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Longest common subsequence problem using dynamic programming involves finding the longest subsequence that is common to two or more given sequences.

Longest Common Subsequence- Dynamic Programming | Data structures and algorithms
Longest Common Subsequence (LCS) - Recursion and Dynamic Programming
Longest Common Subsequence Problem using
1. Recursion
2. Memoization
3. Dynamic Programming

#lcs #algorithm #longestcommonsubsequence #daa #datastructures

Longest Common Subsequence Problem solution using recursion
Given two sequences, find the length of longest subsequence present in both of them.
A subsequence is a sequence that appears in the same relative order, but not necessarily contiguous.

For example, “abc”, “abg”, “bdf”, “aeg”, ‘”acefg”, .. etc are subsequences of “abcdefg”

In this video, I have explained the procedure of finding out the longest common subsequence from the strings using dynamic programming(Tabulation method). It is also known as bottom-up approach.

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About :-
The longest common subsequence (LCS) problem is a classic problem in computer science and is often solved using dynamic programming. A subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.

The LCS problem is widely used in various applications, including text comparison, DNA sequence analysis, version control systems, and more. By identifying the longest common subsequence between two sequences, we can determine their similarities and differences, which can be valuable in many fields.

Dynamic programming is a common approach to solve the LCS problem efficiently. The key idea behind dynamic programming is to break down a complex problem into smaller overlapping subproblems, solve each subproblem only once, and store the results for future use. In the case of the LCS problem, dynamic programming helps us build a table that stores the lengths of the longest common subsequences for different prefixes of the given sequences.

The dynamic programming solution for the LCS problem typically involves the following steps:

Initialize a table with appropriate dimensions to store the lengths of the LCS for the prefixes of the sequences.
Traverse the table row by row, starting from the first row and first column, and fill in the values based on the following rules:
If the characters at the current positions in both sequences are the same, the value in the current cell is one plus the value in the diagonal cell (top-left).
If the characters are different, the value in the current cell is the maximum of the value in the cell above or the value in the cell to the left.
Once the table is fully filled, the bottom-right cell will contain the length of the longest common subsequence.
To find the actual subsequence, start from the bottom-right cell and backtrack through the table by following the rules used for filling the table:
If the characters at the current positions are the same, include the character in the subsequence and move to the diagonal cell.
If the characters are different, move to the cell with the larger value among the cell above and the cell to the left.
Continue this process as shown in the tutorial

In conclusion, the longest common subsequence problem is a fundamental problem in computer science, and its dynamic solution provides an efficient way to find the length and actual subsequence that is common to multiple given sequences. This approach is widely applicable and has been instrumental in various fields where sequence comparison and analysis are required.


Cover topics:-
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longest common subsequence code
longest common subsequence (lcs)
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longest common subsequence explanation

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