Graph Data Structure 4. Dijkstra’s Shortest Path Algorithm

This is the fourth in a series of computer science videos about the graph data structure. This is an explanation of Dijkstra’s algorithm for finding the shortest path between one vertex in a graph and another. Indeed, this explains how Dijkstra’s shortest path algorithm generates a set of information that includes the shortest paths from a starting vertex and every other vertex in the graph. It also mentions why Dijkstra’s shortest path algorithm is an example of a greedy algorithm.

Пікірлер: 815

  • @daringdarius5686
    @daringdarius56864 жыл бұрын

    I don't know if you know this, and this is 4 years late, but this is one of the cleanest, easiest to understand video's (conceptually-wise) for Dijkstra's. I've seen several, but this! This is the best one. :)

  • @ComputerScienceLessons

    @ComputerScienceLessons

    4 жыл бұрын

    Great to hear! :)KD

  • @vijayalakshmi0714

    @vijayalakshmi0714

    2 жыл бұрын

    @@ComputerScienceLessons lol, but i'm listening even now, best explanation. Keep it up

  • @eatbreathedatascience9593

    @eatbreathedatascience9593

    2 жыл бұрын

    I agree fully. Best !

  • @tudorradu5848

    @tudorradu5848

    Жыл бұрын

    @@ComputerScienceLessons He's right! It was veryyy easy to understand. Thank you

  • @555aboud

    @555aboud

    5 ай бұрын

    stunning, clear explanation. Thank you so much!!!

  • @assansanogo1343
    @assansanogo13437 жыл бұрын

    FINALLY SOME CLEAR STUFF. almost crying

  • @OscarSotomayor

    @OscarSotomayor

    7 жыл бұрын

    jaja...you made my day

  • @MinecraftLetstime

    @MinecraftLetstime

    6 жыл бұрын

    Me too!!

  • @SkyWalker9669

    @SkyWalker9669

    4 жыл бұрын

    said what i wanna say

  • @exactzero

    @exactzero

    4 жыл бұрын

    HAHAHAHAHA

  • @veggieblues

    @veggieblues

    3 жыл бұрын

    mood

  • @SouravendraKrishnaDeb
    @SouravendraKrishnaDeb4 жыл бұрын

    We won't be visiting A, again. Me: CRIES LOUDLY

  • @ComputerScienceLessons

    @ComputerScienceLessons

    4 жыл бұрын

    A was no fun. :) KD

  • @ashutoshthite

    @ashutoshthite

    3 жыл бұрын

    🦍🦍😂😂

  • @trulyharsh

    @trulyharsh

    3 жыл бұрын

    Wiz Khalifa's "See You Again" Plays in The Background

  • @user-wq2iv3cq2h

    @user-wq2iv3cq2h

    3 жыл бұрын

    i laughed hard reading this

  • @royazut550
    @royazut5507 жыл бұрын

    !!!finally a good and simple explanation oh tears of joy... may the gods bless you with bugless codes

  • @neelparekh9846

    @neelparekh9846

    4 жыл бұрын

    "May the gods bless you with bug-less codes." I'm going to use that a lot.

  • @neptechbyte

    @neptechbyte

    3 жыл бұрын

    haha epic comment bro

  • @adityapappu4963
    @adityapappu49634 жыл бұрын

    This is literally one of the cleanest, simplest, no-nonsense beautiful explanations of an algorithm I have ever watched on KZread. Amazing. To-the-point. Crisp. And so easy to understand and digest. THANK YOU.

  • @reiniervanleeuwen9815
    @reiniervanleeuwen98155 жыл бұрын

    This has to be the best explanation of Dijkstra's Shortest Path algorithm... Thanks a lot!

  • @ComputerScienceLessons
    @ComputerScienceLessons7 жыл бұрын

    Hi FTP My scenario is for a non-directed graph (you can go backwards and forwards on any edge), so all the nodes can indeed be reached. However, for a directed graph, some nodes may be unreachable from the given start, as you have intimated. Dijkstra's algorithm finds the shortest paths only to the nodes that can be reached from the starting node. (if there is no path to a node from the start, it's irrelevant). The loop will end when all 'reachable' vertices have been visited. By the way, Dijkstra's algorithm doesn't work if the graph edges have negative weights.

  • @TANEM315
    @TANEM3157 жыл бұрын

    You sir are BY FAR the BEST teacher of algorithms on KZread or anywhere else I've seen algorithm lectures. THANK YOU FOR POSTING THIS! With your well-paced, methodical style you could probably teach anything!!!!

  • @amine_fadssi
    @amine_fadssi Жыл бұрын

    The best video on the internet explaining the Dijkstra’s algorithm, thanks a lot sir.

  • @ComputerScienceLessons

    @ComputerScienceLessons

    Жыл бұрын

    You're welcome :)KD

  • @matthewsattam1982
    @matthewsattam19827 жыл бұрын

    Extremely clear, extremely well put together visually. Well done, and thank you.

  • @ComputerScienceLessons

    @ComputerScienceLessons

    7 жыл бұрын

    I really appreciate your comment. Thanks.

  • @trellas3689

    @trellas3689

    8 ай бұрын

    extremely

  • @mikefriedman9573
    @mikefriedman95735 жыл бұрын

    Absolutely the best explanation. Cleared up any and all lingering questions in my mind.

  • @hadeneh
    @hadeneh6 жыл бұрын

    I signed in just to like this video.

  • @magicianwizard4294

    @magicianwizard4294

    4 жыл бұрын

    and to comment apparently

  • @hariprasathgcse3381

    @hariprasathgcse3381

    Жыл бұрын

    U r loyal

  • @Jbbubanic5434
    @Jbbubanic5434 Жыл бұрын

    I can't believe how well done this video was made. I appreciate your hard work at a visual representation of this algorithm.

  • @lewistian7975
    @lewistian79755 жыл бұрын

    BEST explanation of Dijkstra's algorithm EVER!

  • @johnstorm589
    @johnstorm589 Жыл бұрын

    Even 6 years later, this is still the best explanation ever

  • @mikelanigan9601
    @mikelanigan96015 жыл бұрын

    I must commend the quality and clarity of this video: it is by far the best video I've seen on KZread to date on the subject of explaining Dijkstra's Algorithm. There are so many other videos that do not deal with the problem of keep a record of the shortest route sufficiently systematically enough, in my opinion. This video is systematic, showing the use of a table to perform the algorithm very clearly. Instruction of this level is not accidental; my congratulations to those involved in its production and execution. You have done the domain of Computer Science the world of good. Keep up the great work!

  • @ComputerScienceLessons

    @ComputerScienceLessons

    5 жыл бұрын

    Thanks for the great comment Mike.

  • @taruchitgoyal3735
    @taruchitgoyal37358 ай бұрын

    I haven't found a better tutorial than this for understanding and computing distances using Dijkstra's algorithm. Thank you so much.

  • @ComputerScienceLessons

    @ComputerScienceLessons

    8 ай бұрын

    You are most welcome :)KD

  • @timuralmamedov1900
    @timuralmamedov19006 жыл бұрын

    Great explanation! Finally, I understood it. The table really helps to not get lost. Thank you so much!

  • @Satharus
    @Satharus5 жыл бұрын

    Thank you! This is the single best video explaining the algorithm on KZread.

  • @Museko
    @Museko7 жыл бұрын

    I'm watching a bunch of your videos to review for my Algorithms exam. Thanks a bunch for making these!

  • @ComputerScienceLessons

    @ComputerScienceLessons

    7 жыл бұрын

    Thanks for the comment. It's good to hear you're finding them useful. :)

  • @jackych5055
    @jackych50553 жыл бұрын

    man this Dijkstra guy deserved a nobel prize for it

  • @ComputerScienceLessons

    @ComputerScienceLessons

    3 жыл бұрын

    He was a clever chap! :)KD

  • @MinecraftLetstime
    @MinecraftLetstime6 жыл бұрын

    By far the best video for explaining this algorithm! Perfect.

  • @SpaceDisco1
    @SpaceDisco14 жыл бұрын

    It's really interesting, how sometimes one thorough example can clear up everything.

  • @markh1791
    @markh17912 жыл бұрын

    The clearest, and most succinct, explanation of Dijkstra's algo I've seen. Thanks!

  • @ronglass5968
    @ronglass59683 жыл бұрын

    The VERY clearest and well-paced explanation by far! Thanks!

  • @ComputerScienceLessons

    @ComputerScienceLessons

    3 жыл бұрын

    You are too kind :)KD

  • @MimicalThought
    @MimicalThought6 жыл бұрын

    We are learning about Dijkstra's Shortest Path in my Data Communications course and this video explains the algorithm much more clearly than my professor had attempted to explain in our lecture video / notes. Thank you very much, in just 10 minutes I was able to understand something I was spending 30-60 minutes on. Well done!! :)

  • @tundet8963
    @tundet89637 жыл бұрын

    Excellent work, Clarity, and explanation at all stages. Thanks, keep up the good work

  • @tartarus1322
    @tartarus13224 жыл бұрын

    I wish I could upvote this more than once. It is honestly a brilliant, clear, and concise explanation

  • @ComputerScienceLessons

    @ComputerScienceLessons

    4 жыл бұрын

    You are very kind. Thanks. :) KD

  • @chinthalaadireddy2165

    @chinthalaadireddy2165

    Жыл бұрын

    @@ComputerScienceLessons But really it's awesome video.. the best info in the least possible time.. Thank you so much from India 🥰

  • @Moggery
    @Moggery2 жыл бұрын

    Fantastically clear and concise. Makes my revision an absolute dream, I can’t thank you enough. 10/10

  • @ComputerScienceLessons

    @ComputerScienceLessons

    2 жыл бұрын

    Thank you. Delighted to help :)KD

  • @alpharussel653
    @alpharussel6532 жыл бұрын

    An entire computer science degree courses embedded in this amazing channel. Thank you. Not all heroes wear a cap.

  • @Monochones87
    @Monochones872 жыл бұрын

    Lovely, this has been the clearest explanation I've seen so far for Dijkstra's algo. Seriously, thank you so much!

  • @ComputerScienceLessons

    @ComputerScienceLessons

    2 жыл бұрын

    Thanks for saying so. You're most welcome :)KD

  • @5he1tied
    @5he1tied5 жыл бұрын

    This is the fourth video I had to watch. Only one that explains clearly, thanks.

  • @tumarisyalqun7327
    @tumarisyalqun73275 жыл бұрын

    This is so far the best explanation I have seen, thank you so much!

  • @ietskaag552
    @ietskaag5524 жыл бұрын

    Seriously, I've been looking at so many pseudocodes and incomprehensible python scripts without any clear explanation on how the algorithm actually works. I salute you. This has helped me so much. I can't thank you enough.

  • @ComputerScienceLessons

    @ComputerScienceLessons

    4 жыл бұрын

    Yo are most welcome :)KD

  • @Aca99100
    @Aca991004 жыл бұрын

    I have never seen a video with such clear and step-by-step explanations. Good job here!

  • @ComputerScienceLessons

    @ComputerScienceLessons

    4 жыл бұрын

    I appreciate the comment. Thanks. :) KD

  • @jacklimestone2559
    @jacklimestone25595 жыл бұрын

    Thank you! This really helped me out with my assignment! Nice accent, clear explanation, and visually pleasing.

  • @ayasswain
    @ayasswain6 жыл бұрын

    Wonderfully explained. The best video i have come across so far on Djikstra's Algorithm.

  • @nitesh4146
    @nitesh41462 жыл бұрын

    This is the best video on Dijstra's Shortest path algorithm I have viewed on KZread. Kudos!

  • @aquilazyy1125
    @aquilazyy11253 жыл бұрын

    This is very enlightening. I’ve come up with a similar algorithm myself that uses a simple width-first or depth-first search, but I’ve never thought of that we should first calculated the vertex with the least known distance! Thanks for sharing it.

  • @ComputerScienceLessons

    @ComputerScienceLessons

    3 жыл бұрын

    Don't thank me, thank this guy :)KD en.wikipedia.org/wiki/Edsger_W._Dijkstra

  • @babakbekhradmanesh871
    @babakbekhradmanesh8712 жыл бұрын

    Thanks for your extraordinary explanation. This is literally one of the simplest explanations of an algorithm I have ever watched on KZread.

  • @ComputerScienceLessons

    @ComputerScienceLessons

    2 жыл бұрын

    Thank you. You are very welcome:)KD

  • @leox8888
    @leox88882 жыл бұрын

    Really appreciate this video. As a network engineer, i have read many book about how SPF works but this one is the best. And i can also develop the code based on this video. One thing I was stuck for a while is when having the directed graph (shorted path), it is a bit tricky to print all the shortest path considering ecmp case.

  • @lawrencedennison-hall9642
    @lawrencedennison-hall96424 жыл бұрын

    Such a clear and coherent explanation. Watched the Craig n Dave video on this previously but this is such a clearer explanation. Understand this now cheers!

  • @ComputerScienceLessons

    @ComputerScienceLessons

    4 жыл бұрын

    Glad you found it useful. There is nevertheless some good stuff on Craig n Dave's channel :)KD

  • @andresnieves9018
    @andresnieves90186 жыл бұрын

    If you can't explain it simply, you don't understand it well enough. Beautifully done. Thank you!

  • @javadsabbagh8939
    @javadsabbagh89396 жыл бұрын

    Thank you, Kevin. Very understandable and clear.

  • @abooth1707
    @abooth17074 жыл бұрын

    Best explanation I've ever seen of this. Thank you so much!

  • @JamshadAhmad
    @JamshadAhmad4 жыл бұрын

    This video is a definition of precise and concise explanation. Thank you very much.

  • @TourGuideFTW
    @TourGuideFTW7 жыл бұрын

    The way you explained the algorithm was just great, thanks a lot for making this video!

  • @ComputerScienceLessons

    @ComputerScienceLessons

    7 жыл бұрын

    Tnx for the feedback :)

  • @swethapuskoor7314

    @swethapuskoor7314

    4 жыл бұрын

    Computer Science can you explain bellman ford too

  • @dimensionalblade2778
    @dimensionalblade27783 жыл бұрын

    Damn such a nice tutorial. Also you're making stuffs for VB, you're like the dream channel I've been searching.

  • @GavinLon
    @GavinLon5 жыл бұрын

    This is a great video. You have provided a very simple but clear explanation.

  • @smith1923
    @smith19237 ай бұрын

    This is by far the best video I've seen on this algorithm. It is clear and doesn't skip any steps.

  • @ComputerScienceLessons

    @ComputerScienceLessons

    6 ай бұрын

    Thank you :)KD

  • @supernenechi
    @supernenechi3 жыл бұрын

    You explained this so incredibly clearly! It's really not that hard at all! Thank you so much!

  • @ThewOrldIssqUare
    @ThewOrldIssqUare3 жыл бұрын

    Thanks for this! As others have said, this is one of the clearest explanations on youtube!

  • @ammarulhassan5851
    @ammarulhassan58513 жыл бұрын

    After spending lots of time on other videos and stuff finally, I have understood "Dijkstra’s" Thanks to this LEGEND.

  • @ComputerScienceLessons

    @ComputerScienceLessons

    3 жыл бұрын

    You are most welcome :)KD

  • @sanseverything900
    @sanseverything9002 жыл бұрын

    Thank you for including the psuedo-code at the end. Really helped me get an idea of how I should structure my own code!

  • @ComputerScienceLessons

    @ComputerScienceLessons

    2 жыл бұрын

    Glad to help :)KD

  • @BrendonWilliams
    @BrendonWilliams7 жыл бұрын

    Best explanation I could find. Thanks.

  • @ulfinawakjira1977
    @ulfinawakjira19773 жыл бұрын

    This is by far the best video I've seen on this subject it made implementation very easy and the explanation is the best I've ever seen so thank you very much!

  • @hgjghjkhify
    @hgjghjkhify Жыл бұрын

    Appreciate this video. Watched a number of others about Dijkstra's Algorithm and couldn't understand HOW and at what stage another path is evaluated. It wasn't until I saw the graph and how we can track the changes that it somehow brought the entire algorithm into crystal clear focus. Thanks!

  • @ComputerScienceLessons

    @ComputerScienceLessons

    Жыл бұрын

    You are most welcome :)KD

  • @GANDHIXtv
    @GANDHIXtv11 ай бұрын

    Best video on Dijkstra's by a considerable margin. Subbed.

  • @selvalooks
    @selvalooks5 жыл бұрын

    i used to think this "Dijkstra’s Shortest Path Algorithm" is not for me to understand :) , now i can do it even getting from sleep after watching this video , thanks a ton !!!

  • @forestpfeiffer1370
    @forestpfeiffer13703 жыл бұрын

    Finally, an example that makes sense, wonderful job!

  • @ComputerScienceLessons

    @ComputerScienceLessons

    3 жыл бұрын

    Glad to help :)KD

  • @JaffarBrar
    @JaffarBrar4 жыл бұрын

    Crying in disbelief 😭😭. Finally some clear explanation. Thank youuuuu

  • @ComputerScienceLessons

    @ComputerScienceLessons

    4 жыл бұрын

    You are very welcome. Glad to help. :) KD

  • @young-julee7899
    @young-julee78997 жыл бұрын

    D E A D

  • @ComputerScienceLessons

    @ComputerScienceLessons

    7 жыл бұрын

    Accidental!

  • @yunyizhu8358

    @yunyizhu8358

    5 жыл бұрын

    kinda scary when it turns red lol

  • @MarkTheMadMan

    @MarkTheMadMan

    5 жыл бұрын

    haha i saw this instantly, maybe its a sign :/

  • @celsiusfahrenheit1176

    @celsiusfahrenheit1176

    3 жыл бұрын

    (ʘᗩʘ')

  • @iansugg3496

    @iansugg3496

    3 жыл бұрын

    Me after my Data Structures and Algorithms final exam

  • @dawnjinx4962
    @dawnjinx49624 жыл бұрын

    I FINALLY UNDERSTAND THANK YOU SO MUCH!!!! This was the most concise and easy to follow video I've managed to find on this algorithm

  • @ComputerScienceLessons

    @ComputerScienceLessons

    4 жыл бұрын

    You are most welcome. I usually ask my students to check their understanding by working through it with a different graph. :)KD

  • @nathanriches9547
    @nathanriches95472 жыл бұрын

    Thanks James May. This was a great episode of Top Gear

  • @RustysAdventures
    @RustysAdventures Жыл бұрын

    This video is a game changer. Understood it in one shot. Brilliant!

  • @ComputerScienceLessons

    @ComputerScienceLessons

    Жыл бұрын

    Thank you :)KD

  • @michellelopez5264
    @michellelopez52646 жыл бұрын

    mannnn, i've been trying to find the missing link with this stuff and your video finally shined some light on the subject!

  • @alejandrobonilla3201
    @alejandrobonilla32015 жыл бұрын

    You are the best on explaining... Thanks a lot!

  • @DentrifixoRam88
    @DentrifixoRam886 жыл бұрын

    Hi from Argentina. After watching 4 other videos I can say this is the best explained solution steps I've found so far. Thanks!!

  • @ComputerScienceLessons

    @ComputerScienceLessons

    6 жыл бұрын

    Tnx

  • @amskumar
    @amskumar5 жыл бұрын

    Best video on Dijkstra I've seen so far. Thanks for doing it with so much clarity.

  • @user-lh2cq7yy6b
    @user-lh2cq7yy6b Жыл бұрын

    Man this content mind-blowing clear and simple explained, great work

  • @nehascorpion
    @nehascorpion2 жыл бұрын

    Very well explained! Best video so far on this algorithm. Thanks a ton.

  • @_elguet5787
    @_elguet57873 жыл бұрын

    thank you I was really struggling implementing this algorithm in real coordinates, i realized coordinates are like grid/trees if you zoom it, and i could apply your ideas and explanation to find the shortest path available in a set of xyz 'real' coordinates! awesome.

  • @theobserver4794
    @theobserver47944 жыл бұрын

    two hours of a boring lecture vs 10mins cool explanation. thanks mate

  • @ComputerScienceLessons

    @ComputerScienceLessons

    4 жыл бұрын

    You're very welcome :)KD

  • @Jack-hd3ov
    @Jack-hd3ov4 жыл бұрын

    After watching about 5 videos on this algorithm, yours has made it crystal clear. Thank you.

  • @ComputerScienceLessons

    @ComputerScienceLessons

    4 жыл бұрын

    You're very welcome. :)KD

  • @Jack-hd3ov

    @Jack-hd3ov

    4 жыл бұрын

    @@ComputerScienceLessons Your A* explanation is also the best I found

  • @mdotub71
    @mdotub717 жыл бұрын

    Excellent graphical and verbal explanation, very simple and coherent. Thanks for your video.

  • @ricp
    @ricp Жыл бұрын

    This explanation is by far the Best I've seen.. This is crystal clear , thank you very much!

  • @ComputerScienceLessons

    @ComputerScienceLessons

    Жыл бұрын

    You are very welcome, and thank you :)KD

  • @q1chen
    @q1chen2 жыл бұрын

    This 10mins video >>> 45mins video from my lecturer. LEGEND🙏

  • @whiningmachine
    @whiningmachine2 жыл бұрын

    Fantastic explanation. Indeed, it's the best, clearest, simplest, and most useful resource by far that I've found after hours of searching. Thanks for making it!

  • @ComputerScienceLessons

    @ComputerScienceLessons

    2 жыл бұрын

    Thank you - and you are most welcome :)KD

  • @faisalsal1
    @faisalsal12 жыл бұрын

    This video is your shortest path to learn Dijkstra Algorithm.

  • @ComputerScienceLessons

    @ComputerScienceLessons

    2 жыл бұрын

    🤡 :)KD

  • @chrise202
    @chrise2024 жыл бұрын

    You know this is the best illustration and guideline for implementing it on youtube.

  • @ComputerScienceLessons

    @ComputerScienceLessons

    4 жыл бұрын

    Thanks :) KD

  • @danielm7755
    @danielm77553 жыл бұрын

    You've just earned yourself a new subscription champ! Great video! I love it!

  • @ComputerScienceLessons

    @ComputerScienceLessons

    3 жыл бұрын

    Thank you and you are most welcome :)

  • @RubainG
    @RubainG7 жыл бұрын

    Awesome video ! This made me clear how to simplify and program the Seam algorithm!

  • @kexiuliu6692
    @kexiuliu66925 жыл бұрын

    Really good show of the algorithm. thanks a lot.

  • @stuffboutthegovermet
    @stuffboutthegovermet9 ай бұрын

    So easy to follow. Best video I’ve seen on this algorithm

  • @chrismorris3056
    @chrismorris30567 жыл бұрын

    Very clear explanation. Well done!

  • @ComputerScienceLessons

    @ComputerScienceLessons

    7 жыл бұрын

    Tnx Chris

  • @ddddchannel837
    @ddddchannel8374 жыл бұрын

    Extremely clear and well thought out video. Thanks for uploading!

  • @ComputerScienceLessons

    @ComputerScienceLessons

    4 жыл бұрын

    You are very welcome. Thanks for the comment. :)KD

  • @eduardbenedic9844
    @eduardbenedic9844 Жыл бұрын

    This is just phenomenal

  • @sabeen7794
    @sabeen77947 жыл бұрын

    great video ... you really have the spirit of a teacher ... thanks for making this one.

  • @ice_cube918
    @ice_cube9182 жыл бұрын

    This is the best explanation of Dijkstra's algorithm I have seen!! I especially like the last summary part.

  • @ComputerScienceLessons

    @ComputerScienceLessons

    2 жыл бұрын

    Thank you. Glad to help :)KD

  • @leonidsukharnikov2563
    @leonidsukharnikov25634 жыл бұрын

    Perfect video! Clear examples, understandable English and ... no profanity.

  • @ComputerScienceLessons

    @ComputerScienceLessons

    4 жыл бұрын

    Glad you liked it. Thanks for the comment. :) KD

  • @S3b1Videos
    @S3b1Videos6 жыл бұрын

    Most efficient video on dijkstra's algorithm out there :)

  • @andreasvasd8802
    @andreasvasd88025 жыл бұрын

    Congrats! Very well explained!

  • @binoyskumar
    @binoyskumar6 жыл бұрын

    Perfect! keep it coming. Well explained

  • @hiroKoichi
    @hiroKoichi5 жыл бұрын

    Very clear example and nice explanations!

  • @alvaro1728
    @alvaro17285 жыл бұрын

    Thank you for this brilliant explanation!

  • @hanbrianlee
    @hanbrianlee5 жыл бұрын

    Omg.. out of like 10 dijkstra vids i attempted to eatch this is the best

  • @ahmedsaid8180
    @ahmedsaid81802 жыл бұрын

    Thank you very much! I have been trying understand this algorithm for 5 hours and I finally got it now "thanks to you"!

  • @ComputerScienceLessons

    @ComputerScienceLessons

    2 жыл бұрын

    You're most welcome :)KD

  • @miller5565
    @miller55653 жыл бұрын

    I couldn’t have asked for a clearer video, thank you sir.

  • @ComputerScienceLessons

    @ComputerScienceLessons

    3 жыл бұрын

    You're most welcome :)KD

  • @KamalMettananda
    @KamalMettananda3 жыл бұрын

    This explains it perfectly. Thank you so much.

  • @Funnybone_FB
    @Funnybone_FB2 жыл бұрын

    Brilliant. Very well-done and clear explanation. Thank you for this!

  • @ComputerScienceLessons

    @ComputerScienceLessons

    2 жыл бұрын

    Thank you. You are most welcome :)KD