Why Longest Common Substring in DSA Typescript?

The Big Idea

Discover how to find the longest matching part between two texts without endless guessing!

The Scenario

Imagine you have two long texts and you want to find the longest part that appears exactly the same in both. Doing this by reading and comparing every possible part by hand would take forever!

The Problem

Manually checking every possible substring is slow and confusing. You might miss some matches or spend hours comparing parts that don't match. It's easy to make mistakes and waste time.

The Solution

The Longest Common Substring method quickly finds the longest matching part between two texts by using a smart way to compare all parts at once. It saves time and avoids mistakes.

Before vs After

✗ Before

function findLongestCommonSubstringManual(text1: string, text2: string): string {
  let longest = '';
  for (let i = 0; i < text1.length; i++) {
    for (let j = 0; j < text2.length; j++) {
      let k = 0;
      while (i + k < text1.length && j + k < text2.length && text1[i + k] === text2[j + k]) {
        k++;
      }
      if (k > longest.length) {
        longest = text1.substring(i, i + k);
      }
    }
  }
  return longest;
}

✓ After

function longestCommonSubstring(text1: string, text2: string): string {
  const dp: number[][] = Array(text1.length + 1).fill(0).map(() => Array(text2.length + 1).fill(0));
  let maxLength = 0;
  let endIndex = 0;
  for (let i = 1; i <= text1.length; i++) {
    for (let j = 1; j <= text2.length; j++) {
      if (text1[i - 1] === text2[j - 1]) {
        dp[i][j] = dp[i - 1][j - 1] + 1;
        if (dp[i][j] > maxLength) {
          maxLength = dp[i][j];
          endIndex = i;
        }
      }
    }
  }
  return text1.substring(endIndex - maxLength, endIndex);
}

What It Enables

This lets you quickly find the longest exact matching part between two texts, which helps in many areas like spell checking, DNA analysis, and plagiarism detection.

Real Life Example

When checking if two documents share a copied paragraph, the Longest Common Substring helps find the longest copied section automatically, saving hours of manual reading.

Key Takeaways

Manual comparison is slow and error-prone.

Longest Common Substring uses a smart table to find matches fast.

This method helps in text analysis, biology, and more.

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