Knuth-Morris-Pratt (KMP) Pattern Matching Substring Search - First Occurrence Of Substring
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Question: Given a string s and a pattern p, determine if the pattern exists in the string. Return the index of where the first occurrence starts.
Further Explanation From Tuschar Roy: • Knuth-Morris-Pratt(KMP...
The Brute Force
The naive approach to solving this is looking in s for the first character in p.
If a match is found we begin a search from that index, call it i (for intersect).
We compare the 2nd character of p with index i + 1 of s
We compare the 3rd character of p with index i + 2 of s
...and so on until we have matched to all of p without either having overrun s or having found a mismatch between characters being compared.
We can then return i as our answer.
It doesn’t work well in cases where we see many matching characters followed by a mismatching character.
Complexities:
Time: O( len(s) * len(p) )
In a simple worst case we can have
s = "aaaaaab"
p = "aaab"
The problem is that for each first character match we have the potential to naively go into a search on a string that would never yield a correct answer repeatedly.
Other Algorithms
There are three linear time string matching algorithms: KMP (nuth-Morris-Pratt), Boyer-Moore, and Rabin-Karp.
Of these, Rabin-Karp is by far the simplest to understand and implement
Analysis
The time complexity of the KMP algorithm is O(len(s) + len(p)) "linear" in the worst case.
The key behind KMP is that it takes advantage of the succesful character checks during an unsuccessful pattern comparison subroutine.
We may have a series of many comparisons that succeed and then even if one fails at the end, we should not repeat the comparison work done since we already saw that a series matched.
What we will do is very similar to the naive algorithm, it is just that we save comparisons by tracking the longest propert prefixes of pattern that are also suffixes.
The key is that everytime we have a mismatch we try our best to prevent going backwards in s and repeating comparisons.
Algorithm Steps
We will preprocess the pattern string and create an array that indicates the longest proper prefix which is also suffix at each point in the pattern string.
A proper prefix does not include the original string.
For example, prefixes of “ABC” are “”, “A”, “AB” and “ABC”. Proper prefixes are “”, “A” and “AB”.
For example, suffixes of "ABC" are, "", "C", "BC", and "ABC". Proper prefixes are "", "C", and "BC".
Why do we care about these??
We know all characters behind our mismatch character match.
If we can find the length of the longest prefix that matches a suffix to that point, we can skip len(prefix) comparisons at the beginning.
The key reason we care about the prefix to suffix is because we want to "teleport" back to as early in the string to the point that we still know that there is a match.
Our goal is to minimize going backwards in our search string.
Complexities:
Time: O( len(p) + len(s) )
We spend len(p) time to build the prefix-suffix table and we spend len(s) time for the traversal on average.
Space: O( len(p) )
Our prefix-suffix table is going to be the length of the pattern string.
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HackerRank: / @hackerrankofficial
Tuschar Roy: / tusharroy2525
GeeksForGeeks: / @geeksforgeeksvideos
Jarvis Johnson: / vsympathyv
Success In Tech: / @successintech
++++++++++++++++++++++++++++++++++++++++++++++++++
This question is number 7.13 in "Elements of Programming Interviews" by Adnan Aziz (they do Rabin-Karp but same problem, different algorithm)
Table of Contents: (I'm literally screaming. I'm sorry. I want to redo this video to make it better.)
Introducing The Creators The KMP Algorithm* 0:00 - 0:15
Problem Introduction With The Naive Approach 0:15 - 2:30
Why The Naive Approach Is Not Good 2:30 - 2:45
Walkthrough How The Algorithm Works 2:45 - 8:14
Building The Suffix-Proper-Prefix Table 8:14 - 12:34
Using The Suffix-Proper-Prefix Table In Traversal Walkthrough 12:34 - 15:08
Time & Space For The Table Build Step 15:08 - 15:51
Time & Space For The Traversal Step 15:51 - 16:08
Overall Time & Space 16:08 - 16:25
Summarizing Our Learnings 16:25 - 16:40
Wrap Up (Begging For More Subs) 16:40 - 17:05
*All 3 of the creators published the final paper together.
That's good enough, I was looking for info on distributed substring searching of very large string. It gives me nice refresh on the basics.
great
11:50 was the tricky part as we use KMP logic again in building the table itself.
it is the best explanation I found on youtube of KMP algo, no need to redo it
Hey ., this is great ,,, greater than geeks for geeks really !!!
BRO STOP YELLING AT ME I ALREADY SUBBED I KNOW YOU'RE GOOD
hahaha ok
Back To Back SWE jk😂 thanks for the vids
@@dimejifaluyi1759 yw fam
😃
paused to find this comment
An algorithm invented by 3 people and they expect us to come up with this in 45 min. Makes sense
Fun fact: Dijkstra came up with his algorithm within 20 minutes while having a walk.
Leetcode "easy"
@@salmanbehen4384 Fun Fact : Dijkastra was thinking about this for a long time.
those algo interview questions are the most meaningless things ever.. system design is kind of interesting...but algo..jesus
well its popular so its good to know it
You're the best explainer of algorithms I've ever seen. The extra very visible colored text on the screen while you're explaining also makes a huge difference.
I never knew I needed this kind of teaching which makes me feel like im scolded in order to understand why a box is incremented.
lmao, sorry, old video, forgive me
@@BackToBackSWE Thats actually helped me to understand easily.Best way to teach is to stress key point to understand that concept
I had a hard time understanding KMP but you broke it down so well and I get it now. This goes for all the videos I've watch from you, thank you!
nice
I really like your passion and felt very involved during the video
So far it’s the most approachable KMP video I’ve seen.
I vote for keeping the speed and voice as is, they allow the video to stand out in a good way
ye
Thanks to you I'm one less algoritm away towards achieving my dream. So thanks for the good work and keep it up ;))
Yuh. Go achieve them dreams.
I trust This dude's Teaching skills with my career, He's so CLEAR, To the Point and explains in Simple Language that no TH-cam Channel Does that. Absolutely Loved it.
Now that's a cool explanation of a seemingly difficult concept. The thing is you cannot watch this video without some sort of preparation. You have to understand the limitations of the naive approach and then think of a logical method/alternative to overcome that. Only after that, when you watch the video and implement the algo, would it become clear to you...
Good job with the video, guys!!
yeah, this video is ok
Your explanations are amazing! This is the first time I fully understand the kmp algorithm. Thanks a lot! Keep up the good work ;)
thanks and ok.
people commenting "stop yelling" and all I see is the passion with which you are trying to teach us in the simplest way possible. I came here after watching 2-3 vids but your video cleared all my doubts. Thank you for making this video.
after lots of videos about Knuth-Morris-Pratt algorithm i just understood how it works...when we have dismatch we just go one step behind and we look at the value of that step and thats it!this is where the i goes(index)..pfff at last!THANKSSSSSSS.LOVE YOU BOY
hahaha! try this 5 day free mini course for some good content backtobackswe.com/
@@BackToBackSWE im on my way to this...many thanks from a Greek postgraduate in Maths and Statistics.
Calm down a bit you good.
hahahahahahahaha, thanks
@@BackToBackSWE ...Yes.. please slow down.. That will help the audience to process what you are saying.
@@peeyar2000 ok
@@BackToBackSWE 100% disagree with this comment. your cadence and charisma is half the reason this is all working so well. currently watching through EVERY video on this channel. It's literally the best resource I've ever found on this stuff.
@@jonathanfoster5106 hahahahaha ay, wassup, local to this topic they are right and their comments are attesting to the explanation's weakness and incomplete nature. Globally what you observe are correct.
Thanks, man!
This is the Best ever explanation on TH-cam. I was stuck on this algorithm for hours
After reading a bit on Internet and then coming to your video. I got it straight into my head. Really well explained but people really need to have some background before watching such algorithms to just grasp it at one go.
Thanks man
Oh yeah, this video is old and made in an "ok" fashion
Thank you from my heart.
I was about to give up on this algorithm, until I found this video, I appreciate this work so much.
Awesome explanation! Don't worry, the way you're explaining is not screaming. It is rather the enthusiasm with which you explain a problem and I have seen that enthusiasm in almost every video of yours.
Looking forward to more of your explanations. Kudos to you!
thanks
I love the way you reply literally every single comment in this channel, this shows how much you like what you're doing. And indeed we can see it in your eyes while explaining! Thanks so much for bringing content with such quality and love! I don't usually write comments on TH-cam but this channel made me stop for some few minutes to write this.
I don't like what I'm doing, 70% of the time I hate it. I am just dedicated to whatever I start, it must end successfully at any cost.
@@BackToBackSWE Hahaha really you don't like it? I was 100% sure you loved it because you put so much energy into explaining the algorithms to us.
I guess I was wrong then...
The only one to explain the "THE TRICKY PART WHICH SO MANY OTHERS SO CONVENIENTLY SKIP"
ok
This is the first time I understood KMP algorithm. Thanks a lot!
nice
Finally .... best video to undersand kmp algo clearly
thanks - the video is decent
if there is any topic i am searching on utube nd u have a video on it. i just simply watch it first, and then continue my research(that most of the time is not even needed, as u clear all the related concepts). thanks
Didn't understand this during college... but you sir made me understand this within minutes... Great explanation :)
great
Wow, I applaud your dedication to try and reply to all the comments mate! Good stuff and honestly I should've discovered this channel before!
hey
Great Video,KMP is now crystal clear to me .Thanks !!!
Love from India♥
Honestly..This is the best explanation out there on youtube....Thanks:)
eh
Thanks bro best explanation available on internet
Really a superb explanation underlined and outlined all components of the algorithm in a very strategic way. The best thing about your videos is the energy you impart over the explanations about the tricky part or sth unintuitive. Thanks.
thx
Good lord glad I found you! This is the best explanation I've found! Thank you! Will be following. Don't slow down your enthusiasm makes it fun.
ye lol
Finally, I understand this one! Thank you, you're a hero.
best Explanation so far on Internet
ye
Your explanation is the best among many TH-camrs.
thx
Very nice video! it's also interesting to know that we can consider the time complexity as O(n), because if we add an early exit condition for when p is longer than s (where we directly return -1), then we can affirm that m cannot be greater than n, so in the worst case, m would be equal to n, which gives 2n, and by removing the constant, we get a time complexity of O(n)
ye
The best explanation all over the internet. Hats off to you sir!
sure
I'm doing leetcode looking for jobs right now, and this was really helpful! I actually understood how the algorithm works for once, instead of the video just showing the algorithm working. Thanks!
Like your style of explaining. One of the videos that kept my attention through the end and not bore me to lose focus. Thanks!!
great and sure
I usually watch you at 2x speed but after seeing the comments, I slowed you down back to 1x to see whats up. You talk unbelievably slow in comparison to 2x LOL I have no idea what people are on about. That said, got stuck on this algo in my lectures but this made it crystal clear cheers
Fascinating. Hello.
Amazing Amazing explanation buddy! Could not find many on TH-cam explaining as clearly. Thanks.
sure
Watched several KMP videos and it is the first one that made me understand
great
Greatly explained, i saw a couple other videos but yours made me really understand it
It would be nice to elaborate at 11:55 why "i" becomes the value of P[i-1] and not rolls all the way to zero.
It is a little tricky but I will try, we want to minimize the number of times we roll back to 0. So if there is a miss match,we check if we there is a suffix which is also a prefix in the string we have checked till now, if it is there then we make value of i point at the end of the suffix, which is stored in P[i-1] And if it is not there we directly make i=0. Hope that helps :)
I got confused on the topic quite a bit, but this video explains it real clearly, thanks man, this is greatly appreciated
this video is ok
It would really be helpful if you also make videos on some mathematical topics like Number Theory, Combinatorics, Modular Arithmetics, and whichever are important for competitive programming. There are very limited videos on the internet available on these topics and most of them are not well explained. Thanking you in advance 💙
I would but our focus is on interviews and helping people around that vs competitive programming. I would but we have to pursue our core mission.
Non-indians felt you were yelling, I felt exactly like my classroom :) (Sad-Music in background)
🤣🤣🤣💯
This is the "BEST" explanation of KMP that ever existed!
It is very helpful than the other long KMP articles.
nice
No it was the perfect pace! Good way to keep people engaged in the explanation :)
yo
Goated at explaining advanced algos!
Brilliant explanation - certainly one of the best for the KMP algorithm. I like how you focus on the intuition behind the algorithm, as opposed to the traditional textbook approach. Have you considered writing a book on algorithms?
Very good explanation, you didn't miss any detail of the Algorithm thats what I liked.
ye
Best video on KMP
thanks
This is the underrated youtube channel on programming
nah we are just "rated"
Hey dude, thanks for the great vids. I do not know how and why, but somehow your logical explanation of the stuff just rocks compared to many many others. Pls keep doing the good stuff, bro.
cuz im average intellect and decided to do all this
Ohhh I didn't know that you were teaching so fast as compared to your latest videos. I think that was excitement😁😁. But you were fantastic same as you are now
Yeah my b, old videos
I love his energy. Hard to loose focus.
Happy Holidays! Really glad to help 🎉 Do you know about the 5 Day Free Mini Course? Check it out here - backtobackswe.com/
watched at speed 0.75....:)
Same
@@B85046 😭
Nice explanation but I just realized I was holding my breath while watching this video. Just calm down a bit man.
hahahahaha, I know: backtobackswe.com/im-sorry
Having an example and working through it step by step is very helpful
Your video is great! Thank you.
thx
just did read other comments, saying slow-down, you don't need to slowdown or low your vice....You voice pitch and speed is perfect, which demands audience attention, so your speed and voice pitch is very important! it has energy and vibe bro! keep it up! one request don't cut/cut video just make it continuous, because its like fragments/clusters for brain! kind of distraction!!!
lol thx
You are very confident and good explanation, thanks!
Thank you!
i feel yours channel vedios have one solid content for every topic i search
every doubt is getting cleared one single veido ..wow thank u soo much bro
yes and great.
dude you deserve more likes
thanks
You've got the gift of explaining the concept
You are becoming my first choice for learning any new algorithm. Keep uploading👍 Hats off👏
Thank you, glad you liked it 😀
Do check out backtobackswe.com/platform/content
and please recommend us to your family and friends 😀
Thank your for making KMP really clear
sure
Whenever I don't understand an algorithm, I come to this page. Dude shout at me like my high school track and field coach, but it definitely gets in my head
great to hear - hahahaha, fuck interviews I hate this. No one was going to go and do this and teach in an academic manner that makes sense. We still haven't lived up to the mission/vision I set out with...it's why I get mad...99% of those who understand something won't go teach it, let alone give up their free time and do it for the internet and teach it well.
rant
I wish you had gone into a bit more details regarding how the complexity is O(m + n). It's not that trivial as you can see that there's a nested loop which is going back and forth in case of both the build table and traversal. I figured it out though.
BTW absolutely love your explanations and the energy.
yeah
Yes , I had a hard time understanding the complexity,
keep the same pace and enthu..ur making life simple..keep up the way ur doing it...
Was about to kms , this algo was so hard to understand, but man you saved me so much time plus you made me understand it really easily ( I have a caveman brain sorry for No punctuations in the paragraph :^) ) Thank you for this vid ❤
thank you for this content, it helped me a ton!! I loved how hyped you were explaining this algorithm, great job!
Man you are great, all your explanations are deep and clear, thanks for your videos 🙌🙌
Bro one of the best explanations. I will check all your content. Keep it up
great
Thanks a lot. Really helped in understanding clearly !
sure!
Hey buddy, I still don't get it :(
This video is ok, one of my first ones, I will redo it one day. Can be made much clearer.
watch it again bcz i did and it worked.
you are great ,you explain like goddddddd
ye
What if we never face a suffix == prefix , what is the time complexity in this case? Is KMP still preferable to Rolling-Hash ?
Wonderful explanation!
thanks
your content is just superb ..u are just amazing
thx
I didn't actually finish watching the video but a question popped in my mind. What if the suffix is not also a prefix, like in the first example where the sequence was aaaap, does the algorithm still work?
Have a great day handsome!
Yay I think I understand it at last, thanks man!
I hope I am never asked this question, great explanation.
This is amazing. SO clear. Explain every single part of it.
great
Shouldn't the Suffix-Proper-Prefix Table only go up to the search pattern's length - 1? A mismatch after the pattern's length would mean the pattern was already found and matching was already finished.
Dude, thanks. That's the most elaborative explanation I came across. Good work!
ye
best kmp video on ytb
this is the funniest contrast ive experienced in a while. Came here because my prof is a asmr-nap-mediation-device, but you... you might be TOO exited. But ive understood it... so thx i guess ?
you always make me understand even the hardest algorithm
ye
Best explanation for this question is here!
Kudos!
Find the longest suffix which is also the prefix to save us from reverting the searching. Thanks!
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Good video!! Look a few other before this one. This is the first one make me understand.
great
Thanks for the video but it still went over my head. May be I should come back here once again when I learn other algorithms.
yeah the video is ok - one of my first videos
Great video. A bit slower for slightly more involved stuff would be perfect or repeat with a second example that would help reinforce the explanation. Great job as always.
ok
Thank you so much for this! Great video!
Finally got it!!! Thank you so much!!
best kmp explanation on youtube
nah, Tuschar's is better...for now :)
@@BackToBackSWE you're very modest 😉
@@marlegagaming1274 no I'm srs
Unrelated but Donald Knuth's last name is pronounced like "Ka-Nooth" Great explanation, very clear.
noted, thanks!
Thanks for the video, it really helped me a lot.
nice
Same here boss...😁
Why use KMP when you can use RegEx? Is regex not allowed in technical interviews? Otherwise, a great explanation. I'm binge-watching all your videos!
thx and nice