The Dynamic Programming Approach

Dynamic programming offers an efficient solution to this problem by breaking it down into smaller subproblems and storing their solutions to avoid redundant calculations. At each step, we build upon the solutions of the smaller subproblems until we arrive at the solution for the entire problem.

Let's Dive into the Code

Without further ado, let's see how we can implement the LCS algorithm in JavaScript:

function longestCommonSubsequence(str1, str2) {
const m = str1.length;
const n = str2.length;

const dp = Array.from(Array(m + 1), () => Array(n + 1).fill(0));

for (let i = 1; i <= m; i++) {
for (let j = 1; j <= n; j++) {
    if (str1[i - 1] = str2[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]);
    }
}
}

let i = m, j = n;
let result = '';
while (i > 0 && j > 0) {
if (str1[i - 1] === str2[j - 1]) {
    result = str1[i - 1] + result;
    i--;
    j--;
} else if (dp[i - 1][j] > dp[i][j - 1]) {
    i--;
} else {
    j--;
}
}

return result;
}

// Example usage:
const str1 = "ABCDGH";
const str2 = "AEDFHR";
console.log("Longest Common Subsequence:", longestCommonSubsequence(str1, str2)); // Output: "ADH"

Breaking Down the Code

• We start by initializing a 2D array dp to store the lengths of the longest common subsequences for different prefixes of the input sequences.
• We iterate through each character of both strings and fill the dp array accordingly.
• Finally, we backtrack through the dp array to reconstruct the longest common subsequence.