Longest Common Substring in DSA Typescript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the Longest Common Substring problem?

It is the problem of finding the longest sequence of characters that appears in the same order and contiguously in two given strings.

beginner

Which data structure is commonly used to solve the Longest Common Substring problem efficiently?

A 2D array (dynamic programming table) is used to store lengths of common suffixes of substrings ending at different positions.

intermediate

In the dynamic programming approach, what does dp[i][j] represent?

dp[i][j] represents the length of the longest common substring ending at position i-1 in the first string and j-1 in the second string.

intermediate

What is the time complexity of the dynamic programming solution for Longest Common Substring?

The time complexity is O(m * n), where m and n are the lengths of the two input strings.

beginner

How do you update the dp table when characters at positions i-1 and j-1 do not match?

Set dp[i][j] to 0 because the substring must be contiguous, so no common substring ends at these positions.

What does the Longest Common Substring problem find?

A The longest sequence of characters appearing anywhere in both strings

B The longest sequence of characters appearing contiguously in both strings

C The longest sequence of characters appearing in only one string

D The shortest sequence of characters appearing in both strings

The problem finds the longest contiguous sequence common to both strings.

In the DP table, what does a zero value at dp[i][j] mean?

A No common substring ends at i-1 and j-1

B Characters at i-1 and j-1 match

C Longest substring length is 1

D Strings are identical up to i and j

Zero means no common substring ends at those positions because characters differ.

What is the main difference between Longest Common Substring and Longest Common Subsequence?

A Substring must be contiguous; subsequence can skip characters

B Subsequence must be contiguous; substring can skip characters

C Both require contiguous characters

D Both allow skipping characters

Substring requires characters to be next to each other; subsequence allows gaps.

What is the space complexity of the standard DP solution for Longest Common Substring?

A O(m + n)

B O(1)

C O(m * n)

D O(max(m, n))

The DP table uses space proportional to the product of the string lengths.

If two strings are 'abcde' and 'abfde', what is their longest common substring?

A 'abc'

B 'de'

C 'fde'

D 'ab'

'ab' is the longest contiguous sequence common to both strings.

Explain how the dynamic programming table is built for the Longest Common Substring problem.

Think about comparing characters and building up substring lengths step by step.

Describe the difference between Longest Common Substring and Longest Common Subsequence with examples.

Focus on continuity and skipping characters.

Practice

1. What does the Longest Common Substring problem find between two strings s1 and s2?

easy

A. The longest sequence of characters that appear in order but not necessarily contiguously

B. The total number of common characters between the two strings

C. The longest sequence of characters that appear contiguously in both strings

D. The shortest substring that contains all characters from both strings

Solution

1. Step 1: Understand substring vs subsequence

   A substring is a continuous part of a string, while a subsequence can skip characters.

2. Step 2: Define Longest Common Substring

   It finds the longest continuous sequence of characters present in both strings.

3. Final Answer:

   The longest sequence of characters that appear contiguously in both strings -> Option C

4. Quick Check:

   Longest Common Substring = continuous match [OK]

Hint: Look for continuous matching characters, not scattered ones [OK]

Common Mistakes:

• Confusing substring with subsequence
• Thinking order doesn't matter
• Counting total common characters instead

2. Which of the following TypeScript function signatures correctly represents a function to find the longest common substring length between two strings s1 and s2?

easy

A. function longestCommonSubstring(s1: string, s2: string): number

B. function longestCommonSubstring(s1: number[], s2: number[]): string

C. function longestCommonSubstring(s1: string, s2: string): string[]

D. function longestCommonSubstring(s1: string, s2: string): void

Solution

1. Step 1: Identify input types

   The inputs are two strings, so parameters should be string.

2. Step 2: Identify output type

   The function returns the length of the longest common substring, which is a number.

3. Final Answer:

   function longestCommonSubstring(s1: string, s2: string): number -> Option A

4. Quick Check:

   Input strings, output number length [OK]

Hint: Match input/output types to problem description [OK]

Common Mistakes:

• Using arrays instead of strings as input
• Returning string or array instead of number
• Using void return type mistakenly

3. What is the output of the following TypeScript code?

function longestCommonSubstring(s1: string, s2: string): number {
  const m = s1.length, n = s2.length;
  let maxLen = 0;
  const dp: number[][] = Array(m + 1).fill(0).map(() => Array(n + 1).fill(0));
  for (let i = 1; i <= m; i++) {
    for (let j = 1; j <= n; j++) {
      if (s1[i - 1] === s2[j - 1]) {
        dp[i][j] = dp[i - 1][j - 1] + 1;
        maxLen = Math.max(maxLen, dp[i][j]);
      }
    }
  }
  return maxLen;
}

console.log(longestCommonSubstring('abcde', 'abfde'));

medium

A. 2

B. 3

C. 4

D. 1

Solution

1. Step 1: Compare characters of 'abcde' and 'abfde'

   Matching continuous substrings are 'ab' at start and 'de' at end, both length 2.

2. Step 2: Find longest continuous match

   Longest common substring length is 2.

3. Final Answer:

   2 -> Option A

4. Quick Check:

   Longest common substring length = 2 [OK]

Hint: Check continuous matching parts, not scattered matches [OK]

Common Mistakes:

• Counting non-continuous matches
• Confusing longest common subsequence with substring
• Off-by-one errors in indexing

4. The following TypeScript code attempts to find the longest common substring length but has a bug. What is the bug?

function longestCommonSubstring(s1: string, s2: string): number {
  const m = s1.length, n = s2.length;
  let maxLen = 0;
  const dp: number[][] = Array(m).fill(0).map(() => Array(n).fill(0));
  for (let i = 1; i <= m; i++) {
    for (let j = 1; j <= n; j++) {
      if (s1[i - 1] === s2[j - 1]) {
        dp[i][j] = dp[i - 1][j - 1] + 1;
        maxLen = Math.max(maxLen, dp[i][j]);
      }
    }
  }
  return maxLen;
}

medium

A. Loop indices should start from 0 instead of 1

B. dp array is initialized with wrong size causing index errors

C. maxLen is not updated inside the loop

D. Comparison uses wrong characters from strings

Solution

1. Step 1: Check dp array initialization

   dp is created with size m x n but accessed with indices up to m and n (1-based), causing out-of-bound errors.

2. Step 2: Correct dp size

   dp should be (m+1) x (n+1) to safely use 1-based indexing in loops.

3. Final Answer:

   dp array is initialized with wrong size causing index errors -> Option B

4. Quick Check:

   dp size must match loop indices [OK]

Hint: Match dp size with loop ranges to avoid index errors [OK]

Common Mistakes:

• Not adding +1 to dp dimensions
• Starting loops at 1 but dp size too small
• Ignoring index out-of-bound runtime errors

5. Given two strings s1 = 'xabxac' and s2 = 'abcabxabcd', what is the length of their longest common substring?

hard

A. 3

B. 5

C. 6

D. 4

Solution

1. Step 1: Identify common substrings

   Common substrings include 'abx' and 'abxa'. 'abxa' is length 4 and appears in both strings.

2. Step 2: Confirm longest substring length

   No longer continuous substring than length 4 exists in both strings.

3. Final Answer:

   4 -> Option D

4. Quick Check:

   Longest common substring length = 4 [OK]

Hint: Look for longest continuous matching sequence visually [OK]

Common Mistakes:

• Counting non-continuous matches
• Choosing shorter common substrings
• Confusing substring with subsequence