Edit Distance Problem Levenshtein in DSA Javascript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the Edit Distance (Levenshtein distance) between two strings?

It is the minimum number of single-character edits (insertions, deletions, or substitutions) required to change one string into the other.

beginner

Which operations are counted in calculating the Levenshtein distance?

Insertion, deletion, and substitution of a single character each count as one operation.

intermediate

What is the base case when using dynamic programming to compute Levenshtein distance?

When one string is empty, the distance is the length of the other string (all insertions or deletions).

intermediate

How does the dynamic programming table for Levenshtein distance get filled?

Each cell represents the minimum edit distance between prefixes of the two strings, computed using values from neighboring cells (top, left, and top-left).

beginner

Why is Levenshtein distance useful in real life?

It helps in spell checking, DNA sequence analysis, and natural language processing by measuring how similar two strings are.

Which of the following is NOT an operation counted in Levenshtein distance?

A Insertion

B Deletion

C Substitution

D Transposition

Levenshtein distance counts insertion, deletion, and substitution. Transposition is counted in a different distance called Damerau-Levenshtein.

What is the Levenshtein distance between "cat" and "cut"?

A 1

B 2

C 3

D 0

Only one substitution (a -> u) is needed to change "cat" to "cut".

If one string is empty and the other has length 5, what is the Levenshtein distance?

A 1

B 5

C 0

D Cannot be determined

You need 5 insertions or deletions to convert an empty string to a string of length 5.

In dynamic programming for Levenshtein distance, what does the cell dp[i][j] represent?

A Distance between prefixes of length i and j

B Length of the longer string

C Number of substitutions only

D Distance between full strings

dp[i][j] stores the minimum edit distance between the first i characters of one string and the first j characters of the other.

Which real-life application uses Levenshtein distance?

A Calculating factorial

B Sorting numbers

C Spell checking

D Drawing graphics

Spell checking uses Levenshtein distance to find words close to a misspelled word.

Explain how dynamic programming helps compute the Levenshtein distance between two strings.

Think about how you compare smaller parts of the strings step by step.

Describe a real-life scenario where calculating the Levenshtein distance is useful and why.

Think about when you want to find words or sequences that are almost the same.

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