Lecture 8: Hashing with Chaining

[@sergeykholkhunov1888]

00:55 dictionary 05:10 dict in Python 06:30 motivation 13:40 simple approach 17:50 prehash 24:00 hashing 30:15 chaining 42:05 hash functions

[@bobbob3630]

@ everyone saying this guy is amazing, and wishing their teacher was like this, this guys is insanely good, he started university when he was 12, got his bachelors degree when he was 14, and completed his PhD thesis when he was 20. He's the youngest every teacher at MIT

[@w1d3r75]

The real goat 🐐

[@Utuber5000]

Example= MIA(2*2)------>4, M-77 I-105 A-97, Equation= sum of axes divided by array boxes and then 77+105+97 / divided by 11, which is the number of array boxes. 279/11=8 , I know afterwards I would find the next index number for the new key/name given , its just that I wrote this down about a year ago , but the part about how I found the axes 77,105,& 97 is missing , so can u renew my memory on how I go about finding the axes again?

[@dragon_warrior_]

@@Utuber5000 okaaaayyyyy

[@Gustavo_Rojas]

and he looks like he's 10! =)

[@justbedouin6437]

what his name ??

[@gladysmayettepatricio5726]

Awesome lecture! I can't imagine the number of books he have read and the skills he have mastered to be this good. So much respect sir. You are worth emulating!

[@olivercopleston]

The core strength this man displays with that chalk-handing is god-like.

[@Xaminn]

Especially at 1.5 speed lol

[@wilhelm.reeves]

@@Xaminn 😜

[@reassume4826]

I can read here many people are complaining that if they had teacher like this lecturer,they would be happy. But the matter of fact is they all have him. Eric is teaching that's what teacher does , it's your job to make as much use of it and donate for such causes once you succeed in life.

[@georgelin8019]

I'm jealous of those MIT students, so lucky to have such a great prof.

[@juliocardenas4485]

Yet, we are all here 😎. Good for you for learning on your own

[@7th_CAV_Trooper]

So many cool things going on beyond the lecture content. First, the movable boards. That is so cool. Never saw anything like this before in my 53 years. Second, Erik's writing style on the board is very clear. Headings underlined, numbers circled, etc. It's all very on-purpose and makes me wonder if that comes from formal training or if Erik devised it on-the-fly. The content is great too. He explains the concepts with the ease of someone with deep understanding. Loving this series.

[@roflbot101]

Thank you, Mr. Demaine, for rocking the chalk like you rock the ponytail: with gusto and aplomb.

[@SneakyMrSnake]

This teacher is awesome

[@jackfever405]

+Snake agree

[@SumoCumLoudly]

He had bachelors degree at age 14 and phd at 20

[@csl1384]

@NameHe was 30 or 31, born in 1981. But who cares? The lecture is awesome all the same.

[@Utuber5000]

Example= MIA(2*2)------>4, M-77 I-105 A-97, Equation= sum of axes divided by array boxes and then 77+105+97 / divided by 11, which is the number of array boxes. 279/11=8 , I know afterwards I would find the next index number for the new key/name given , its just that I wrote this down about a year ago , but the part about how I found the axes 77,105,& 97 is missing , so can u renew my memory on how I go about finding the axes again?

[@companymen42]

My Algorithms teacher is shit. She reads off her power point VERBATIM!! I want my money back because this guy has taught me more than she ever could.

[@RohanAnand417]

Dude same...

[@NikitaYVolkov]

God I wish I had teachers like that.

[@weizhixie9678]

Now you have it. How is your algorithms?

[@wilhelm.reeves]

@@weizhixie9678 XD

[@Marko-up6js]

my professor just gave us about 6 simple very dry PP slides, gave us starter code with data structure and gave us a pop quiz. I wish this guys was my professor.

[@User-cv4ee]

If anyone is curious, hash('\0B') does NOT equal hash('\0\0C') (or '\0\0c') anymore in python (ipython 7.13)

[@starogre]

This guy is a genius. He founded his first software company when he was 8 with his dad. At 10 he graduated high school (not validictorian) and went on to university. At 13 he graduated university and sold his company for 1.2 million dollars. He went on to win a Politzer prize and patent for a computerized fabrics machine. MIT asked him to start teaching at the age of 16 and here we are.

[@fleurdecerisier9550]

😵🤯

[@roblox_vidzz8494]

is this satire

[@RagHelen]

He's right! In Python, the id of an object is equal to the hash of the id. d = { 'a': 1, 'b': 2, 'c': 3 } for key,value in d.items(): print(key) print(id(key)) print(hash(id(key))) Output: a 5045920 5045920 b 5044240 5044240 c 4964624 4964624

[@SirHirnschaden]

i would love to have a prof. like this :D i sleept in so many time in our class about hashing x.x but he get me the motivation! greets from germany!

[@austinahne]

He starts talking about at chaining at 30:15.

[@chinglinwen]

I thought he just skipped the solution to the problem 1 of map to non-negative integer. which relate to hash functions.

[@Hideot0]

Actual hashing is only addressed at 24:00

[@JayPatel12928]

Coolashacka thanks a lot for that....

[@mheepooh7413]

Thanks mate

[@TheMasterfulcreator]

@JustOne this is literally their actual course

[@manojmd6315]

Thanka

[@GaryCh]

MIT is so freaking lucky. At UPenn and Temple, I had to write notes like a madman because no lectures were recorded. I wasted sooo much time writing notes and trying to write fast enough that the lecture was pretty much pointless, and resulted in me basically reviewing notes and asking questions at a later time.

[@GaryCh]

An aside I notice when I was like WTF why is no one writing notes

[@MrGencyExit64]

Gary C I never took notes ever and graduated top of my class; it's best just to pay attention to the lecture in class and then use a textbook for anything concrete.

[@SrbijaaBree]

This guy is even more awesome at 1.5 speed

[@icosmini]

Also at 2.0

[@horotat]

@@icosmini Agree

[@patmaloyan620]

hahahah. I keep forgetting this and these comments keep saving me. 1000% focus increase.

[@beypazariofficial]

@@patmaloyan620 yeah yeah. it's awesome to listen the courses at 1.5 or 2.0 speeds and it's increasing the focus. absolutely great. and we're finishing it in less time too. tons of time saved, thanks for the youtube videoplayer.

[@bosshaug5672]

This guy is awesome, even 9 years later, still better than my professors. i just wish I had a CS prof that could speak english :/

[@TheNikatlas]

@siddarth kamaria There is a Collection of hash functions you can use. 'a' and 'b' are random chosen in the beginning. Since then you must use the same hash function.

[@luisdanielmesa]

40:30 how could they not laugh at that???? It's gold.

[@and1fer]

+Luis Daniel Mesa Velasquez can u explain the star wars reference?

[@vasiliskourepinis4329]

+and1fer Star Wars, A New Hope, Ben kenobi to the stormtrooper: "These aren't the Droids your looking for"

[@spidLL]

+Luis Daniel Mesa Velasquez probably because they never watched it :(

[@luisdanielmesa]

spider :´(

[@pixelhunter0]

hash("\b0")=hash("\0\0C")=64 means that two different keys map to the same thing, 64. ideally you want if hash(x)=hash(y) then x=y that means the keys are the same. but sometimes we can have a collision where x!=y.

[@websoftwaredeveloperijtiha3093]

It's so cool that these top schools release courses like this one online free of charge. I may not get a chance to go to MIT

[@Speed4Runs]

now that's the typical nerd look you would get after becoming an algorithms teacher. love it.

[@abdallaelmedani8933]

You are an amazing teacher, Erick :-) Btw "Hasheesh" in Arabic means "marijuana"!!

[@srinikethvelivela9877]

15:46 Why something is hard to associate with integers

[@wolfinthesuit]

If teaching in 2022 was like this I would really be mf Genius in Data structure and IT, unfortunately they only stream videos and you MUST UNDERSTAND IT ALONE

[@airy_co]

damn this videos are so damn cool, i wish i had an actually good teacher like him

[@vasiliskourepinis4329]

The lecture was awesome, but the starwars reference was even better!

[@이효건-o4o]

Thank you teacher for just being there

[@prateeksinghal630]

I didn't even feel when those 50+ minutes passed!!

[@harryzhang5984]

Who else is Still watching this video in 2021??? Great lecture!

[@moabsmithbey9583]

I love how he explain the algorithem problems also he look young.

[@mitocw]

Thanks for your comments! A little trivia: Erik Demaine became MIT's youngest professor in Fall 2001: news.mit.edu/2003/demaine-0226.

[@guilhermeborges4097]

Dopest class, much better than my dear teachers, or almost dear... whetheaver, thanks!!!!

[@cammiltaank]

At 33:15 Erik draws a linked list to store multiple items where their key collides. How does one retrieve the correct item on a lookup? The keys themselves seem to be absent from the linked list, so how do you know which item to return?

[@dergons]

I think the assumption is that the item is a tuple with the key and corresponding value. As in the Python implementation explained earlier in the video.

[@asshole9191]

The key is immutable for each object. Otherwise you couldn't reconstruct it later on. So either you calculate the key for each object in the list anew or you save tuples.

[@hrishikeshkulkarni2856]

Wow MIT has masterpiece teachers!

[@VideoHub81]

24:08 hashish vs hashing

[@Utuber5000]

Example= MIA(2*2)------>4, M-77 I-105 A-97, Equation= sum of axes divided by array boxes and then 77+105+97 / divided by 11, which is the number of array boxes. 279/11=8 , I know afterwards I would find the next index number for the new key/name given , its just that I wrote this down about a year ago , but the part about how I found the axes 77,105,& 97 is missing , so can u renew my memory on how I go about finding the axes again?

[@VideoHub81]

@@Utuber5000 how's this related to my comment?

[@it41tanmayaron26]

@@Utuber5000 yeah, it can be done. I did something similar to this some time ago

[@SD-gp3xx]

@MIT Opencourseware While explaining simple uniform hashing, Erik suggested that independence is necessary but is independence really necessary? The expected length of a chain comes out the same whether you assume independence or not. My solution without assuming independence: let R1 be indicator random variable for the event that a random key falls into the 1st bucket. R2 be the independent random variable for the event that a random key falls into the 2nd bucket and so on. Initially assume all slots or buckets are empty. A chain length becomes length one when a random key falls into one of the slots and remains the same when it falls into any other bucket. So, l1 be the length of chain in the first slot; l2 be the length of chain in the second slot and so on. So, total length of chain would be l= l1+l2+l3+...+lm. So, expected length of chain E(l)= E(l1+l2+l3+...+lm)= E(l1)+ E(l2)+ E(l3)+...+E(m).... (by linearity of expectation which does not need independence). E(l1)= 1.1/m+ 0.(1-1/m)= 1/m = E(l2)= E(l3)=...=E(lm) So, E(l) would be n/m. I did not assume independence. Where did I go wrong? Someone please explain.

[@kishorebabu8470]

They are actually seat cushions.... Srini explains that the seats in the hall are uncomfortable to sit on for long durations. So a cushion is a perk one earns for answering questions. I wouldn't be surprised if there a cult angle to the scenario though.

[@WeirdAlSuperFan]

Lolwut

[@GeekMonsterWindel]

Pillows?! Wow that's peculiar. I almost thought that was some sort of secret invitation to a underground brainiac party held by him (he has that cult leader quality).

[@VuHoang-vh6nj]

professor is really an heavy job

[@metaldetectingmichigan6050]

Did anyone else notice the blunt behind the guy’s ear at 1:48 😂😂😂

[@juliawenkmann8510]

What is he throwing at 17:07 ?

[@gavinchou3022]

42:14 hash function fundamentals.

[@tanvishinde805]

Does anyone feel why the lecture is bounded by time, I just he feel he explains whatever knowledge he has in how much ever time he needs for it. Awesome lecture @ErikDemaine

[@damienrochford2230]

What is the difference between a prehash and a hash function? I didn't feel totally clear on that point after this lecture.

[@Orww]

It's also known as hashing (prehash) and compression (hash), maybe that helps

[@augustopaiva9154]

if the key are not an intergers, you use the prehash to make then in a intergers and then use the hash fuction. I think.

[@Gukslaven]

Yeah I've never heard of a prehash and hash the way he describes it. I know it as: the hash function turns an object into an integer. And the compression function gives you some integer within the bounds of the underlying array. A google search doesn't give that many results for pre-hash or prehash so... my guess is the are less popular terms (?)

[@elle1718]

From my understanding, prehash merely turns your non-int keys into integers but does not address the problem of space, so you hash the resultant integer using a more complex hash function which should theoretically convert the integer into another integer within a specific set of integers with m as the upper bound

[@rdwells]

The "prehash" is a function that converts the state of the key object to an integer; the "hash" function converts it to a hash table index. This is a logical division of labor; the key type "knows" how to convert the object to an integer, and the hash table "knows" how to convert that integer to a hash table index. But neither of them has to know anything about the other. What he's calling the prehash is done in Java, for example, by overriding the Object.hashCode() method; in C++, it is generally done by define a hash class and implementing operator(). The hash function then generally uses either the division method or the multiplication method, as described in the video. I personally prefer the multiplication method since it works with hash table sizes that are powers of 2, and that allows you to use the table resizing discussed in the next lecture in this series.

[@shivanshuraj7175]

a Very much satisfying place to learn cs

[@idontevenlikehavingagoogle8077]

i dont even know why i go to class anymore..cept for midterms

[@gherbihicham8506]

For that useless piece of paper that says doing some shitty handwork by some professor is a better way to be recognized on the job market than learning by your self .

[@iFloops]

Gherbi Hicham You're very misguided.

[@gherbihicham8506]

stampsr92 Elaborate please ...

[@ionezgb]

+Gherbi Hicham Employer doesn't have time to test every job applicant so he/she wants a proof of knowledge issued by institutions which he/she trusts same way you want to use medicine approved by official institution for testing medicine.

[@gherbihicham8506]

ionezgb I didn't say every job , sure i won't go to someone without a medicine degree if i felt pain , some jobs just need to be certified by an institution , some can only be proven by institution , again how on earth are you going to prove that you can prescribe drugs without a university degree ? that's not my point , my point is that a lot of jobs don't need a university degree at all and its good respectable well payed jobs as well, being a programmer for example can have multiple other proofs of knowledge other than a University degree , good projects on Github , a good Stackoverflow reputation count , even down right list of the projects you've built and several other things can land you a job as a developer in a lot of places, infact some jobs will even require things like your programming profile. This misconception that you need college in order to work a proper or a well paying job is just getting ridiculous, a lot of people don't have the time nor the financial resources to engage in a university program, and a lot of people who enrole in college for a useless liberal arts degree only find themselves several years later with no job and a massive loan , University shouldn't be for every one , and not everything needs a degree . This is coming from someone who spent 5 years at college for a masters in Computer Science .

[@sidnarayan438]

I died laughing at his references, Erik Demaine is such a cool geek

[@brandonmacdonald7802]

What was the vampire reference?

[@deb5976]

amazing class. Thanks for making this public

[@PrateekGuptacs]

That was an awesome lecture. Thanks MIT :)

[@ShubhamSinghYoutube]

Hashing is cool ~ Erik Demaine

[@justbedouin6437]

I like the way when he explains hash meaning hhh.. Thank you

[@katsunoppo]

he is handing pillows - see the first lecture of the series, there is some explanation

[@bedekelly5474]

If a and b are random, does that make the hash function non-deterministic? Do we have to cache the calculated hashes in order to look items up in a hash table after they've been inserted?

[@nguyennguyenphuc5217]

maybe a and b are chosen from very first and stored as constants

[@anteconfig5391]

@Bede Kelly I was wondering the same thing. I think maybe yes.

[@abhishekraj7713]

Literally a good explanation I got❤

[@cammiltaank]

At 28:30 Erik says m = O(n) is optimal, but would m = n + O(1) not be more optimal (based on what we know so far)?

[@nayuki2020]

lmao. come on dude be nice

[@cammiltaank]

I'm just curious if m = n + O(1), or if I have missed something. I realise that n is O(n). If we can state that the constant factor is 1 then why not?

[@asshole9191]

You misunderstood the big O notation. O(f(n)) means the following: we have an actual function g(n) whose values are all smaller or equal to c * f(n) for a constant c. This is, of course, only if you are bigger than a certain value n_0. If f(n) = 1, we only have c, thus g must be constant as well. If we write something like n + O(1) we mean that you add a constant to n, whatever that might be.

[@giordanobruno9601]

Imagine having a professor this good and not bothering to show up on time.

[@Zerpentile93]

Thanks for uploading this.

[@svnthsz3r]

Big Thanks from Austria!! :D

[@girishkariappa7386]

50 minutes worth watching this vid

[@ronnypolle4350]

i love MIT! i love EriK Demaine!

[@landanparker911]

the issue with collision, if the developers had just taken the string of bytes, appended itself, for example /0B and /0/0C, turn that into /0B + B0/, and /0/0CC0/0/ so that you have palindromes, the collision should occur less if at all, instead of using the raw string of hash.

[@englishconversation590]

Thanks teachers, lession is awesome.

[@陈建勇-b1v]

I love these videos!

[@Utuber5000]

Example= MIA(2*2)------>4, M-77 I-105 A-97, Equation= sum of axes divided by array boxes and then 77+105+97 / divided by 11, which is the number of array boxes. 279/11=8 , I know afterwards I would find the next index number for the new key/name given , its just that I wrote this down about a year ago , but the part about how I found the axes 77,105,& 97 is missing , so can u renew my memory on how I go about finding the axes again?

[@paulmarkert5907]

Ok, I'm inspired. Time to go code.

[@Topbitcoinexchanges]

Excellent lecturer. Bravo sir

[@coderopes2983]

These courses are awesome N helpfull

[@unev]

Why non-negative integers restriction is a problem? Why can't we just throw out the minus sign?

[@damienrochford2230]

Collisions. Not that that is the end of the world, but at that point in the lecture we are assuming that there's a unique integer-key for every value.

[@unev]

Kudos, Damien

[@damienrochford2230]

No problem!

[@asshole9191]

In the beginning it was said that the key is the index in the array, so if you have negative integers as keys, you have to have negative indexes. Later on, it is said, that you have some kind of prehashing, that gets rid of most assumptions.

[@randomxyz2608]

hey man , u alive?

[@OMGitsjustperfect]

I understand how to put stuff in the hashtable, what I don't understand is how to look it back up. If your key is random, how do you know which key to look up?

[@electricgirltakesonworld2384]

can someone explain key space? why is memory allocated to key space a problem in direct access tables?

[@andres3398]

Great teacher !

[@kzterminator]

ak+b mod p and p is a huge number? ain't that just equal to ak+b?

[@siddharthkamaria]

How can 'a' and 'b' be random? If we call the hash function another time it might generate another values for 'a' and 'b'. I'm unclear what is he referring to by describing 'a' and 'b' as random...Any help would be appreciated.

[@willmorgan8830]

Excellent explanation. A++

[@raseshgupta6276]

You are awesome! Big Thanks

[@lharsh175]

38:50 That's what she said

[@twittertalks3934]

why are they talking about pointers if there is no function of pointer in python can anyone answer that please

[@lordsambhav]

@39:11 "Sadly in the real world, you don't have independence."

[@a.a7907]

Thank you for the video. I have question. Why don't we instead of using hash table and liked list together, use two hash tables and link them with a unique queue.

[@eagerassaultixopi4558]

Its called double hashing and it will leave us with more unallocated space.

[@Cruz0e]

3:05 what's the point to override a key? nothing changes I guess he meant to override the item not the key

[@rishikaushik8307]

why don't we use a pointer to another dictionary instead of a linked list?

[@TankNSSpank]

Why does it suck to have the division method for hashing? I can't see why he metioned half of the table would be used if m is the power of 2.

[@TankNSSpank]

I see it now.

[@black-sci]

Can someone tell what's difference between hash and prehash.

[@rafaaaaaaa1]

Could someone show me an implementation of 46:00?? Please

[@rdwells]

Let M be your hash table size, which must be a power of 2, and let r be the integer such that M=2^r. Let a be the multiplier, and k is the hash of your key. Finally, let w be the size, in bits, of an int. Then h(k) = (((int)(a * k)) >> (w-r)) & (M-1) To break this down, you multiply the key by a, truncate that to an int (if your language doesn't already do that), and shift right enough to move the top r bits into the low-order bits. If your shift operator is logical (fills the top bits with zeroes), you can skip the final bitwise 'and'; otherwise, the 'and' is necessary to strip off any 1 bits resulting from an arithmetic shift of a negative number.

[@64standardtrickyness]

Can someone explain what the point of this is? You mapped your universe to a small array but each index of the array contains a linked list and the entire universe fits into the array so the array has to use a lot of memory so I don't see how this solves problem (2) gigantic memory

[@DeepROde]

Earlier if you had to look for a specific key, you had to travel whole universe. Now you just need to go to specific location.

[@etg9080]

writing with chalks and erasing with hands?

[@allopeth]

24:11 In case you are wondering... Hashing has nothing to do with hashish ... LOL ! :D

[@wowzande]

halfway through this lecture, just wondering , can i use this information if im coding in c++ or will some of the stuff be different. Im currently learning hashing for my advanced algorithms class, someone let me know so i don't waste my time or go off in a tangent.

[@rallokkcaz]

No tangent, you're probably kind of screwed. And yes it will be different by vast margins, C++ has std::hash_map and std::unordered_map. However if you need to implement a hash map, it's not the same.

[@MegaVuhung]

awesome instructor

[@amsallakhani4871]

Blackboards are the key

[@seaoftears1]

excellent course

[@aditijuneja1848]

32:29 there are linked lists, can we have unlinked lists?

[@adijo123]

Wonderful lecture.

[@chaitanaya677]

so, is the key converted to an int before performing the hash functions

[@rdwells]

Yes. See my reply above to Damien Rochford.

[@benyaminbeyzaie301]

why they don't talk about expression trees?!

[@zhegemingzigouchang]

5:07 don't you look at me.

[@thedadar]

why you not use a projector?