The key thing to remember here is that not only is this efficient processor wise; RPN is also efficient memory wise. You don't have to keep track of multiple variables all over the place; everything you need to complete your operations is in the stack in the order you are going to have to process them. It's a very tidy system and a core component of computing that is normally hidden by higher level languages.
So many of these videos are brilliantly educational that I have started editing and improving the captions for people like myself who are hard-of-hearing or deaf. If you find my changes suitable, please use and alter them as you please. I have so far done this for two videos and intend to continue if you will approve the changes. It is the least I can do for such a great channel. :)
It's interesting to watch these coding videos because of the benefits it brings to my own logic. Coding is incredible at showing different ways to do the same thing. Before watching this video, I'd never thought in mathematical terms any different from infix notation. It's incredible to see how that suddenly changes the approach to the entire problem. Long story short, thank you for uploading these, Brady and Sean.
Wonderful video. I first encountered an fell in love with RPN when I got my HP 32SII, back in high school. It was so great. You never needed parentheses and you could enter formulas by reading left to right. So nice to hear Prof. Brailsford explain the history and explain why it was so great.
Funny how just the small hint of the title instantly made it clear to me just what the benefit of postfix notation was. I hadn't actually thought about it until now.
A number of years ago I tried learning a programming language that used RPN and couldn't quite understand how it all went together... I wish I had this video back then, it explains things very simply and make sense out of something that has had me confused for over a decade. Thank you professor!
I remember when I first learned about this a Comp. Sci. course at uni. The prof. was printing out a tree using a recursive method and just moved the print out statement between different conditions to convey the idea to us. Really cool stuff. :D
Best and most easy to understand explanation I've seen of RPN and stacks. Professor Brailsford always does a good job of breaking things down like this,
I remember having a similar reaction as Professor Brailsford here when I was first introduced to postfix notation and their relation to stacks. It's just brilliant! Absolutely a match made in heaven :D
Prof Brailsford is great! I'm really enjoying all the Computerphile videos, you've got some great people to talk to, and they're really well edited! Thanks Sean, keep them coming :)
Thank you! Please do more videos like this. My compsci professor would always mention the stack but never took the time to explain it, and the book we were using was only focused with teaching the basic semantics of the language. This seems like an important concept to know if you're trying to optimize run time.
I have a calculator app on my tablet that I usually keep in rpn mode. Makes it easier to do bulk operations and it makes sure the calculator doesn't mess up the order of operations.
If you understand this, you pretty much understand everything you need to know to program a language called "Forth". Forth is a brilliant language that is as low level as C (its almost superpowered assembly code) but can be as expressive and powerful as LISP. Its often used for programming very low level stuff, and thus gets called a "toaster language" (Because you might program the chip in a toaster with it). The most astonishing result of forth is;- you can program very very low level stuff without ever needing to set a register.
My first contact with RPN was in a maths exam when I had forgotten my calculator. The teacher was kind enough to let me borrow hers but it was RPN. The first couple of minutes I thought I was as good as dead but I got used to it surprisingly quickly.
Damn. One of my assigments is to program a calculator which interprets a string in postfix notation. After watching this video that's an laughably easy task. Just have to push everything on a stack and I'm as good as done. I can understand now why they like RPN.
Brilliant as usual. Reminds me of a friend at the "classes préparatoires" who tried to convince me that his HP stack calculator was way more fitted and nimble than my casio fx 180 P. I couldn't argue and felt a bit clumsy. 30 y. ago, feels like yesterday.
i cannot explain how big of a smirk i had when he started talking about loading values into registers, and then using the arithmetic unit... its such a cool process
A lot of the older RPN calculators didn’t use a stack system and instead used 4 registers that just transposed with each other, which was about 2 hz faster (practically null), but it limited you to 4 numbers in the “stack” without needing to use variables. This actually was less limiting than you might expect, but it is nice to have an actual stack that’s limited only to the calculator’s memory.
I am so glad you started a podcast with CGPGrey. I had seen your numberphiles videos before and found them interesting but had no idea compterphiles existed until I decided to look at what your many other channels actually are (idea for future pod cast to mention all your channels and what they actually are)As a computer science student I found this very helpful. Thank you!
The programming language called Forth, invented by Charles H. Moore has stacks and reverse Polish notation at it's very heart. It's an incredibly powerful and beautifully simple language.
Hello there, i must say, this is one of the best videos i have ever seen on this subject, right now i am studying for a Compiler Design class and i must say, i just loved it, so much clarity, if you are able to, please give my thanks to your colleagues and also thank you, tell them to keep it up
Excellent. I've been waiting for this one, I suggested it last year as a topic for Numberfile. RPN takes a while to learn but once you get it things become so much easier.... I'd be lost without my HP48G calculator (which doesn't have an "=" button but has an "ENTER" button instead).
I've had a HP50G for 4 years now. I'm so much used to RPN notation that I have trouble using "normal" calculators with any efficiency :D RPN is a much faster and error proof way to tackle hairy expressions. RPN users unite! :D
batsali99 I had my first taste of programming on a 28S, and ever since then I haven't been able to get away from RPN. I now own two 50G's and a 35S. I love how "=" is a secondary function. It really discourages people from "borrowing" my calculators.
This seems such a cooler notation than the standard one. Especially in computing it gets incredibly confusing with operands. Some have higher priority, some go right to left some left to right amd stuff...
A great explanation of stacks and polish notation. Would love to see a follow-up on how things like brackets and unary (negative -) operators work with this.
You don't need brackets as you control precedence by order of the operands and operators For example 4;5;6;+;x might be (5+6)x4, whilst 4;5;+;6;x would be (4+5)x6. Hope you can follow my notation - had to use x as a multiplier as asterisk seems to cause bold type. The system I work with uses semi-colons to indicate a push and then calculates left to right pushing the the result from the last operator back onto the stack.
I love this. when I made a scripting interpreter with compiler in c I used reverse polish notation in my compiled scripts. id never heard of this before today but it made the most sense. especially when parsing nested function calls.
Loved my HP-15 with its RPN and 4 level stack. Many still think it was the best scientific calculator ever made. Enough for Hewlett Packard to put out a limited edition in 2011, *_22 years_* _after the original had been discontinued_! Mine went to silicon heaven after almost 30 years of use. I make do with an RPN calculator on my PC.
Great video. This is as good an explanation of RPN as I have ever seen. RPN is especially useful when dealing with computers because it lays out the information in the same way the machine has to use it. It is however not great for non machines like humans. We do not use the information the same way a machine does. We see the entire line at once and then evaluate it. It is why I prefer TI calculators over HP calculators. I prefer to let the machine evaluate then execute the line. That makes life simpler for me. I really do not care if it is simpler for the machine. I would recommend an HP calculator for anyone going into Computer Science or Engineering because these two disciplines require such heavy use of computers and writing original code it is useful in thinking in these program steps to begin with.
Not trying to start an argument, pun intended, but RPN is more natural than you think. If when you were being taught arithmetic they taught you to arrange your numbers vertically, you were using RPN. The dawn of the digital calculator actually caused a lot of confusion. TI's follow the throwback that early calculators only had three registers since only one operand could be preformed at a time. HP's stack flow is an analog to the conventional vertical 'pen and paper' method.
I have a modern scientific calculator which only gets used for some of the more advanced calculations I need to do when I'm not at my computer. But it is so much faster and easier to deal with complicated equations using a RPN calculator, as you type the values in the same order you would if you were solving it yourself. Now that you can get RPN calculator applications for cell phones, and not have to fork out a load of money, doing calculations couldn't be easier.
I owuld of liked the video to continue the explanation on how it then evaluates (a+b)+c in reverse polish stack notation... but great video, this is something i always wanted to know, how a stack evaluates stuff!
Very good lecture! LISP languages use the opposite: forward polish notation. There parentheses are required to show where the list of operands end for a operator.
I love RPN calculators. They’re so much faster to use, incredibly intuitive once you understand how to use them, it uses less keystrokes, the system runs faster because it doesn’t need to “compile” the code, and nobody ever will want to borrow it after you show them how to use it. 😆
I always like presenting prefix/infix/postfix via binary trees when teaching people how to translate them. for example if you build a binary tree of the equation "a+b*c", where operands are leaves and operators are nodes, you'd get a tree that looks like this. ( + ) / \ ( a ) ( * ) / \ ( b ) ( c ) Now take your finger and start directly above the root of this tree. Draw an outline counter-clockwise around the tree hugging all the leaves and nodes. if you want to write this tree in prefix simply write down the node/leaf whenever your finger passes directly to the left of it. For infix is when you passes directly below one. And for postfix is when you pass directly to the right of one. In the end you would get these results prefix: +a*bc infix: a+b*c postfix: abc*+
I remember being very frustrated about writing in FORTH because it was a stack based language and the specific compiler I was using didn't allow you to make changes, you had to type everything right at ONCE! I tried 5 hours to make something that would have taken 30 minutes in LUA. ahh good days.
In high school math competitions, you had to be using an RPN calculator if you wanted to be competitive in calculator event. After HP quit making them, the rules had to be changed to grandfather the discontinued models. HP32S-II
There is just one thing that could be misunderstood in RPN. It does not always take 2 operants. For instance in "a b - abs" abs (absolute value) would take only one argument, because. The number of operants simply depends on the operator (and no - you can't "a b c +" only "a b c + +"
