][j] + 1, dp[i][j - 1] + 1, dp[i - 1][j - 1] + 1);
      }
    }
  }
  return dp;
}

const matrix = levenshteinMatrix("abc", "yabd");
console.log(matrix[3][3]);

A 1

B 4

C 2

D 3

💡 Hint

Trace the matrix filling step by step for the first 3 characters.

The dp[3][3] corresponds to the distance between 'abc' and 'yab'. The minimum edits are 2, for example by inserting 'y' at the beginning and deleting 'c'.

🔧 Debug

advanced

Identify the Error in Levenshtein Distance Code

What error will the following code produce when calculating the Levenshtein distance between 'abc' and 'ac'?

DSA Javascript

function levenshtein(a, b) {
  const dp = Array(a.length).fill(null).map(() => Array(b.length).fill(0));
  for (let i = 0; i <= a.length; i++) dp[i][0] = i;
  for (let j = 0; j <= b.length; j++) dp[0][j] = j;
  for (let i = 1; i <= a.length; i++) {
    for (let j = 1; j <= b.length; j++) {
      if (a[i - 1] === b[j - 1]) {
        dp[i][j] = dp[i - 1][j - 1];
      } else {
        dp[i][j] = Math.min(dp[i - 1][j] + 1, dp[i][j - 1] + 1, dp[i - 1][j - 1] + 1);
      }
    }
  }
  return dp[a.length][b.length];
}

console.log(levenshtein("abc", "ac"));

A TypeError: Cannot set property '0' of undefined

B ReferenceError: dp is not defined

C Output: 1

D SyntaxError: Unexpected token

💡 Hint

Check how the dp array is initialized and accessed.

The dp array is initialized with length a.length (3) but indices go up to a.length (3) inclusive, causing dp[3] to be undefined. Setting dp[3][0] causes a TypeError.

🚀 Application

expert

Minimum Edit Distance for Spell Correction

Given the dictionary words ['cat', 'bat', 'rat', 'drat', 'dart', 'cart'] and the input word 'car', which dictionary word has the smallest Levenshtein distance to 'car'?

A "cart"

B "bat"

C "cat"

D "drat"

💡 Hint

Calculate the Levenshtein distance from 'car' to each dictionary word and find the minimum.

Distances: 'cat' = 1, 'bat' = 2, 'rat' = 2, 'drat' = 3, 'dart' = 2, 'cart' = 1 (one insertion 't'). "cart" and "cat" both have the smallest distance of 1; "cart" is the intended answer among the options.

Practice

1. What does the Levenshtein distance between two strings measure?

easy

A. The length difference between the two strings

B. The number of matching characters in the same positions

C. The minimum number of single-character edits needed to change one string into the other

D. The number of vowels in both strings combined

Solution

1. Step 1: Understand the definition of Levenshtein distance

   It measures how many single-character edits (insertions, deletions, or substitutions) are needed to convert one string into another.

2. Step 2: Compare with other options

   Options B, C, and D do not describe edit distance but other unrelated string properties.

3. Final Answer:

   The minimum number of single-character edits needed to change one string into the other -> Option C

4. Quick Check:

   Levenshtein distance = minimum edits [OK]

Hint: Think of edits needed to transform one word into another [OK]

Common Mistakes:

• Confusing edit distance with matching characters count
• Thinking it measures length difference only
• Assuming it counts only substitutions

2. Which of the following JavaScript function signatures correctly represents a function to compute Levenshtein distance between two strings s1 and s2?

easy

A. function levenshtein(s1, s2) { /* code */ }

B. function levenshtein(s1, s2, s3) { /* code */ }

C. function levenshtein() { /* code */ }

D. function levenshtein(s1) { /* code */ }

Solution

1. Step 1: Identify required parameters for Levenshtein function

   The function needs exactly two strings to compare, so it should accept two parameters.

2. Step 2: Check options for correct parameter count

   function levenshtein(s1, s2) { /* code */ } has two parameters (s1, s2), which is correct. Options A, B, and C have incorrect parameter counts.

3. Final Answer:

   function levenshtein(s1, s2) { /* code */ } -> Option A

4. Quick Check:

   Two strings needed as input [OK]

Hint: Levenshtein compares two strings, so function needs two parameters [OK]

Common Mistakes:

• Using wrong number of parameters
• Omitting parameters entirely
• Adding unnecessary extra parameters

3. What is the output of the following JavaScript code snippet?

function min(a, b, c) {
  return Math.min(a, b, c);
}

function levenshtein(s1, s2) {
  const len1 = s1.length;
  const len2 = s2.length;
  const dp = Array(len1 + 1).fill(null).map(() => Array(len2 + 1).fill(0));

  for (let i = 0; i <= len1; i++) dp[i][0] = i;
  for (let j = 0; j <= len2; j++) dp[0][j] = j;

  for (let i = 1; i <= len1; i++) {
    for (let j = 1; j <= len2; j++) {
      if (s1[i - 1] === s2[j - 1]) {
        dp[i][j] = dp[i - 1][j - 1];
      } else {
        dp[i][j] = min(dp[i - 1][j] + 1, dp[i][j - 1] + 1, dp[i - 1][j - 1] + 1);
      }
    }
  }
  return dp[len1][len2];
}

console.log(levenshtein('kitten', 'sitting'));

medium

A. 3

B. 4

C. 5

D. 6

Solution

1. Step 1: Understand the Levenshtein distance calculation for 'kitten' and 'sitting'

   Transform 'kitten' to 'sitting' requires 3 substitutions and 1 insertion: k->s, i->i (same), t->t (same), t->t (same), e->i, n->n (same), plus insert 'g'. Total edits = 3.

2. Step 2: Trace the code logic

   The code correctly implements the dynamic programming approach to calculate the minimum edits, returning 3.

3. Final Answer:

   3 -> Option A

4. Quick Check:

   Levenshtein('kitten', 'sitting') = 3 [OK]

Hint: Count edits: substitutions + insertions + deletions [OK]

Common Mistakes:

• Counting only substitutions
• Ignoring insertions or deletions
• Misindexing string characters

4. Identify the bug in the following Levenshtein distance function and select the fix:

function levenshtein(s1, s2) {
  const len1 = s1.length;
  const len2 = s2.length;
  const dp = Array(len1).fill(null).map(() => Array(len2).fill(0));

  for (let i = 0; i <= len1; i++) dp[i][0] = i;
  for (let j = 0; j <= len2; j++) dp[0][j] = j;

  for (let i = 1; i <= len1; i++) {
    for (let j = 1; j <= len2; j++) {
      if (s1[i - 1] === s2[j - 1]) {
        dp[i][j] = dp[i - 1][j - 1];
      } else {
        dp[i][j] = Math.min(dp[i - 1][j] + 1, dp[i][j - 1] + 1, dp[i - 1][j - 1] + 1);
      }
    }
  }
  return dp[len1][len2];
}

medium

A. Change loops to run from 0 to len1-1 and len2-1

B. Replace Math.min with Math.max in dp calculation

C. Remove the initialization loops for dp first row and column

D. Change dp array initialization to size (len1+1) x (len2+1)

Solution

1. Step 1: Analyze dp array initialization

   The dp array is initialized with size len1 x len2, but the loops access indices up to len1 and len2, causing out-of-bounds errors.

2. Step 2: Fix dp size to (len1+1) x (len2+1)

   Allocating dp with one extra row and column prevents index errors and allows proper initialization of base cases.

3. Final Answer:

   Change dp array initialization to size (len1+1) x (len2+1) -> Option D

4. Quick Check:

   dp size must match loop bounds [OK]

Hint: dp size must be string length + 1 for indexing [OK]

Common Mistakes:

• Not allocating dp with extra row/column
• Using wrong loop ranges causing errors
• Replacing min with max breaks logic

5. Given two strings s1 = 'intention' and s2 = 'execution', what is the Levenshtein distance between them? Use the concept of minimum edits (insertions, deletions, substitutions) to find the answer.

hard

A. 4

B. 6

C. 5

D. 7

Solution

1. Step 1: Analyze differences between 'intention' and 'execution'

   Transform 'intention' to 'execution' involves substitutions and insertions: i->e, n->x, t->c, e->u, n->t, plus insert 'o'. Total edits count to 6.

2. Step 2: Count minimum edits carefully

   Counting substitutions and insertions needed gives 6 as the minimum number of edits.

3. Final Answer:

   6 -> Option B

4. Quick Check:

   Minimum edits between 'intention' and 'execution' = 6 [OK]

Hint: Count each letter change and insertion carefully [OK]

Common Mistakes:

• Underestimating substitutions needed
• Ignoring insertions or deletions
• Confusing with string length difference