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
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This question is number 7.13 in "Elements of Programming Interviews" by Adnan Aziz (they do Rabin-Karp but same problem, different algorithm) - Věda a technologie
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 !!!
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
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
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
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.
The only one to explain the "THE TRICKY PART WHICH SO MANY OTHERS SO CONVENIENTLY SKIP"
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.
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.
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!
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
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 CZcams 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...
I trust This dude's Teaching skills with my career, He's so CLEAR, To the Point and explains in Simple Language that no CZcams Channel Does that. Absolutely Loved it.
thank you for this content, it helped me a ton!! I loved how hyped you were explaining this algorithm, great job!
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
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
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.
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
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
This is the first time I understood KMP algorithm. Thanks a lot!
nice
Dude, thanks. That's the most elaborative explanation I came across. Good work!
ye
Thanks, man!
This is the Best ever explanation on CZcams. I was stuck on this algorithm for hours
Great video! Very well explained, as usual. Thank you.
haha this vid is decent..old thought too...I wanted to redo it but I never did
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
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.
Amazing content. I've been going through your videos and they are so helpful!
This is amazing. SO clear. Explain every single part of it.
great
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
Man you are great, all your explanations are deep and clear, thanks for your videos 🙌🙌
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
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?
Amazing Amazing explanation buddy! Could not find many on CZcams explaining as clearly. Thanks.
sure
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
The best explanation all over the internet. Hats off to you sir!
sure
Finally got something worth watching... thanks buddy
hahahahaha ok, thx, I want to redo this but yeah
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
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.
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
Honestly..This is the best explanation out there on youtube....Thanks:)
eh
Awesome! What a concise explanation.
Thanks
Greatly explained, i saw a couple other videos but yours made me really understand it
Didn't understand this during college... but you sir made me understand this within minutes... Great explanation :)
great
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
Your explanations are *dope*
thx.
I like how you personally react to almost all comments. Keep up the good work bro :)
Thanks a lot. Really helped in understanding clearly !
sure!
Thank you, bro, for the brief explanation. I have one question for string pattern matching in a different approach. What does it make the two-pointer technique (sliding widow technique) slower than this Algorithm?
I'm not sure, I don't remember this too much
Really like the way you explained! thanks man!
sure
Congratulations, awesome explanation!
thanks :)
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.
This was awesome man! Finally I understood the algo!
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 :)
OMG, this video is soooo great!!! love it
Good video!! Look a few other before this one. This is the first one make me understand.
great
watched at speed 0.75....:)
Same
@@B85046 😭
best Explanation so far on Internet
ye
Only thing I am not able to understand is when making prefix-suffix array, if i and j mismatches why do we make i=arr[i-1]; what diff does it make?
It is very helpful than the other long KMP articles.
nice
Bro one of the best explanations. I will check all your content. Keep it up
great
Yay I think I understand it at last, thanks man!
Watched several KMP videos and it is the first one that made me understand
great
Thanks for the video, it really helped me a lot.
nice
Same here boss...😁
Was really having trouble understanding this algo..This helped a lot :-)
great
you are really fantastic bro, I watched your videos on dynamic programming, they were just awesome and this is also like "Bawaal".
nice
Love your channel!!
thanks
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.
Finally got it!!! Thank you so much!!
Thank you so much such a crystal clear explanation with example..
sure
it was a great help. Thanks man
what a marvelous explanation thanks! :)
it is ok
This is the "BEST" explanation of KMP that ever existed!
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.
Non-indians felt you were yelling, I felt exactly like my classroom :) (Sad-Music in background)
🤣🤣🤣💯
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
Can I use KMP pattern matching algorithm in leetcode question implement strstr() ? I tried to write KMP algo and leetcode is giving me acceptance with 6ms, but if I use brute-force approach you explained (match first character of pattern and text, if match move forward till end of pattern), leetcode is giving me 0ms. Theoretically, KMP should be faster than the later approach. right?
Great Explanation, thanks!
thx
amazing explanation, keep the good work going
ye
What if we never face a suffix == prefix , what is the time complexity in this case? Is KMP still preferable to Rolling-Hash ?
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 😀
Finally .... best video to undersand kmp algo clearly
thanks - the video is decent
Finally, I understand this one! Thank you, you're a hero.
Great Video,KMP is now crystal clear to me .Thanks !!!
Love from India♥
I cannot thank you enough for this
sure
Great explanation, thank you!
sure
you always make me understand even the hardest algorithm
ye
This is the underrated youtube channel on programming
nah we are just "rated"
GREAT！Really helpful :)
I love you.
Thanks man, very good explanation!
You are very confident and good explanation, thanks!
Thank you!
I've seen 1-indexed pi tables and 0 indexed pi tables, does it matter which one you use? Also, if the pattern (substring) you are trying to find doesn't have any repeating characters this algo would be as bad as the brute force approach right?
Perfect explanation. Thank you so much!
Thank you, glad you liked it 😀
Do check out backtobackswe.com/platform/content
and please recommend us to your family and friends 😀
Hi, what is the point in making an entry in the border table for the last character in the substring? As there cant be a mismatch that requires its use? Once you get to that point in the substring you'll either find a match and the algorithm terminates, or you find a mismatch and look at the border of the table[0...7]
Really nice explanation !!! :D
thanks
best explanation so far. thanks a lot
ye
Thank you so much for this! Great video!
best explanation! Loved it!
thx
No it was the perfect pace! Good way to keep people engaged in the explanation :)
yo
When creating the table if on a match we are incrementing i then what if you again find a `d` in string `dsgwadsdsg` - the table should be 0 000012123 right so how will third 'd' gets its length as 1 if we have incremented 'i' already.