7.3 Traveling Salesman Problem - Branch and Bound

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  • Опубліковано 2 жов 2024
  • Traveling Salesman Problem - Branch and Bound
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КОМЕНТАРІ • 749

  • @aasthayadaw4846
    @aasthayadaw4846 Рік тому +125

    Heyy...
    The timing is 2:49 am.
    Today is my exam on 10 o'clock.😅
    I read some comments that they have their exams on the day they saw this video.
    So I just want share this 😁
    That I'm also seeing this video on my exam day . ☘️🙃🏝️
    Hope that my exam will go well🤞🏻.......

  • @bernieheveron1929
    @bernieheveron1929 4 роки тому +967

    I'm helping my daughter do her homework during the Covid-19 lockdown and this is the clearest description of branch and bound that I have seen. I looked at several websites and videos. Thank you for your help!

    • @raunvk
      @raunvk 4 роки тому +89

      God bless your soul. Wish every father was like you.

    • @Kostas.mp3
      @Kostas.mp3 4 роки тому +47

      you are an awesome father sir hope she does good in the exams

    • @Anubis10110
      @Anubis10110 4 роки тому +21

      Hope all fathers are like you

    • @drewfranco4279
      @drewfranco4279 3 роки тому +9

      I dont mean to be off topic but does anybody know a trick to get back into an Instagram account??
      I somehow lost the account password. I would love any assistance you can offer me

    • @sinanmohammadnahian4768
      @sinanmohammadnahian4768 3 роки тому +5

      Hope you have done vaccination properly. Stay safe

  • @ritiksingh6137
    @ritiksingh6137 4 роки тому +230

    Sir you are the best...infact my class teacher teaching in the class after watching your video's lecture 😊

    • @sanchitmangal1196
      @sanchitmangal1196 4 роки тому +19

      Acha bhai fir to aap glt college mein pdte ho..... Aap unki classes chod ke yhi dekh liya kro taki apko pura smjh aaye.....Esse cllg se bdiya to cllg hi na ho bs formalities ho rhi hai or bacho ke paise mein aag lg rhi hai....fees ke liye sbse phle ayenge but in case of quality they are making fools. Atleast yr unko guide to ache se kre but wo bhi nhi hota, cllg bs naam ke liye hai baki Thanks to UA-cam and such teacher's on UA-cam jinke wajah se hme achi directions mil pati hai.....

    • @Libertoso
      @Libertoso 4 роки тому +3

      lol he's a fraud then

    • @ajinkyaadhotre5336
      @ajinkyaadhotre5336 4 роки тому +2

      @@Libertoso why ??

    • @Libertoso
      @Libertoso 4 роки тому +1

      Because he either doesn't know what he's teaching and is just copying ya boi, or he knows the topic but doesn't know how to teach it

    • @ajinkyaadhotre5336
      @ajinkyaadhotre5336 4 роки тому +21

      @@Libertoso or maybe he finds abdul baris methods more simpler than the methods he/she learnt , its good the teacher is a learner and still keeps updating methods

  • @teluguknowledge42
    @teluguknowledge42 5 років тому +64

    Tnk u very much Sir
    Your explanation way is very clear & awesome👌

    • @ak689
      @ak689 Рік тому +5

      Your channel is bigger than the teacher's channel.

  • @hmanshu_p
    @hmanshu_p 5 років тому +324

    I had my DAA exam today, and I am pretty sure that I am going to top this one. The same question came in my exam today for a whopping 18 marks! Thanks, Abdul Bari Sir for giving us the support the college couldn't give. 😊😊

  • @arcee6212
    @arcee6212 6 років тому +280

    sir i couldn't attend any of the daa lectures at my college due to an internship and every lecture you've taken is a treasure!..my orals went amazing thanks to the way you clear fundamentals and I'm feeling more confident for my finals too! Thank you so much sir!

    • @arnobchowdhury1804
      @arnobchowdhury1804 5 років тому +15

      how did you get an internship? can you please guide me too?

    • @subbareddyd544
      @subbareddyd544 5 років тому +6

      Bro how you got internship tell us please

  • @austinmarius850
    @austinmarius850 4 роки тому +92

    This is so extremely well done. I can’t thank you enough for sharing this in such a well detailed manner. You’re a gifted teacher.

    • @danialmalik9509
      @danialmalik9509 3 роки тому +2

      how he has found the cost of node 5 7 8 ?

    • @OpOp-ck2dt
      @OpOp-ck2dt Рік тому

      Sir mere cllg me que. Yhi aaya tha usme diagonal me infinity ki jagah 0 tha to meme infinity put kf diya sahi hoga kyaa

  • @ovidiunicolaetuca9312
    @ovidiunicolaetuca9312 4 роки тому +2

    The videos on branch and bound do not seem very useful as you explain the method for solving a problem, but not how to deduce the formula for "pruning" a node. You are teaching us a solution, but not how to come to the solution ourselves by deducing the formula through a logical or mathematical approach.

    • @ovidiunicolaetuca9312
      @ovidiunicolaetuca9312 4 роки тому

      ​@@abdul_bari Thank you. That is not to say I do not appreciate all the content you have provided. : ) Keep up the good work! The world needs more people like you.

  • @indrajitbanerjee5131
    @indrajitbanerjee5131 4 роки тому +38

    Hello Sir,
    You explained it really well and made an "NP" hard problem just a cake walk.

  • @brandonasdfd3232
    @brandonasdfd3232 6 років тому +42

    Abdul Bari, I've been watching a couple of your videos to cram for my final and you're incredibly helpful. I give my most gratuitous thank you.

    • @OpOp-ck2dt
      @OpOp-ck2dt Рік тому

      Sir mere cllg me que. Yhi aaya tha usme diagonal me infinity ki jagah 0 tha to meme infinity put kf diya sahi hoga kyaa

  • @DevpatelGurjar-i8v
    @DevpatelGurjar-i8v 3 місяці тому +3

    i think the cost from 4 to 3 is wrong it should be 37 correct me if I am wrong

  • @夏天晴-f1v
    @夏天晴-f1v 2 роки тому +17

    I think there is an error for the Node6(2) to Node10(5), it should have a remained cost for 11, the true cost should be C(2,5) + Cost(Node6) + ReducedCost(place(5,1)) = 0 + 28 + 11 = 39

    • @hemantshirsath6153
      @hemantshirsath6153 Рік тому +1

      Yes you are right .

    • @Hyd35
      @Hyd35 Рік тому +4

      No here we also make( 5,1) as infinity bcuz we have to return from 5th node to 1st node..thus the cost at 2,5 is 28..which is crrct said by sir..

  • @hafizsakib2734
    @hafizsakib2734 7 місяців тому +1

    After watching full video I've decided I will not answer from this Travelling Salesman question containing set😅

  • @gourunarneeth4968
    @gourunarneeth4968 3 роки тому +10

    Sir In second sub tree I got cost from 1 to4 to 3 cost(3)=37 but in the video it was 50. Anybody faced the same.

  • @aaradheyasharma2272
    @aaradheyasharma2272 4 місяці тому +2

    sir allah mubarak!!

  • @vandanavarshini9904
    @vandanavarshini9904 Рік тому +9

    I've been referring your videos to most the topic from my syllabus. I could able to cover 4 units out of 5 units which is like "I'm going to get 80/100 for sure in my final exam". Thank you so much sir !

  • @fatimamaj7964
    @fatimamaj7964 2 роки тому +3

    Shouldn't the cost between 1 an 5 be 26 not 31? or I am wrong?!

    • @Roshan-ui9jt
      @Roshan-ui9jt 3 місяці тому

      Yeah Im getting same answer

    • @abhishekjagtap778
      @abhishekjagtap778 13 днів тому

      No ur wrong make 5th col infinity then u have to reduce matrix further so in second row u have to minus 11 from 12 so now eqn will be 4,5 plus cost of parent plus reduction that will be 0+25+11 : 36

    • @abhishekraaz8090
      @abhishekraaz8090 10 днів тому

      Bro we have minimum value 2 they why we will go for 11​@@abhishekjagtap778

  • @sowmyah.s.81
    @sowmyah.s.81 Рік тому +1

    Can anyone pls tell quickly how it is 50 for (4,3)

  • @manh9105
    @manh9105 Рік тому +1

    How to find who is commenting from India. Look for word 'Sir' in comments. Indians know how to respect their teachers!

  • @brianotte8696
    @brianotte8696 5 років тому +6

    Seriously Abdul, this is fantastic quality instruction. My only feedback - the audio is a bit difficult at times. I would consider upgrading your microphone. Do that, and I can see a lot more people consuming your content.

  • @timothyjulian6817
    @timothyjulian6817 3 роки тому +9

    I'm so happy that I just entered the university last year. Imagine entering university without this video, I would be dead inside

  • @user-mb1gx5sb4d
    @user-mb1gx5sb4d 3 роки тому +8

    Sir,wondered how ur teaching is so perfect and clear...!!😊

  • @jonnylee7440
    @jonnylee7440 4 роки тому +4

    Hello, Sir, thx for your video! But I think we should add the cost from 3-1 at last, because the saleman must go back to the first city, so the right answer is 28+3=31, right?

  • @CARDANO-er8s
    @CARDANO-er8s 9 місяців тому +1

    11:16 why 12 was reduced to infinity ..??

  • @HARIHaran-ks7wp
    @HARIHaran-ks7wp 4 роки тому +5

    The most exhausting Mr. Bari video ever LoL

  • @saunakroy2587
    @saunakroy2587 6 років тому +13

    Watched all your UA-cam videos from scratch. Teaching in that way, which is simple to understand and will also be quickly absorbed by the students is an ART. You have got this brilliant ART sir. I have grasped all these concepts before college via your videos. Thanks a lot for providing knowledge for free. You are a real teacher and i hope that you will continue teaching us more through your videos.

  • @yashalrailkar2457
    @yashalrailkar2457 2 роки тому +1

    Sir cost of 5 should be 26 right? as 1+25+0 please confirm

  • @wilbertcoandadiputra2487
    @wilbertcoandadiputra2487 8 місяців тому +6

    Bro is carrying my cs major

  • @silentHunter123
    @silentHunter123 Рік тому +2

    nightmare if comes in exam :(

  • @sabahoda4262
    @sabahoda4262 3 роки тому +10

    May Allah bless you with all what you ever expect for,
    Alhamdullilah concept is quite clear for me, I'm watching all your videos with full interest. And this subject is now my favourite because of you sir.

  • @vivekrobotics
    @vivekrobotics 2 роки тому +1

    Nicely Explained. But I doubt on 2 to 5 there is no edge, so how 1-4-2-5-3-1 can be the path (hamiltonian cycle)?

    • @sjhuz01
      @sjhuz01 2 роки тому

      I thought the same, but look again at the graph - yes, there is a curved edge from 2 to 5, and from 1-5.

  • @NehaReddyPolimera
    @NehaReddyPolimera 4 місяці тому +1

    sir this problem is wrong ,means method is correct taking values are messed up

  • @bhushanambhore8378
    @bhushanambhore8378 Рік тому +5

    If you have habit of reading comment before watching any teaching video like me to know if the video have positive comments or if it worth to watch, then you don't need to come to comment section before watching Abdul sir's video, this sir has the best explanation of DSA topics on the whole UA-cam.. Come here after watching the full video to appreciate his excellent teaching skills..

  • @Flutterdev6391
    @Flutterdev6391 3 роки тому +2

    I got the concept after watching 2 times thanks sir
    But I thought this is not to fine solve in University exam because it's take too much time

  • @revivingfaith17
    @revivingfaith17 Рік тому +1

    🐶🦧🐯🐗🐏🐃🐂🏛🌐🌍🗽🏦🛼🚲🚊🌠🌖🕢🌝🎉🎁🎑⚾🏈🎖🧤👕👔👔📠📞📞📓📃🚭🚫🚰🚹🚱⬅

  • @aakashsangar3844
    @aakashsangar3844 5 років тому +4

    Thank u for such an explanation I have seen your videos before a day of my exam kudos! We are paying hefty fees structure to the college's nothing else.useless teachers like a worm who is eating our hard earned money.

  • @matthewtane7886
    @matthewtane7886 Рік тому +4

    I thank God every single day for your existence. You are a massive help to university students in Indonesia.

  • @insaneSageGuy
    @insaneSageGuy 5 років тому +11

    Aao srm walo aao!😂

  • @shivanshsagar1209
    @shivanshsagar1209 Рік тому +1

    App step 7 cross check kariya q ki solve karne par dusra answer aa rha hai . Or jo answer aap likho ho board par wo QUANTUM se copy ki ho

  • @akshanshsingh3429
    @akshanshsingh3429 Рік тому +2

    Maut aa jaye lekin ye question exam me na aaye

  • @fatehaliyev2017
    @fatehaliyev2017 4 роки тому +2

    What is the point of reducing the matrixes if you are going to add up the length of the path in the end any way?

    • @kunalsaini2126
      @kunalsaini2126 4 роки тому

      did you get that now?
      if yes, plz help🙏🙏

  • @chhana09
    @chhana09 2 роки тому +3

    With all due respect Sir, if the cost from 3 to 1 is very very large and if return path to node 1 not considered (as leaf node), will it still give optimal result?

  • @vishwajeetlad3405
    @vishwajeetlad3405 5 місяців тому +1

    Sir please check the sound of the video it's not that good! Hope you pay attention towards the quality if the sound!!!

  • @rishabhdiwaker2254
    @rishabhdiwaker2254 10 місяців тому +1

    salesman ro dega sir 😥😥😥😥😂😂

  • @azizsobirin8227
    @azizsobirin8227 Рік тому +2

    very help me on my college

  • @salmanpandey8150
    @salmanpandey8150 6 років тому +5

    Sir I am from SRM university . ALL YOUR videos have been really helpful and have scored good marks in my algorithm paper . Thank you once again sir

  • @chrisogonas
    @chrisogonas 3 роки тому +6

    WOW, that was an amazing illustration. Thanks Bari!

  • @ravikumartholuchuri8414
    @ravikumartholuchuri8414 3 роки тому +1

    sir node 1 to node 5 cost check once

  • @skrafee
    @skrafee 5 років тому +10

    superb explanation great work sir !!! Masha Allah

  • @sanju_katwal
    @sanju_katwal 5 місяців тому +1

    But sir how it is possible to go on 5th vertex from 2nd directly bcoz if u see graph then in between path of 2 to 5 there is vertex 3 also and there is no direct path to gon on 5th vertex

  • @vijayaraghavan1805
    @vijayaraghavan1805 5 років тому +11

    Sir, Thanks for your very good explanation. Keeping aside the matrix and looking the solution from the graph point of view, we do not have direct connection from 2 to 5 in the graph.
    While taking the direct connected vertices of 1 you got 2 3 4 5 which seems to be valid. But when taking the direct connected vertices of 2 why did you take 3 and 5. 5 don't seem to have direct connection to 2. Please explain

    • @eshwarshastry2941
      @eshwarshastry2941 2 роки тому

      Same thing struck my mind

    • @OpOp-ck2dt
      @OpOp-ck2dt Рік тому

      Sir mere cllg me que. Yhi aaya tha usme diagonal me infinity ki jagah 0 tha to meme infinity put kf diya sahi hoga kyaa

  • @Sweety12519
    @Sweety12519 2 роки тому +2

    Thank u so much sir well explained 😌

  • @vikassamaje4895
    @vikassamaje4895 4 роки тому +1

    Traveling Salesman Problem - Branch and Bound-------the solution contains to travel from node 2 to 5. But in actual graph there is no edge between the nodes 2 and 5. Hence the solution found is incorrect.

  • @koradaravisrithammayyababu4077
    @koradaravisrithammayyababu4077 5 років тому +2

    Sir, here you didn't take the possibility of visiting vertices multiple times
    Example: weights of edges:
    5 -> 4 = 16,
    5 -> 2 = 4,
    2 -> 4 = 4
    hence 5 -> 2 -> 4 = 8
    from the approach in the video if vertex 2 is already visited, then we won't come across the possibility of 5 -> 2 -> 4
    Could you please give an alternative solution where vertices can be visited multiple times

    • @anonymous_4276
      @anonymous_4276 2 роки тому

      Won't that needlessly increase the cost? Unless negative costs are involved, I don't see the point of revisiting a visited vertex.

  • @jaisurya7481
    @jaisurya7481 2 роки тому +2

    The Best and the clear explanation sir...Thank you so much for this video sir...😊😊😊😊

  • @amolsandeep1038
    @amolsandeep1038 2 місяці тому +1

    Me in exam hall opening video and writing the answer😂😂

  • @lblohith
    @lblohith 2 місяці тому +1

    Sir congratulations for 1million subscribers🎉🕺

  • @gautigauti5939
    @gautigauti5939 5 років тому +2

    sir poora paper hi bata dia aapne to. mai bhi tha namu ke sath iska comment neeche hi hogga. zabardast ek dum sir thank you

  • @manojmanu-ub7rz
    @manojmanu-ub7rz 6 років тому +18

    Thanks sir you helped a lot for my daa exam

  • @atuldeore2402
    @atuldeore2402 Рік тому +1

    very nice explained

  • @techieforall
    @techieforall Рік тому +1

    he teached dsa to us in our campus

  • @sourabh17287
    @sourabh17287 Рік тому +1

    Reasoning behind the steps are missing. Video covers all the steps but don't relate it to why we are doing so and how does it translate in a real world.

  • @himadrishah6100
    @himadrishah6100 3 роки тому +6

    You saved my semester!
    Thanks a ton. 😊

  • @mrsmile1387
    @mrsmile1387 2 роки тому +1

    20:45 mistake , right?
    have to make 3 rd row 2nd col as infinite ..but he assigned infinity to 3,1

  • @anshikatyagi4624
    @anshikatyagi4624 3 роки тому +2

    Everything is Best.
    But voice is not clear.

  • @aparajitakumari2936
    @aparajitakumari2936 2 роки тому +1

    How did you find the cost of node 7 and 8 ?
    For node 7 ,the cost from 4 to 3 is 12 and cost of node 4 is 25 and there is no reduction,so it should be 37 .

  • @ahmettavli4205
    @ahmettavli4205 4 роки тому +1

    I don't understand how you calculate the cost of the 7th node 50?

  • @kamilkaya5367
    @kamilkaya5367 3 роки тому +1

    How we get to the node 2 to node 5 in the solution found? There is no direct path to that node. This shouldn't be feasible solution.

  • @hussainraza3104
    @hussainraza3104 5 років тому +15

    Sir I have my exam tomorrow of Design and Analysis of Algorithms , i must say you are such a great help for clearing concepts and doubts,at most of the places i refer to you not books.
    At some places you have told methods and explained but algorithm are missing.
    Thanks alot.
    May God Bless you.

  • @steevebinubaby2698
    @steevebinubaby2698 Рік тому +1

    Going to write exam tomorrow 😅

  • @jyothijohnson8422
    @jyothijohnson8422 4 роки тому +3

    Sir, could you please explain the method on how to proceed if the minimum cost is found in more than one nodes. How to perform the selection?

    • @madhoshyagnik3679
      @madhoshyagnik3679 4 роки тому +1

      I think you can choose either of them, considering the case.Of course if the choice is wrong then the bounding function would kill the node and you would have to backtrack and choose the other one!

  • @Greg-mo8bd
    @Greg-mo8bd 5 років тому +6

    Would've spent hours on this topic if I read the theory alone 😇thank you sir

  • @amanjoshi7259
    @amanjoshi7259 5 років тому +12

    Sir, you're great so blessed to study this from you... I would like to tell you that, I seriously don't know anything about this, but... I saw your lecture and I seriously understood.! hats off to you sir.!

  • @chandrimakumar8533
    @chandrimakumar8533 4 роки тому +1

    Why don't you code anything btw I anyway love your lectures they are quite interesting.

  • @akashrawat5679
    @akashrawat5679 3 роки тому +2

    I will opt for another question in my exam 😁

  • @TechwithRakesh2288
    @TechwithRakesh2288 2 місяці тому

    I did not understand cost value fore node 7 and 8 how it came 50 and 56 for node 7 CRS+ RRS=0 the cost of node 4 is 25 and intersection i=4 and j=3 is 12. 25+12+0=37 how it came 50

  • @prafullamishra9567
    @prafullamishra9567 5 років тому +3

    First of all thank you Sir for this superb , understandable concept😊 sir... i have a problem! Sir , i solved for
    cost(7), which is 38 but your is 50. Is i'm wrong or there's a mistake in writing?☺ plz help. @Abdul_Bari

  • @abthki78
    @abthki78 10 місяців тому +3

    Matrix for node 7 is wrong C[4,3] is 37 not 50

  • @samsoorshinwari5738
    @samsoorshinwari5738 4 роки тому +4

    Hello Dear sir!
    i am from afghanistan studying in a private university in india i just wanna say thanks to you,your teaching method is excellent .
    Thanks sir

  • @Niteshkumar-zd3kr
    @Niteshkumar-zd3kr 6 років тому +1

    In node 6 the path is from 4->2 you changed 4th row and 2nd column to infinity and 2->1 to infinity. Why you did not changed 2->4 to infinity?? and please reply

  • @abhilashkp6864
    @abhilashkp6864 5 років тому +2

    After finding the cost of each node, you are checking which one is smallest. But you are also checking all the nodes (for example : node 6 is having cost 28, but while checking, you also include nodes 2,3 and 5 which is not selected in the first time.)
    So my doubt is, what if one of those nodes (2,3 or 5) had smaller cost than the newer ones (6,7 and 8)?

    • @harshkanani6605
      @harshkanani6605 2 роки тому +1

      Yes I also have a same doubt

    • @guilhermedabolsa927
      @guilhermedabolsa927 Рік тому

      If some other node had smaller cost, then yes, you should change and expand that node. Always the smallest one, at least in this implementation... there are other strategies

  • @vallepuchandana9984
    @vallepuchandana9984 5 років тому +4

    Tq you very much sir, this way was very easy and understanding also. 🙏🙏🙏🙏🙏🙏

  • @pixel_Programer
    @pixel_Programer 2 роки тому +1

    sir ,r u from sri sairam engineering college,chennai TN

  • @bealone6657
    @bealone6657 3 роки тому +1

    Sir..matrix will be given or else should we take by our own?

  • @karthickanbu6011
    @karthickanbu6011 5 років тому +8

    Liked the term "Travelling salesperson problem" instead of salesman. Awesome explanation too. Thanks

  • @82Escudero
    @82Escudero 4 роки тому +1

    Hi
    I really enjoyed this class, it is very explanatory.
    What is the name of this relaxation? Lagrangian relaxation?
    Thank you

  • @steved.1091
    @steved.1091 6 років тому +6

    For travelling from node 1 to node 2, row 1 and column 2 are set to infinity because after that node 1 cannot travel to any other node and no other node can travel to node 2. Am I thinking right, or there is something more to it?

  • @anandlaggishetti9275
    @anandlaggishetti9275 3 роки тому +1

    its really very very best teaching that i need not to revise this topic again by listing once its very clear and very clarity Thankyou sir

  • @fasirahman1987
    @fasirahman1987 4 роки тому +2

    smjaya acha jitna smjaya smj aa gya but jo auto fill kia solve aap ny wo ghalat hai

  • @maahisosankar6482
    @maahisosankar6482 5 років тому +4

    how it posible to move frm 2 to 5...

  • @priyamanthra112
    @priyamanthra112 4 роки тому +1

    Thank u now i saw ur approximation algorithms using via traveling salesman

  • @violet9720
    @violet9720 2 роки тому

    Thank you soo much Abdul Bari,😊
    امكن مكنة في الهند كلها🫡

  • @ramsart_gifthouse
    @ramsart_gifthouse 3 роки тому +1

    Thank you so much sir, really helpful video. God bless you😊

  • @NJblaster
    @NJblaster 5 років тому +4

    Thank you sir ..but one problem is that i cant find out last value (1 to 5) value ans 31 can you explian it

    • @jaysurya29
      @jaysurya29 4 роки тому

      It's 30 bro not 31 (25+5+0)

  • @ignite5355
    @ignite5355 4 роки тому +1

    Sir, I looked at the video but my confusion is there is no path between 2-5 so how come answer is 1-4-2-5-3 ???

    • @ashfaq8238
      @ashfaq8238 4 роки тому +5

      Bro there is path. Check the graph again. There is a curved drawn between 1 - 5 and 5 - 2 aswell

  • @shubhamkumarsingh4778
    @shubhamkumarsingh4778 4 роки тому +2

    Abdul sir bht accha kaam krte ho aap😇🙂

  • @afsananasrin4700
    @afsananasrin4700 7 місяців тому +1

    isn't at 15:11 the equation C(1,5) + r + ^r = 1 + 25 + 0 = 26?

    • @sanofar0598
      @sanofar0598 4 місяці тому

      Yes crct for me also 26

    • @sanofar0598
      @sanofar0598 4 місяці тому

      For me also 26

    • @ancitadfernandes8243
      @ancitadfernandes8243 Місяць тому

      No it should be C(1,5)+r+r^=1+25+5=31
      As we are adding up 2 and 3 the minimum of 2 nd and 5th row.

  • @nakadindin
    @nakadindin 4 роки тому +12

    you're the best sir i literally can't survive this semester if it weren't for you thank you so much

    • @OpOp-ck2dt
      @OpOp-ck2dt Рік тому +1

      Sir mere cllg me que. Yhi aaya tha usme diagonal me infinity ki jagah 0 tha to meme infinity put kf diya sahi hoga kyaa

  • @SRNR_PODCAST.
    @SRNR_PODCAST. 3 роки тому +1

    a goldmine in UA-cam.

  • @sadeghkhosravi
    @sadeghkhosravi Рік тому +1

    It was great, thank you for your explanation🙏🙏