The Nineteenth Byte

ASCII-only

4:05 AM

@Downgoat is basically getter

@Downgoat also yes PyTek does this

Pavel

@ASCII-only It literally is a getter, but in expression-body form.

ASCII-only

@Pavel IIRC we're already doing that

Pavel

Mm. Do functions have expression-body form?

ASCII-only

4:32 AM

Not sure

Haven't really done much on functions haha

But we're definitely going to include that

New Main Posts

0

Q: Logical Puzzles related to tree structure

There are numerous programming problems are related to tree structure. example, displaying the hard drive, displaying a dropbox content, categorization, tree editors etc., example, displaying 1,000 records in a tree will fail. however it can be resolved via breadcrumb which is very efficient as...

binary-tree

Pavel

Language idea: foo(a, b) is syntax sugar for foo(a)(b) and (a,b)=> is a=>b=>. If a function normally takes two operators, you can call it with one, save that result for later, and then call it with the second operator. The uselessness of this feature is astounding, I'm sure, but intresting to consider anyway.

ATaco

It'd be nice so you can do add(1,2) or add2=add(2); add2(1)

ASCII-only

@Pavel ... that means you can't do overloads...

Leaky Nun

@Pavel isn't that just haskell?

Pavel

4:42 AM

IDK haskell

ASCII-only

@Pavel Also. This is what & is for (IIRC)

Pavel

@ASCII-only C got along just fine without those

Leaky Nun

@Pavel wiki.haskell.org/Currying

Pavel

@ASCII-only What's that

ASCII-only

@Pavel ... doesn't mean it was very nice having no overloads...

Pavel

4:43 AM

@LeakyNun Right but haskell doesn't convert functions with multiple args to a curried function automatically

ASCII-only

@Pavel (f&2)(...args) == f(2,...args)

Pavel

What language is this

ATaco

Me equa.lua library is implicitly curryable :P

Pavel

ASCII-only

@Pavel Cheddar, but pretty sure VSL will do this too

ATaco

4:45 AM

require"equa"
local add = x+y
print(add(3)(4))

Returns 7.

And add(3,4) does too.

Pavel

Lua is a terrifying language.

ATaco

That's just me abusing lua

Sane lua won't let you do that.

But here's a library that doesn't care about sane lua

I wrote it because anonymous functions in lua are too bulky.

function(s)return s:rep(3)end becomes #rep(s,3)

The # just casts it to a function, to make it more compatible with standard lua functions.

Adám

@Pavel Where is this from?

@ASCII-only Works in J. In APL, that's ∘.

ASCII-only

@Adám Makes sense :P

Pavel

@Adám discord dm.

We were talking about spaceships and I mentioned grade up/down

Adám

4:53 AM

@Pavel Ah.

ATaco

TitleCase = gsub(s,"(%w)(%w*)",#(upper(x)..lower(y))) Titlecase func! :D

(I like this library too much)

Adám

@ATaco Dyalog APL: TitleCase←'(\w)(\w*)'⎕R'\u1\l2'

ATaco

With credit, it's still a lot shorter than lua's default solution of TitleCase = function(s)return s:gsub('(%w)(%w*)',function(x,y)return x:upper()..y:lower() end)end

Adám

@ATaco But what do all the sugar chars do? (s,,#(..))

ATaco

Well, in lua .. is the concat operator, simple enough.

Destructible Lemon

5:02 AM

I'm not sure how my spaceship koth would work anymore

Pavel

@Adám So ⎕R returns monadic function?

ATaco

s is a protoexpression, as defined by the library.

#() casts another protoexpression to a function, which gsub can use.

# is just the length operator, but I took control of it.

Adám

@Pavel Actually, it returns an ambivalent function. Used monadically, it does the expected PCRE replace on the given string(s). Used dyadically, it reads from the right-arg file and outputs to the left-arg file.

ATaco

When the function is called, it substitutes s (the only protoexpression it has access to), with the argument. We'll say "Hello, world!" for this case. then, the expression is gsub("Hello, world!", '(%w)(%w*)', #(upper(x)..upper(y))). This is satisfactory for gsub to run (because it thinks the third argument is a function, not a protoexpression), so it passes the replacement args in each case to the function, which substitues x and y for each match. If that makes any sense.

Pavel

@Adám When you say file you mean actual storage file or is than an APL term?

Adám

5:07 AM

@Pavel An actual file on disk.

Pavel

Huh. That's a little odd, actually.

Adám

@Pavel Why?

Pavel

Well normally built-in functions don't directly operate on files, I guess.

You'd generally always go through a File.Write call or equivalent.

Adám

@Pavel APL system functions (begin with ⎕) often do.

Pavel

Ah, right. Forgot about ⎕ being System.

Which sorta makes me wonder why ⎕A yields the alphabet.

APL is a weird language.

ATaco

5:12 AM

I was going to do another text dump on my protoexpressions, but chatexchange was like "That's a little large there taco", and I was like "Yeah, good point"

Adám

@Pavel Why? ⎕ names can be constants, variables (including namespaces and classes), functions, or operators.

Pavel

"Alphabet" doesn't look like a system constant.

ATaco

What system cares about the alphabet :P

Adám

I do find that it comes in handy for quickly doing base conversions, column header generation, etc.

ATaco

Not denying it's usefulness, it's just curious that it's a system variable, rather than some other constant table.

Pavel

5:18 AM

^

Adám

@Pavel Try it online! using a nice selection of system names.

ASCII-only

@Pavel System.String.Alphabet :P

Pavel

Cool. Also, TIL how to use NTIE/NCREATE

@ASCII-only /o_o

ASCII-only

@Pavel Not actually a thing, that would just be its equivalent in C# if it existed

Pavel

No I understand

Destructible Lemon

5:37 AM

ok so I thought of an rps variant that could possibly be used for a koth

ASCII-only

@DestructibleLemon umop.com/rps101.htm :P

Destructible Lemon

@ASCII-only I can't access this at this time

ASCII-only

@DestructibleLemon web.archive.org

Destructible Lemon

@ASCII-only that was not it and also that game is not actually that cool for a koth tbh

ASCII-only

@DestructibleLemon Hence the :P

Destructible Lemon

5:42 AM

what I was thinking is that you have tokens for each attack, and when you're out of tokens for an attack you can no longer use it

speaking of which this could be combined sort of with rps 101, or higher

maybe I will actually sorta use RPS 101 for this idea

Adám

@Pavel Nice. There's a whole family of them. See help.dyalog.com/16.0/Content/Language/System%20Functions/… under Native Files (hence the ⎕N…, and as opposed to APL component files)

Pavel

Thanks

New Main Posts

6:03 AM

0

Q: Why doesn't this regex match what is intended

I have rules for valid email address. A username must begin with an alphabetic character. It may be followed by any number of additional alphanumeric characters or any of the following special characters: . (period), - (hyphen), _ (underscore), or + (plus). A domain name must end with an alphabe...

regular-expression python

-1

Q: Input number and set them in lowest and highest order and sum up order

I need a program that will accept numerical inputs from the user until they enter a zero. The program will track some information about the numbers the user inputs and will display these after the user has finished entering new values. It will also perform some basic statistics on the inputs and ...

programming-puzzle

ATaco

Why I love lua :P

ASCII-only

> immidently

TBH it's not that different from how JS does it

ATaco

JS lets you do ``, but that's it.

Lua lets you use All the constructors!

(Besides functions and numbers)

Pavel

@ATaco Ruby lets you define method_missing, which operates on data when no valid method is provided.

So you can do that but without needing to add the w.

Or even quotes, for that matter.

ATaco

Example?

Pavel

6:18 AM

@ATaco destroyallsoftware.com/talks/wat

ATaco

I don't really have time to watch a talk.

Pavel

It's 4 minutes and it's the best thing you'll see all day.

John Dvorak

@ATaco your loss

ATaco

(I'm at work, my manager would be pissed if they caught me)

ASCII-only

@Pavel Why is this linked so often D:

caird coinheringaahing

6:19 AM

@NewMainPosts Hey look a double whammy of off-topicness!

John Dvorak

@ASCII-only because it's so good

Pavel

@ASCII-only Because I can't get it to work on my machine so I link it every time I tell people about method_missing

ATaco

Well at least lua has consistency :P

Pavel

Yeah, there is the fact that Ruby like to introduce breaking changes a lot.

And occasionally not tell anyone about it, except to remove a function from the docs.

ATaco

Come home to simplicity, come home to Lua.

Pavel

6:21 AM

And then redefine that function to always return 0 instead of removing it.

With the justification that "An undocumented function can do whatever it wants"

John Dvorak

@Pavel example?

Pavel

@JohnDvorak Object#methods, and actually it returns an empty array, not 0. It was replaced with a different method.

John Dvorak

Well... if it was undocumented...

Adám

CMC popularity-contest: Wat in your language of choice.

ATaco

What do you mean by, wat?

Adám

6:26 AM

@ATaco Simple expression with unexpected answer.

Pavel

@JohnDvorak But it was documented in 1.x, and it did what was expected.

Then they removed it from the docs without telling anyone, and replaced it.

@Adám Lua, x bytes: Literally anything as far as I can tell

John Dvorak

@Adám duplicate: destroyallsoftware.com/talks/wat

Adám

@JohnDvorak Not just Ruby and JS, obviously.

John Dvorak

@Pavel the real wat here is what you apparently think "literally" means

ATaco

@Pavel This is only if you do to it what I do to it.

Pavel

6:28 AM

@JohnDvorak Every example of Lua I've seen in my life has been ATaco demonstrating a new wat.

So I feel justified in saying that.

John Dvorak

Then you should look up some real code

Pavel

¯\_(ツ)_/¯

ATaco

require"equa"
func = b^a+c
print(func(3,2,1))

Returns 9.0

Pavel

Adám

underhanded APL: subtraction

Pavel

6:30 AM

s/-/:

Edit ninja'd

ASCII-only

@Pavel Can't get what to work

Pavel

method_missing.

ASCII-only

@Pavel You forgot the last slash

Pavel

It always seems to crash my repl

ASCII-only

@Pavel 0/10 how can you not get it to work

Pavel

6:31 AM

@ASCII-only It's a discord command not a sed command

ASCII-only

@Pavel You're doing it wrong

@Pavel Didn't they remove it

Pavel

@ASCII-only Sorry I meant skype command

ASCII-only

Aug 26 at 4:05, by ASCII-only

@Pavel $m=self;def method_missing(n,*a)raise NoMethodError,''unless self==$m;a.length>0 ?n.to_s+' '+a[0].to_s: n.to_s;end

ATaco

Lua, 175 bytes Try It Online!

ASCII-only

@ATaco ^^ :P

Pavel

6:33 AM

I don't know what that does.

I can't figure it out.

ASCII-only

@Pavel >_> <_< >_> <_< It's a reply to one of your messages, if you forgot pls read transcript

ATaco

Sets the the function that's called when a string is called to print its self and its arguments, then return the last argument it was passed, which is another string.

Pavel

@ASCII-only I don't think I understood it back then either

method_missing is black magic as far as I'm concerned

Challenger5

Python: Try it online!

This doesn't work because you can't assign attributes to str

Pavel

@Challenger5 Yeah I'm getting a traceback on that

Oh nvm

Challenger5

6:36 AM

You'd expect it to be allowed since they were trying to eliminate the distinction between builtin classes and user-defined classes

ASCII-only

@Pavel tio.run/##JYzLDoIwEEV/ZRYkBSGEtQRduVQ/wBhSYICJ7dTMlIVfX1/…

Pavel

Yeah C# doesn't let you overload operators for preexisting types either.

ATaco

Delet black magic

Pavel

@ASCII-only This bothers me even more knowing that ruby uses puts and not print

ASCII-only

@Pavel Who said ruby doesn't have print

Pavel

6:38 AM

I'm not saying it doesn't have print

I'm saying using print in ruby bothers me.

ASCII-only

@Pavel :P

@Pavel ok you have your newline now, happy?

Pavel

Yes

ASCII-only

@Pavel Well I much prefer print over sys.stdout.write

Pavel

I've been using $> <<

ASCII-only

You've been using what O_O

Challenger5

6:40 AM

It even works if you subclass str and change that: Try it online!

@ASCII-only Shorthand to print.

Pavel

$> is an alias to sys.stdout. Appending anything to sys.stdout writes it.

ATaco

C (gcc), 33 bytes m(p(Why is this allowed C. Why.))

ASCII-only

@Challenger5 better

Challenger5

Wut how can you do that

Subclassing is magical...

Pavel

@ATaco Because preprocessor

ASCII-only

6:41 AM

@ATaco :P

ATaco

C's preprocessor is gr8

Pavel

ikr

ATaco

I can almost quine in it :P

Pavel

Yep

As far as I can tell that would make you the first.

ATaco

Shame I can't yet quine in it.

Challenger5

6:44 AM

@ASCII-only :P

@Challenger5 :P

:P

@Challenger5 better

:P

This is slightly less ridiculous, but it's still neat.

caird coinheringaahing

6:51 AM

cough Just read through that

TuxCopter

7:53 AM

wtf my internet connection is averaging 10kbps

TuxCopter

8:05 AM

I'm now at 5 o_O

mınxomaτ

9:37 AM

Neat: cs.cmu.edu/~aayushb/pixelNN

orlp

@Lembik why did you delete your question?

Lembik

@orlp I realised it was stupid

orlp

why?

Lembik

or more accurately, that I was being stupid

what I really care about is a good lower bound not the exact value

orlp

@Lembik but I know the exact value

Lembik

9:45 AM

oh!

is there a closed form ?

I will undelete if there is

and apologise

Leaky Nun

hey what's the question :c

Lembik

@LeakyNun it was a math question

Leaky Nun

@Lembik tell me

(alt. undelete it)

Lembik

I want a good lower bound for sum({3k choose 3i} for i from 1 to k)

orlp

well the original question was clearer

given 3k coins, what is the chance that the number of heads is divisible by 3?

Lembik

9:48 AM

sum_{i=1}^{k} {3k choose 3i}

@orlp A much nicer formulation!

I wish I had asked that

orlp

and that's the answer

Leaky Nun

@orlp nice!

I mean, one can figure that out using binomial theorem

and cube roots of unity

orlp

what I did

Leaky Nun

right, that's your approach

orlp

no

Lembik

9:50 AM

blimey

is that at least 1/3?

orlp

no clue

maybe it can be simplified

Lembik

if it was at least 1/3 that would be cool

orlp

but consider a markov chain with 3 states

0, 1, and 2 mod 3

then after each coin we have 1/2 chance of staying in current state

1/2 chance of moving to the next one

giving transition matrix [[1/2,1/2,0],[0,1/2,1/2],[1/2,0,1/2]]

raise that to the power 3k and extract the topleft most coefficient to find your answer

you can find the closed form by diagonalizing the matrix

@Lembik and now the problem is in terms of matrices, so you should be happy :)

Leaky Nun

0.25
0.34375
0.33203125
0.33349609375
0.33331298828125
0.33333587646484375
0.33333301544189453
0.3333333730697632
0.3333333283662796
0.33333333395421505
0.3333333332557231
0.3333333333430346
0.3333333333321207
0.3333333333334849
0.3333333333333144
0.3333333333333357
0.33333333333333304
0.33333333333333337
0.3333333333333333

Lembik

argh

so no nice lower bound

but it does at least tend to 1/3

orlp

9:54 AM

@Lembik define nice

Leaky Nun

lower bound is 1/4

sorry edited

orlp

I gave you an exact algebraic expression

:D

Lembik

if the coin has 5 sides it's even worse :)

orlp

@Lembik but my method is generic :)

@LeakyNun my markov chain method gets those same numbers

Leaky Nun

@orlp nice

orlp

9:57 AM

you summed the binomials?

Leaky Nun

yes

should I use my method?

orlp

[1.0, 0.25, 0.34375, 0.33203125, 0.33349609375, 0.33331298828125, 0.33333587646484375, 0.33333301544189453, 0.33333337306976318, 0.3333333283662796]

[(M**(3*k))[(0,0)] for k in range(10)]

M = np.matrix([[.5,.5,0],[0,.5,.5],[.5,0,.5]])

Leaky Nun

can everyone here render $\text{this}$?

Lembik

so 1/3 seems to be an upper bound

@LeakyNun no!

orlp

@LeakyNun I can with chatjax

Leaky Nun

9:58 AM

@Lembik it's not; see n=2

@Lembik go install ataco chatjax :P

orlp

@Lembik it oscillates around 1/3

Lembik

hang on

orlp

@LeakyNun do you like my solution? :D

Leaky Nun

@orlp I don't really know much about Markov chains

Lembik

@orlp hmm

I get

[sum(comb(3*k,3*i) for i in range(1,k+1))*(1/2)**(3*k) for k in range(1,
...: 10)]
Out[9]:
[0.125,
0.328125,
0.330078125,
0.333251953125,
0.333282470703125,

Leaky Nun

10:01 AM

but I get your method @orlp

I like your solution; you should try out mine :P

Lembik

oh I see my mistake

orlp

@LeakyNun the crazy thing here is though

my method gives a closed form

so we have a closed form for that sum

is that closed form new? it's very nontrivial

Leaky Nun

@orlp binomial theorem and cube root of unity can also provide that closed form

Lembik

[sum(comb(3*k,3*i) for i in range(0,k+1))*(1/2)**(3*k) for k in range(1
...: ,10)]
Out[10]:
[0.25,
0.34375,
0.33203125,
0.33349609375,
0.33331298828125,
0.33333587646484375,

Leaky Nun

by extension we have a closed form for $\displaystyle \sum_{i=0}^{k+1} \dbinom{nk}{ni}$

orlp

10:04 AM

@LeakyNun interestingly wolframalpha doesn't know it

Leaky Nun

@orlp wolframalpha knows shit

@orlp you should use polar form to cancel out the imaginary parts

my lord

orlp

@LeakyNun I can't really be bothered tbh :P

Leaky Nun

$\displaystyle \sum_{i=0}^{k+1} \dbinom{3k}{3i} = \dfrac13(2(-1)^k+8^k)$

and you say WA knows shit

orlp

@LeakyNun doesn't give it for me

oh now it did

@LeakyNun well, there we go :)

I bet that $8$ is really $2^3$

Lembik

so the prob gets arbitrarily close to 1/3 it seems

Leaky Nun

10:07 AM

@orlp sure

Lembik

but oscillates around it

orlp

@LeakyNun this can't be right

Leaky Nun

sorry, to k

orlp

this grows without bound

look at the 8^k term

Leaky Nun

@orlp we haven't divided it by 8^k

orlp

10:08 AM

what is there to cancel it?

ah

Leaky Nun

$\displaystyle \sum_{i=0}^{3k} \dbinom{3k}{i} = (1+1)^{3k} = 8^k$

lmao I linked to k and wrote k+1

orlp

if I wanted to I would've eventually reached that form by simplifying the monster I got

.... eventually

Leaky Nun

right

are you familiar with complex numbers esp polar form?

orlp

@LeakyNun familiar-ish

Leaky Nun

@orlp then what is $(1-i\sqrt3)$?

orlp

10:11 AM

eh which angle had sqrt 3 as sine again

2sin(pi/3)

so

Leaky Nun

are you typing?

orlp

thinking

wait I'm doing this horribly inefficiently though

Leaky Nun

use argand diagram boi

Lembik

oh the sum has a closed form

orlp

never heard of that

Lembik

10:15 AM

I mean a nice real closed form :)

orlp

I know that r = 2

Lembik

$\sum_{j=1}^k\binom{3k}{3j}=\frac13\left(2^{3k}+2(-1)^k\right)-1$

orlp

because 1^2 + sqrt(3)^2 = 4

Leaky Nun

@orlp it's where you plot a number using the horizontal axis as the real axis and the vertical axis as the imaginary axis, and then read of its polar form by pretending that you're using the polar coordinates

@Lembik right

Lembik

@LeakyNun did you already know that?

Leaky Nun

10:16 AM

@Lembik I don't, but I have an approach ready

if I did it then I would figure it out

Lembik

cool

the proof is

$$
\begin{align}
\sum_{j=0}^k\binom{3k}{3j}
&=\frac13\left(\sum_{j=0}^{3k}\binom{3k}{j}+\sum_{j=0}^{3k}\binom{3k}{j}e^{2\pi ij/3}+\sum_{j=0}^{3k}\binom{3k}{j}e^{-2\pi ij/3}\right)\\
&=\frac13\left(2^{3k}+\left(\frac12+i\frac{\sqrt3}2\right)^{3k}+\left(\frac12-i\frac{\sqrt3}2\right)^{3k}\right)\\[3pt]
&=\frac13\left(2^{3k}+2(-1)^k\right)
\end{align}
$$

Leaky Nun

nice

Lembik

not solved by me sadly

but nice :)

orlp

essentially the same as my giant monster though

although written a lot nicer :)

Lembik

I assume this generalises from 3k to ck

orlp

10:19 AM

@LeakyNun $2e^{\frac{5}{3}\pi i}$

Leaky Nun

@orlp so what is its cube?

@Lembik now?

orlp

$8e^{\pi i} = -8$

Leaky Nun

simplified?

good

orlp

@LeakyNun this is a pretty nice example of a problem that's hard to solve without complex numbers

even though neither the problem nor the final solution uses them

Leaky Nun

right

orlp

10:28 AM

@LeakyNun I've used this "problem -> transition matrix -> diagonalize -> closed form" setup before

7

A: finding an explicit formula for a two variable recursion

If $f_{k, n}(x)$ for each $1 \leq x \leq n$ forms a vector $\vec{f_{k, n}}$ of probalities, then: $$\vec{f_{k+1, n}} = \begin{bmatrix} 1 & 1\over 2 & 1\over 3 & \cdots & 1\over n \\ 0 & 1\over 2 & 1\over 3 & \cdots & 1\over n \\ 0 & 0 & 1\over 3 & \cdots & 1\over n \\ \vdots &\vdots &\vdots &...

I have no idea how I would solve it otherwise

Leaky Nun

I see

Lembik

PPCG people are rocking math.se I see :)

orlp

@Lembik not really, at least not me

Lembik

:)

orlp

I like math and I have a bright idea from time to time

but there are tons of people that are infinitely smarter than me on that website

at least in math

especially mathoverflow

I don't even understand the question there the vast majority of the time

Lembik

10:36 AM

MO is a complete mystery to me too

and I assume almost everyone else too :)

orlp

@LeakyNun you know that NAND is functionally complete, right?

and so is NOR

how many functionally complete 3-ary gates are there?

Leaky Nun

@orlp no i dea

orlp

and how many functionally complete n-ary gates

Neil

11:13 AM

I count 6 of the 16 2-ary gates as being functionally complete

although two of those are simply reversed inputs of the other two

New Meta Posts

11:57 AM

1

Q: Linking to the sandbox

Why do people keep posting a link to the sandbox below their question? Isn't the sandbox supposed to serve the OP as a way of getting feedback on a challenge? It seems like a lot of people are mistaking (or am I?) the purpose of the sandbox as a golden ticket to success. Is there an unspoken rule...