Wednesday, December 28, 2016

Episode 1 - Trees and Diameters

If you haven't seen a lecture from Donald Knuth's lecture series on trees, I suggest watching this video. Every year, at the end of the fall semester at Stanford, Donald Knuth gives a lecture on trees, a sort of Christmas tree lecture series. In honor of this, I've decided to give my own Christmas tree lecture, though my treatment will be much less advanced than Knuth's. Instead, I will focus on the basics.

This week I'll cover some fundamental properties of trees. Some of these properties I will prove during the episode; while others I will leave for you to attempt. I'll present a proof sketch of each property to make each proof easier to digest. I still recommend reviewing proof by contradiction and other useful proof techniques.

One technique covered will be finding the diameter of a tree. There are two well-known techniques for finding diameters. But why do they work? Tune in to find out!

See you live! (time, stream, channel)

14 comments:

  1. A good session really helped thanks

    ReplyDelete
    Replies
    1. I use to be a very poor woman who has always not find luck when it comes to playing the lottery. I have been playing lottery since i was 21 years and now i am 45 meaning i have been playing lottery for 24 years. The biggest amount i have ever won in my life was 400 bucks. But one day my story turns to history after i find this man name on the Internet that he is the best when it comes to winning lottery. This man is a very strong voodoo doc who gives out the numbers that can never fail. After all my years of laboring and struggling to win the lottery i finally won ( $27,000,000) Dr Alli is the name, Email: allispellhelp1@gmail.com or contact him on his whatsApp number +2348100772528 this is the only way to win the lottery and the best way

      Delete
    2. I really want to thank Dr Emu for saving my marriage. My wife really treated me badly and left home for almost 3 month this got me sick and confused. Then I told my friend about how my wife has changed towards me. Then she told me to contact Dr Emu that he will help me bring back my wife and change her back to a good woman. I never believed in all this but I gave it a try. Dr Emu casted a spell of return of love on her, and my wife came back home for forgiveness and today we are happy again. If you are going through any relationship stress or you want back your Ex or Divorce husband you can contact his whatsapp +2347012841542 or email emutemple@gmail.com website: Https://emutemple.wordpress.com/

      Delete
  2. Any related problems to solve from codeforces?

    ReplyDelete
    Replies
    1. http://codeforces.com/problemset/problem/455/C

      Delete
  3. Dr. Osofo is a great spell caster, My marriage of 14 years was having a problem and my husband request for a divorce i was so heart broken because i love him so much that i can't let him just go, So i was doing some research on the internet on how to fix up my broken marriage i saw some review about Dr osofo how he help people with a love spell so i contacted him and tell him my problems he only reply me with some words and told me what to do after 48hours you wouldn't believe my husband come back house with much love and caring. kindly contact dr osofo if you have any problem with your relationship or marriage via: (osofo.48hoursolutioncenter@gmail.com )  you can also whatsapp him +2349065749952

    ReplyDelete
  4. EFFECTIVE LOVE SPELL TO GET EX HUSBAND/BOYFRIEND OR EX WIFE/GIRLFRIEND AND CURE HERPES AND INFERTILITY THAT WORKS WITHIN 24 HOURS.

     Contact Dr. Odunga at odungaspelltemple@gmail.com OR Whats App/CALL +2348167159012

    I got my ex husband back to me and also got fertile and gave birth to twin girls after 12 years of marriage.
    When I came online last year, I saw a testimony about Doctor ODUNGA and how he has been helping people with marriage issues and I decided to contact him. We spoke on email at odungaspelltemple@gmail.com and later he gave me his WhatsApp number which is +2348167159012. He assured me he would help me get my ex husband back after 3 years of no contact. Doctor Odunga is the best spell caster I must say. My husband called me after 24 hours of contact. The third day, I received natural herbs for fertility and after using it, I became fertile and conceived. I and my husband reconnected, had sex and I was pregnant. Presently I am happy to say I am the mother of twin girls and this is ALL THANKS TO DOCTOR ODUNGA. I came online to say this If you need help, I believe you are saved with this man.  

    Contact his email at odungaspelltemple@gmail.com

     OR Whats App/Call +2348167159012 and you too will give a testimony too to help others

    ReplyDelete
  5. He left me for a year into another relationship because of me, I quit my job and some where my life was out of track, so I asked him to go for someone else and he left me for someone else. Within a month I thought he’s playing a prank to make me jealous but he was into a serious relationship that he committed to a new lover and ready to propose her for marriage. It took me eight month my boyfriend not wanting to meet me and he gave excuses to avoid, I got confused asking myself how could he do this to me? Later on I saw a page on Facebook: Ex-love back permanently, I gave a try to dr osofo and got helped in the next 5days my lover just called me asking for forgiveness thanks to dr osofo and the doctor told me that it took him time to finalize the work because my boyfriend was already under a woman’s control through the use of spells I call upon all my fellow women who are experiencing the situation now that I passed through to contact doctor at +2349065749952. or email him (  osofo.48hoursolutioncenter@gmail.com   )  

    ReplyDelete
  6. My husband and I were going through a separation, after 9 years of marriage. I have seen that coming due to his reaction towards me. And I was about losing my home, then I had to contact Dr. Sunny, the love spell caster who cast powerful marriage blessings that reunited our marriage back together and also made our union stronger than as it were before. All thanks to Dr. Sunny for reuniting my home back we are living happily now contact Dr. Sunny for any marital problem's thanks to you Dr. Sunny you can contact Dr. Sunny via email solutioncentre911@gmail.com call or WhatsApp Dr. Sunny mobile number +2349056393169

    ReplyDelete
  7. I use to be a very poor woman who has always not find luck when it comes to playing the lottery. I have been playing lottery since i was 21 years and now i am 45 meaning i have been playing lottery for 24 years. The biggest amount i have ever won in my life was 400 bucks. But one day my story turns to history after i find this man name on the Internet that he is the best when it comes to winning lottery. This man is a very strong voodoo doc who gives out the numbers that can never fail. After all my years of laboring and struggling to win the lottery i finally won ( $27,000,000) Dr Alli is the name, Email: allispellhelp1@gmail.com or contact him on his whatsApp number +2348100772528 this is the only way to win the lottery and the best way

    ReplyDelete
  8. WITH A HEART FILLED WITH JOY I WANT TO SAY THANK YOU TO DR LOJA.

    Good day everyone reading my short story, it all started this year when my boyfriend left the house and packed in with his ex from high school i tried all i could on me own to win his heart and no result and now i was already pregnant for him and everything has caused me depressions it was after two months of all the dramas i read a little article where they said this man DR LOJA can cast a spell or say prayers to restore broken marriages. i sent him a message on Facebook and email and this was how everything was restored and today my relationship is back for good our wedding is December 2021. with my experience and few others i have read online and spoken to about DR LOJA i can beat my chest and say this man is real and can help you as well. his contact details are below

    Email; drlojasolutions@gmail.com

    call/ text/ whatsapp ; +2349159144552

    ReplyDelete
  9. Margaret Loughrey
    I never thought that I could be this wealthy after all I've been through trying to meet ends and take care of my family, I used to play lottery but has never be lucky to win until I saw some comments online how he had helped a lot of people win, after first I didn't believe him but still I gave it a try, I wrote him a message on email after few hours he replied back so I told him what I want he assured me success. he also told me what I should do and I did all he requested from me, after some hours he gave me the lucky numbers and showed me where to play so i did as instructed to my biggest surprise I won 27 million pounds (Euromillions). Now I'm rich and happy all thanks to Dr Benjamin for the help, I'm nothing without you. if you need his help to win you can reach him via his email drbenjaminlottospell711@gmail.com and his whatsapp +13344539570 or visit his website Drbenjamintemple.com

    ReplyDelete
  10. Genital herpes is a common sexually transmitted disease, affecting more than 400 million persons worldwide.it is caused by herpes simplex virus (HSV) and characterized by lifelong infection and period reactivation,And the medical doctors has been killing us unknowningly to us with pills they gave us, it caused us heartburn.Antiviral prophylaxis with acyclovir only to help's reduce your pains, I am recommending you all to herbal remedy today, I was able to get rid of HSV2 totally with herbal medication from Great Spiritual farther Dr Alli take a try of his medication and see for your self, reach him via contacts: allispellhelp1@gmail.com or call/WhatsApp+2348100772528

    ReplyDelete
  11. I am Diana Margaret by name from England, so excited to quickly Appreciate Dr Kachi. who helped me win a lot of money a few weeks ago in the lottery,  I was addicted of playing the lottery game, I’ve never won a big amount in the EuroMillions lotteries, but other than losing my ticket, I always play when the jackpot is big. I believe that someday I might as well be the lucky winner. I was in the Aldi supermarket store buying a lottery ticket when I overheard Newsagents reveal saying what happens when someone win a National Lottery jackpot in their shop by a powerful doctor called Dr Kachi, i was not easily convince at first so i went online to do some research about Dr Kachi I saw different kind of manifest of testimony how he have help a lot of people to win big lottery game in all over the worldwide, that was what trigger me to contact Dr Kachi i decided to give him a try and told him i want to be the among of the winner he had helps, Dr Kachi assure me not to worry that I'm in rightful place to win my lottery game and ask me to buy lottery tickets after he have perform a powerful spell numbers and gave to me which i use to play the lottery draw, and won a massive £40,627,241 EuroMillions, After all my years of financially struggling to win the lottery, I finally win big jackpot, this message is to everyone out there who have been trying all day to win the lottery, believe me this is the only way you can win the lottery, contact Call/Text number: +1 (209) 893-8075 Email drkachispellcast@gmail. com

    ReplyDelete