Professional Courses
Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Categories
Interactive Games
Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
Typing
Memory
Math
English Adventures
Knowledge
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Interactive Audio Lesson
Listen to a student-teacher conversation explaining the topic in a relatable way.
Introduction to Longest Common Subsequence
Unlock Audio Lesson
Signup and Enroll to the course for listening the Audio Lesson
Today, we're going to discuss the Longest Common Subsequence, or LCS. To start, can anyone tell me what they think a subsequence is?
Is it like a smaller sequence taken from a larger one, in the same order?
Exactly! A subsequence is formed from a sequence by deleting some elements without changing the order of the remaining elements. Now, why do you think finding the longest common subsequence is important?
I think it helps in comparing two sequences to see how similar they are?
Right! It's crucial in areas like bioinformatics to compare DNA sequences, helping to identify genetic similarities. Let's remember that LCS helps us drop letters if needed while keeping track of the order. That makes it different from finding just common words.
Dynamic Programming Approach
Unlock Audio Lesson
Signup and Enroll to the course for listening the Audio Lesson
Now, let's look at how we can efficiently compute the LCS using dynamic programming. Can someone remind me what dynamic programming is?
Isn't it about breaking problems into smaller subproblems and storing results to avoid recalculating them?
That's spot on! In the context of LCS, we build a table of size m x n and fill it based on certain rules. If elements match, we add 1 to the diagonal cell. If not, we take the maximum of left and above. Can anyone give an example of this process?
For the strings 'abc' and 'ac', if we reach both positions 'a', we add 1 and move diagonally, right?
Exactly! Let's keep practicing these pairings to get good at filling the table.
Applications of LCS
Unlock Audio Lesson
Signup and Enroll to the course for listening the Audio Lesson
Besides bioinformatics, can anyone think of where LCS might be applied in the tech world?
What about comparing text files, like in programming?
Excellent! The `diff` command in UNIX uses the concept of LCS to identify changes between files. Why do you think this is useful?
It helps developers see what has changed and what can be preserved between versions.
Correct! Understanding these concepts is highly relevant in software development, data analysis, and more. Remember, recognizing similarities is key in both genetics and technology.
Introduction & Overview
Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.
Quick Overview
Standard
The longest common subsequence (LCS) problem explores how to find the longest sequence that can be derived from two sequences by dropping some letters without rearranging the remaining letters. This section delves into its computational implications, applications in bioinformatics, and the dynamic programming approach for efficiently solving the problem.
Detailed
Longest Common Subsequence
The longest common subsequence (LCS) is a key problem in computer science and bioinformatics where the goal is to determine the longest subsequence present in both sequences, allowing for the omission of some characters. This section explores both the theoretical aspects and practical applications of LCS.
Key Points
- Problem Overview: LCS differs from the longest common subword as it permits the omission of characters. For instance, between the strings "secret" and "bisect", allowing for drops leads to longer matches (e.g., "sect").
- Computational Significance: Finding LCS is relevant in fields like genetic sequencing, where it helps determine evolutionary similarities by comparing DNA sequences.
- Dynamic Programming Approach: The LCS can be solved in a time-efficient manner using dynamic programming, which relies on constructing a table that records results of subproblems, ultimately leading to an overall solution computed in O(m*n) time.
- Applying LCS: Tools like the UNIX
diffcommand employ the principles of LCS to compare text files, identifying the minimum number of differences by determining shared sequences.
Overall, understanding LCS and its efficient computation is crucial for applications in computer science, especially in areas like bioinformatics.
Youtube Videos
Audio Book
Dive deep into the subject with an immersive audiobook experience.
Introduction to Longest Common Subsequence (LCS)
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
So, we can now look at a slightly more general problem than longest common subword in one which is more interesting computationally. So, what if we do not look for an exact match, but we allow a self should drop some letters. So, we have a subsequence not a subword, it is allows us to drop some letters and now, if you want to know, after dropping some letters, what is the longest match we can find.
Detailed Explanation
The longest common subsequence (LCS) problem differs from the longest common subword problem as it allows for letters to be dropped from sequences instead of requiring exact matches. This flexibility enables us to find longer sequences that match after some letters are omitted. For example, when comparing segments from two words, we can achieve a longer matched sequence by selectively dropping letters.
Examples & Analogies
Think of it like finding the common theme in two stories. If Story A includes the word 'hero' and later drops it to include 'brave', while Story B includes 'bravery', you can still identify that both themes relate to courage, even though not all letters align perfectly.
Applications of LCS
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
So, before we proceed it useful to look at why the longest common subsequence problem is interesting. So, one of the area is an bio informatics. So, biologist are interested in identifying, how close two species are each other in the genetic sense.
Detailed Explanation
The LCS problem is significant in various fields, one of which is bioinformatics. In genetics, evaluating how closely related two species are can be understood through their DNA sequences. A comparison of DNA sequences using LCS helps to unravel similarities and differences, determining genetic relationships and evolutionary processes efficiently.
Examples & Analogies
Imagine two different species of animals, such as a lion and a tiger. By examining their DNA and looking for the longest common sequences, researchers can see how closely related they are, similar to figuring out if two cousins share common traits in a family tree.
Understanding Inductive Structure of LCS
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
So, let us try understanding inductive structure of this longest common subsequence problem directly, not throw the longest common subword. So, the first thing to note is that if I am looking for this longest common subword between these two, supposing I find that a 0, in fact equal to b 0.
Detailed Explanation
The inductive structure of LCS is based on breaking down the problem into smaller subproblems. If two characters from the sequences match, we can combine them into the LCS and then continue searching for matches in the remaining characters. If they don’t match, we explore two possible scenarios: either excluding the first character from one sequence or excluding it from the other. We continue this process until all possible subsequences have been considered.
Examples & Analogies
Think about it like constructing a puzzle. If the first two pieces fit together, you confidently connect them and look for pieces that extend the connection. However, if they don’t, you must try different placements to see which pieces fit best to complete the picture.
Recursion and Dynamic Programming in LCS
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
So, as usual let LCS i comma j, stand for the LCS of the problem starting at a i and b j. So, if a i equal b j as we say, LCS of i j is 1 plus LCS of i plus 1 j plus 1.
Detailed Explanation
In LCS, the recursive formula states that if two characters match, we can increment our count by one and check the subsequent characters. This builds upon the concept of dynamic programming where the solution to each subproblem informs the broader solution. We can also track a value, LCS(i, j), which reflects the maximum LCS found at any point during the recursive calls.
Examples & Analogies
This is like climbing a ladder. Each step forward is a successful match of characters—each rung you reach represents adding to your total height (the length of the LCS). If you can’t climb up one rung, you might need to jump to the next and try again, similar to exploring different character combinations.
Final Steps and Code Implementation of LCS
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
So, the code for the LCS is little bit simpler then for LCW, because we do not have to keep track of these maximum value and varied occurs, because we only need to find the value at 0 c.
Detailed Explanation
The implementation of LCS involves filling out a grid that stores the results of subproblems. The edges of the grid are initialized to zero because LCS with an empty string is zero. As each cell is filled, whether through matching characters or taking the maximum value from adjacent cells, we build up to the final LCS length, which can be found at the point corresponding to the full length of both sequences.
Examples & Analogies
Imagine you're mapping out a city on a grid. Each intersection represents a decision point for your journey. By marking where you successfully navigated streets (LCS), you can trace back the optimal route you’ve taken, understanding how you reached your final destination (the LCS length).
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
-
Subsequence: A sequence derived from another sequence by deleting some elements without rearranging the rest.
-
Dynamic Programming: A computational technique for solving problems by breaking them into smaller, manageable subproblems.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
-
Example 1: Comparing the sequences 'AGGTAB' and 'GXTXAYB'. The LCS is 'GTAB', which has a length of 4.
-
Example 2: For the sequences 'ABCBDAB' and 'BDCAB', the longest common subsequence is 'BCAB', with a length of 4.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
🎵 Rhymes Time
-
To find LCS, you must see, match and align, just wait and be.
📖 Fascinating Stories
-
Imagine two friends comparing their favorite books, each sharing titles but allowing some omissions. Their overlapping favorites make the longest common subsequence.
🧠 Other Memory Gems
-
Remember 'LCS' - 'Look Closely at Same': Look for similar patterns in the sequences by omitting other elements.
🎯 Super Acronyms
Use 'LCS' for 'Longest Common Sequence' - a simple reminder!
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
-
Term: Longest Common Subsequence (LCS)
Definition:
A sequence that can be derived from two sequences by deleting some elements without changing the order of the remaining elements.
-
Term: Dynamic Programming
Definition:
A method for solving complex problems by breaking them down into simpler subproblems and storing the results to avoid redundant calculations.
-
Term: Biological Informatics
Definition:
A field that involves applying computational techniques to analyze biological data, particularly in genetics.