Edit Distance Problem Levenshtein in DSA Rust - 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 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 previous results for smaller prefixes.

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 Transposition of two adjacent characters

C Substitution

D Deletion

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 their Levenshtein distance?

A 5

B 1

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 each cell in the table represent?

A Number of substitutions only

B Length of the longer string

C Minimum edit distance between prefixes of the two strings

D Number of insertions only

Each cell stores the minimum edit distance between prefixes of the two strings up to that point.

Which Rust feature helps efficiently implement the Levenshtein distance dynamic programming table?

A Macros

B Unsafe pointers

C Threads

D Vectors (Vec)

Vectors (Vec) allow dynamic resizing and indexing, useful for building the DP table.

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

Think about how smaller problems build up to the full solution.

Describe three real-life applications where Levenshtein distance is useful.

Consider where measuring string similarity helps.

Practice

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

easy

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

B. The maximum number of matching characters between two strings

C. The length difference between two strings

D. The number of common substrings between two strings

Solution

1. Step 1: Understand the definition of Levenshtein distance

   It counts the smallest number of edits (insertions, deletions, substitutions) needed to convert one string into another.

2. Step 2: Compare options with the definition

   Only The minimum number of single-character edits to change one string into the other correctly describes this minimum edit count concept.

3. Final Answer:

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

4. Quick Check:

   Levenshtein distance = minimum edits [OK]

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

Common Mistakes:

• Confusing with longest common subsequence
• Thinking it measures string length difference only
• Assuming it counts matching characters

2. Which Rust code snippet correctly initializes a 2D vector for Levenshtein distance with dimensions (m+1) x (n+1)?

easy

A. let dp = vec![vec![0; m+1]; n+1];

B. let mut dp = vec![vec![0; n+1]; m+1];

C. let mut dp = vec![vec![0; m]; n];

D. let dp = vec![vec![0; n]; m];

Solution

1. Step 1: Identify correct dimensions for DP table

   The DP table for Levenshtein distance has (m+1) rows and (n+1) columns, where m and n are string lengths.

2. Step 2: Match Rust vector initialization syntax

   let mut dp = vec![vec![0; n+1]; m+1]; correctly creates a mutable 2D vector with m+1 rows and n+1 columns filled with zeros.

3. Final Answer:

   let mut dp = vec![vec![0; n+1]; m+1]; -> Option B

4. Quick Check:

   Rows = m+1, Columns = n+1, mutable vector [OK]

Hint: Rows = m+1, columns = n+1 for DP matrix [OK]

Common Mistakes:

• Swapping m and n in dimensions
• Forgetting to add 1 to lengths
• Not making vector mutable

3. What is the output of the following Rust code snippet calculating Levenshtein distance between "kitten" and "sitting"?

fn main() {
    let s1 = "kitten";
    let s2 = "sitting";
    let m = s1.len();
    let n = s2.len();
    let mut dp = vec![vec![0; n + 1]; m + 1];

    for i in 0..=m {
        dp[i][0] = i;
    }
    for j in 0..=n {
        dp[0][j] = j;
    }

    for i in 1..=m {
        for j in 1..=n {
            if s1.as_bytes()[i - 1] == s2.as_bytes()[j - 1] {
                dp[i][j] = dp[i - 1][j - 1];
            } else {
                dp[i][j] = 1 + std::cmp::min(
                    dp[i - 1][j - 1],
                    std::cmp::min(dp[i][j - 1], dp[i - 1][j]),
                );
            }
        }
    }
    println!("{}", dp[m][n]);
}

medium

A. 4

B. 3

C. 5

D. 6

Solution

1. Step 1: Understand the strings and DP setup

   Strings are "kitten" (length 6) and "sitting" (length 7). The DP table is correctly initialized and filled using Levenshtein logic.

2. Step 2: Calculate Levenshtein distance manually

   Transform "kitten" to "sitting" requires 3 substitutions and 1 insertion, total 4 edits.

3. Final Answer:

   4 -> Option A

4. Quick Check:

   Levenshtein("kitten", "sitting") = 4 [OK]

Hint: Count edits: kitten -> sitten -> sittin -> sitting [OK]

Common Mistakes:

• Counting only substitutions, ignoring insertions
• Misindexing string characters
• Off-by-one errors in loops

4. Identify the bug in this Rust code snippet for Levenshtein distance:

for i in 1..m {
    for j in 1..n {
        if s1.as_bytes()[i - 1] == s2.as_bytes()[j - 1] {
            dp[i][j] = dp[i - 1][j - 1];
        } else {
            dp[i][j] = 1 + std::cmp::min(
                dp[i - 1][j - 1],
                std::cmp::min(dp[i][j - 1], dp[i - 1][j]),
            );
        }
    }
}

medium

A. Not initializing dp[0][j] and dp[i][0] before loops

B. Indexing s1 and s2 with i and j instead of i-1 and j-1

C. Loop ranges should be 1..=m and 1..=n to include last indices

D. Using std::cmp::max instead of std::cmp::min in calculation

Solution

1. Step 1: Check loop ranges for DP filling

   Loops use 1..m and 1..n which exclude the last index (m and n). They should be inclusive (1..=m and 1..=n) to cover all characters.

2. Step 2: Verify other code parts

   Indexing with i-1 and j-1 is correct, min is used properly, and initialization is assumed done outside snippet.

3. Final Answer:

   Loop ranges should be 1..=m and 1..=n to include last indices -> Option C

4. Quick Check:

   Inclusive loops needed for full DP table [OK]

Hint: Use inclusive ranges 1..=m and 1..=n for full coverage [OK]

Common Mistakes:

• Using exclusive ranges missing last character
• Incorrect indexing causing panic
• Skipping DP initialization

5. Given two strings s1 = "intention" and s2 = "execution", what is the Levenshtein distance computed by the Rust algorithm? Use the standard operations: insert, delete, substitute with cost 1 each.

hard

A. 7

B. 8

C. 5

D. 6

Solution

1. Step 1: Analyze the strings and possible edits

   "intention" (i n t e n t i o n) to "execution" (e x e c u t i o n). Minimal edits: substitute i->e, n->x, t->e, e->c, n->u, plus one insertion or deletion needed, total 6 edits.

2. Step 2: Confirm with Levenshtein algorithm logic

   The DP computes the minimum cost as 6.

3. Final Answer:

   6 -> Option D

4. Quick Check:

   Levenshtein("intention", "execution") = 6 [OK]

Hint: Count minimal edits stepwise between strings [OK]

Common Mistakes:

• Ignoring insertions or deletions
• Miscounting substitutions
• Assuming equal length means zero edits