Longest Common Subsequence in DSA Javascript - Build from Scratch

Longest Common Subsequence

📖 Scenario: Imagine you are building a text comparison tool that finds the longest common sequence of characters between two texts. This helps in detecting similarities, like in plagiarism checkers or version control systems.

🎯 Goal: You will write a program to find the length of the longest common subsequence (LCS) between two given strings using dynamic programming.

📋 What You'll Learn

Create two string variables with exact values

Create a 2D array (matrix) to store intermediate LCS lengths

Implement nested loops to fill the matrix using LCS logic

Print the final LCS length

💡 Why This Matters

🌍 Real World

Text comparison tools, version control systems, DNA sequence analysis, and plagiarism detection use longest common subsequence algorithms to find similarities.

💼 Career

Understanding dynamic programming and string algorithms is essential for software engineers working on data processing, bioinformatics, and text analysis.

1

Create the input strings

Create two string variables called str1 and str2 with the exact values "AGGTAB" and "GXTXAYB" respectively.

DSA Javascript

# Your code here

Hint

Use const to declare the strings exactly as shown.

2

Initialize the LCS matrix

Create a 2D array called lcs with dimensions str1.length + 1 by str2.length + 1. Initialize all values to 0 using a loop.

DSA Javascript

const str1 = "AGGTAB";
const str2 = "GXTXAYB";
// Your code here

Hint

Use a for loop from 0 to str1.length inclusive and fill each row with zeros.

3

Fill the LCS matrix with dynamic programming

Use nested for loops with variables i from 1 to str1.length and j from 1 to str2.length. Inside, if str1[i - 1] === str2[j - 1], set lcs[i][j] = lcs[i - 1][j - 1] + 1. Otherwise, set lcs[i][j] = Math.max(lcs[i - 1][j], lcs[i][j - 1]).

DSA Javascript

const str1 = "AGGTAB";
const str2 = "GXTXAYB";

const lcs = [];
for (let i = 0; i <= str1.length; i++) {
    lcs[i] = new Array(str2.length + 1).fill(0);
}
// Your code here

Hint

Use two nested loops and compare characters at i - 1 and j - 1 positions.

4

Print the length of the longest common subsequence

Print the value of lcs[str1.length][str2.length] using console.log.

DSA Javascript

const str1 = "AGGTAB";
const str2 = "GXTXAYB";

const lcs = [];
for (let i = 0; i <= str1.length; i++) {
    lcs[i] = new Array(str2.length + 1).fill(0);
}

for (let i = 1; i <= str1.length; i++) {
    for (let j = 1; j <= str2.length; j++) {
        if (str1[i - 1] === str2[j - 1]) {
            lcs[i][j] = lcs[i - 1][j - 1] + 1;
        } else {
            lcs[i][j] = Math.max(lcs[i - 1][j], lcs[i][j - 1]);
        }
    }
}
// Your code here

Hint

The final answer is stored in the bottom-right cell of the matrix.

Practice

1. What does the Longest Common Subsequence (LCS) between two strings represent?

easy

A. The longest sequence of characters that appear in both strings in the same order, but not necessarily consecutively

B. The longest substring that appears exactly the same in both strings

C. The shortest sequence that can be formed from both strings

D. The total number of characters in both strings combined

Solution

1. Step 1: Understand the definition of LCS

   The LCS is about finding a sequence that appears in both strings in the same order, but characters do not need to be next to each other.

2. Step 2: Differentiate LCS from substring

   A substring requires characters to be consecutive, but LCS allows gaps, so it is not necessarily a substring.

3. Final Answer:

   The longest sequence of characters that appear in both strings in the same order, but not necessarily consecutively -> Option A

4. Quick Check:

   LCS means longest common sequence, not substring [OK]

Hint: LCS allows gaps; substring does not [OK]

Common Mistakes:

• Confusing LCS with longest common substring
• Thinking characters must be consecutive
• Assuming LCS is the combined length

2. Which of the following is the correct way to initialize a 2D array dp of size (m+1) x (n+1) with zeros in JavaScript for LCS dynamic programming?

easy

A. const dp = Array(m+1).fill(Array(n+1).fill(0));

B. const dp = Array.from({length: m+1}, () => Array(n+1).fill(0));

C. const dp = new Array(m+1).map(new Array(n+1).fill(0));

D. const dp = Array(m+1).map(Array(n+1).fill(0));

Solution

1. Step 1: Understand how to create independent inner arrays

   Using Array.from with a function creates new inner arrays for each row, avoiding shared references.

2. Step 2: Analyze each option

   Array(m+1).fill(Array(n+1).fill(0)) shares the same inner array for all rows, causing bugs. Options C and D pass an array to map() instead of a function, causing a TypeError. Array.from({length: m+1}, () => Array(n+1).fill(0)) correctly creates independent arrays.

3. Final Answer:

   const dp = Array.from({length: m+1}, () => Array(n+1).fill(0)); -> Option B

4. Quick Check:

   Use Array.from with function for 2D arrays [OK]

Hint: Use Array.from with function to avoid shared inner arrays [OK]

Common Mistakes:

• Using fill with array directly causing shared references
• Passing an array to map() instead of a function
• Not initializing inner arrays properly

3. What is the output of the following JavaScript code that calculates the length of the LCS for strings s1 = 'abcde' and s2 = 'ace'?

function lcsLength(s1, s2) {
  const m = s1.length, n = s2.length;
  const dp = Array.from({length: m+1}, () => 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;
      } else {
        dp[i][j] = Math.max(dp[i-1][j], dp[i][j-1]);
      }
    }
  }
  return dp[m][n];
}
console.log(lcsLength('abcde', 'ace'));

medium

A. 4

B. 2

C. 3

D. 5

Solution

1. Step 1: Trace matching characters between 'abcde' and 'ace'

   The common subsequence is 'ace' with length 3.

2. Step 2: Confirm DP calculation

   The code correctly fills dp table and returns dp[5][3] = 3 as the LCS length.

3. Final Answer:

   3 -> Option C

4. Quick Check:

   LCS('abcde','ace') = 'ace' length 3 [OK]

Hint: Count matching chars in order, skipping mismatches [OK]

Common Mistakes:

• Counting only consecutive matches (substring)
• Confusing length with total characters
• Off-by-one errors in indexing

4. The following code attempts to compute the LCS length but has a bug. What is the error?

function lcsLength(s1, s2) {
  const m = s1.length, n = s2.length;
  const dp = Array(m+1).fill(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;
      } else {
        dp[i][j] = Math.max(dp[i-1][j], dp[i][j-1]);
      }
    }
  }
  return dp[m][n];
}

medium

A. The inner arrays in dp share the same reference causing incorrect updates

B. The loops start from 0 instead of 1

C. The dp array is not initialized with zeros

D. The comparison s1[i-1] === s2[j-1] is incorrect

Solution

1. Step 1: Analyze dp initialization

   Using fill with an array fills dp with references to the same inner array, so all rows share one array.

2. Step 2: Understand impact on updates

   Updating dp[i][j] changes all rows at column j, corrupting the DP table and causing wrong results.

3. Final Answer:

   The inner arrays in dp share the same reference causing incorrect updates -> Option A

4. Quick Check:

   Array fill shares references, use Array.from instead [OK]

Hint: Avoid fill with arrays; use Array.from for 2D arrays [OK]

Common Mistakes:

• Using fill with arrays causing shared references
• Starting loops at 0 causing index errors
• Incorrect character comparison

5. Given two strings s1 = 'AGGTAB' and s2 = 'GXTXAYB', which of the following is a valid Longest Common Subsequence (LCS)?

hard

A. "GXAYB"

B. "GXTAB"

C. "AGTXB"

D. "GTAB"

Solution

1. Step 1: Identify common subsequences in order

   Check which sequences appear in both strings in order without rearranging characters.

2. Step 2: Validate each option

   "GTAB" appears in both strings in order. Options A, B, and C contain characters out of order or extra characters not matching subsequence rules.

3. Final Answer:

   "GTAB" -> Option D

4. Quick Check:

   Valid LCS must appear in both strings in order [OK]

Hint: Check order and presence of characters in both strings [OK]

Common Mistakes:

• Choosing sequences with characters out of order
• Including characters not in both strings
• Confusing subsequence with substring