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This "sandbox" is a place where Code Golf users can get feedback on prospective challenges they wish to post to main. This is useful because writing a clear and fully specified challenge on your first try can be difficult, and there is a much better chance of your challenge being well received if you post it in the sandbox first.

Sandbox FAQ

Posting

To post to the sandbox, scroll to the bottom of this page and click "Answer This Question". Click "OK" when it asks if you really want to add another answer.

Write your challenge just as you would when actually posting it, though you can optionally add a title at the top. You may also add some notes about specific things you would like to clarify before posting it. Other users will help you improve your challenge by rating and discussing it.

When you think your challenge is ready for the public, go ahead and post it, and replace the post here with a link to the challenge and delete the sandbox post.

Discussion

The purpose of the sandbox is to give and receive feedback on posts. If you want to, feel free to give feedback to any posts you see here. Important things to comment about can include:

  • Parts of the challenge you found unclear
  • Comments addressing specific points mentioned in the proposal
  • Problems that could make the challenge uninteresting or unfit for the site

You don't need any qualifications to review sandbox posts. The target audience of most of these challenges is code golfers like you, so anything you find unclear will probably be unclear to others.

If you think one of your posts requires more feedback, but it's been ignored, you can ask for feedback in The Nineteenth Byte. It's not only allowed, but highly recommended! Be patient and try not to nag people though, you might have to ask multiple times.

It is recommended to leave your posts in the sandbox for at least several days, and until it receives upvotes and any feedback has been addressed.

Other

Search the sandbox / Browse your pending proposals

The sandbox works best if you sort posts by active.

To add an inline tag to a proposal, use shortcut link syntax with a prefix: [tag:king-of-the-hill]. To search for posts with a certain tag, include the name in quotes: "king-of-the-hill".

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Making Minimial Memory Masterpieces

In this challenge you will be asked to write a small computer program to paint an approximation of the painting Fine Wind, Clear Morning.

Your submission

In this challenge we are going to start with a blank canvas. We are going to add an "ant" in the top left corner. You will be telling the ant how to paint the picture by writing its brain.

An ant is a simple creature, at a given time it knows two things.

  • Some memories that it has

  • The color of the pixel it is currently standing on

And at every step the ant consults these two things it knows and then

  1. Draws one pixel of any color where it is standing

  2. Moves one pixel in a cardinal direction

  3. Replaces its all of its memory

The ant can thus be thought of as a function which takes a color and a value and spits out a color, a value and a cardinal direction.

For example here is the brain of an ant that draws a zigzag pattern in red

\$ f(c,m) = \left\{\begin{matrix}(\mathrm{Red}, & \mathrm{South}, & 1) & \mathrm{if} & m = 0\\ (\mathrm{Red}, & \mathrm{East}, & 0) & \mathrm{if} & m = 1\end{matrix}\right. \$

However our canvas is not infinite, so this ant would run into a border eventually. We will stop the ant if it tries to move off, by canceling its move and leaving it on the square it is on. You are free to use this behavior to your advantage.

The one issue here is that currently the ant will never stop, it will just keep painting forever. Which is why ants come with a builtin kill switch. When an ant's memories are equal to an exact value the ant explodes or something, ending the drawing.

Your submission will thus consist of 3 things

  • The starting memory for your ant

  • A description of the ant's function (more on this later)

  • The ending memory for your ant

Scoring

The goal of this challenge is to have the ant that requires the least memory to operate. We will count this by the number of different states your ant's memory can have.

Thus to score your answer you should run it on the canvas provided. Once the ant has finished your score will be the total number of distinct memories used by your ant through the process. We will include the initial memory even if it does not appear again, but you should not count the ending memory (the one that kills the ant).

The lowest score will be the winner.

The painting

The painting will be a low resolution version of the one from the wikipedium. It will use 3 bit color resolution.

I will decide on the exact specific sizes and make the image in a bit.

A valid answer must produce this image exactly when run on the canvas.

Verification Tool

I will make a tool for running and verifying programs, using a standardized format. It will be runnable in browser.

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  • 2
    \$\begingroup\$ Interesting challenge, looks solid. Will there always be at least one empty column between lines or lane dividers, as seems to be in all examples? \$\endgroup\$
    – xnor
    Mar 10, 2020 at 11:08
  • 1
    \$\begingroup\$ With your new clarification, can there be two adjacent lines? Also, can there be an input with just one line, or just empty space? Are trailing empty spaces a possibility? \$\endgroup\$
    – xnor
    Mar 10, 2020 at 11:59
  • \$\begingroup\$ I meant in the input, but I guess whether the output can add or omit them could also be a question. \$\endgroup\$
    – xnor
    Mar 10, 2020 at 12:12
  • 1
    \$\begingroup\$ Yes, I think you answered everything. So, if I got this right, I think this is a uniquely-matching regex of all valid inputs as sequences of columns, with e,l,d indicating empty, lane, and divider: e*(le(e|d)*e|le|l)*le*|e*. \$\endgroup\$
    – xnor
    Mar 10, 2020 at 12:26
  • \$\begingroup\$ @xnor Took a little work to analyze but I think it is. \$\endgroup\$
    – Wheat Wizard Mod
    Mar 10, 2020 at 12:39
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Golf yourself a real calculator [draft]

We will only cover the characters(0123456789+-*/=%ñ) in our tutorial.

The = operations

Unlike most desktop calculators, our household calculator is a tacit language. Therefore it is able to do a lot more than other infix calculators.

Take a simple calculation as an example. The non-scientific calculator does not have the exponentiation operator. What do you do to calculate 2^5?

2*2====

However, there's a shortcut for doing that. Since 2 is already in the expression buffer, you can simply do

2*====

The calculator automatically fills in the current expression during the inputting.

Here is a demonstration of how this works:

(A template for easy copy&paste.

Pressed Key      : 
Expression buffer: 
Output buffer    : 
)

Pressed Key      : 2
Expression buffer: 2
Output buffer    : 2

Pressed Key      : *
Expression buffer: 2 *
Output buffer    : 2

Pressed Key      : =
Expression buffer: * 2
Output buffer    : 4

Pressed Key      : =
Expression buffer: * 2
Output buffer    : 8

Pressed Key      : =
Expression buffer: * 2
Output buffer    : 16

Pressed Key      : =
Expression buffer: * 2
Output buffer    : 32

Implicit 0 before calculation

Suppose you enterede the following expression:

*1

Now, don't get me wrong, the household calculator of course doesn't have pointers. So, why doesn't it raise a syntax error though? (The output is 0 by the way.) Here's why.

The calculator initially has the expression starting at 0, therefore it prepends a 0 to the expression. Therefore the full form of our expression is:

0*1

What we've learned so far

  • The output buffer is a part of the calculator storing the latest-evaluated integer. All entered numbers get appended to the output buffer as well as the expression buffer.
  • The expression buffer is a part of the calculator storing the latest instruction. After a = operator, it stores the latest applied expression for later application.
  • The = operator tries to evaluate the instruction buffer. If that's a syntax error, it tries to evaluate that concatenated the output buffer. If that still fails, it tries to evaluate the output buffer concatenated with the instruction buffer. After that operation, the expression starting from the newest-entered dyadic operator is saved in the expression buffer.
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RRE numbers

Given a single floating-point number (which can potentially be taken as a string), output whether this decimal is an RRE number.

RRE complement for the input number

Say your input is 3.14.

  1. Replace the decimal point by the fraction bar. 3/14
  2. Reciprocal the fraction. 14/3
  3. Evaluate the fraction. 4.666...
  4. Round the decimal point to the same length as the input. 4.67
  5. If the absolute difference between the input and the output is below 2, it's an RRE number. Otherwise, it isn't an RRE number.

Specification

  1. Programs are allowed to give wrong output if the absolute difference is very close to 2.
  2. The integral part of the decimal is always nonzero.
  3. Truthy/Falsy outputs follows the language's convention, or exactly one value for truthy and another for falsy.

Test cases

Here is a sample program I use to generate the test cases.

1.0     -> True
2.9     -> True
3.14    -> True
50.2501 -> True
2.14    -> False
2.11111 -> False
3.1     -> False
51.123  -> False
51.51   -> False
24.12   -> False
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  • \$\begingroup\$ 1) Rounding 4.666... to two decimal places gives 4.67. 2) Floating-point numbers are always subject to precision issues. I think it's best to let the programs take a string representation as input, and state that "programs are allowed to give wrong output if the absolute difference is very close to 2". 3) If the integral part is 0, the algorithm will invoke division by 0. Is handling it part of the challenge? \$\endgroup\$
    – Bubbler
    Mar 27, 2020 at 6:07
  • \$\begingroup\$ 4) For truthy/falsy, it currently reads like I can output the input as-is and say "the program's output format is a RRE number for truthy, a non-RRE number for falsy". What I use is "truthy/falsy following the language's convention, or exactly one value for truthy and another for falsy". \$\endgroup\$
    – Bubbler
    Mar 27, 2020 at 6:13
  • \$\begingroup\$ I don't see how restricted source will fit here. Btw, a big truthy test case: 50.2501 \$\endgroup\$
    – Bubbler
    Mar 27, 2020 at 6:39
  • \$\begingroup\$ @Bubbler Ahh, the challenge is just about checking whether the square of the integral part is close to the the decimal part. Should I post it? \$\endgroup\$
    – user92069
    Mar 27, 2020 at 6:43
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Are these the same time?

Context

When asked about the time (i.e. hours and minutes), people naturally reply with any one of a given set of fairly common sentences:

  • (A) it is M past H
  • (B) it is M to H
  • (C) it is H minus M

Where M above refers to some amount of minutes and H to some amount of hours. Concrete corresponding examples, all referring to the time 3:40 pm:

  • (A) it is 40 past 3
  • (B) it is 20 to 4
  • (C) it is 4 minus 20

Task

Given two of these sentences, output a Truthy value if they represent the same time and a Falsy value if they do not.

Input

Your input will be two sentences of the above, where references to minutes will always be rounded to the nearest multiple of 5 (i.e. the minutes will always be one of 5, 10, 15, 20, ..., 50, 55.

Because all sentences start with "it is " you may ommit that from your input sentences.

Output

A Truthy value if the two times are the same, a Falsy value otherwise.

Test cases

Here is a sample program for checking the test cases.

Sandbox

Should the minutes and hours in the input com as integers instead of English words?

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  • \$\begingroup\$ Interesting challenge. Yes, the minutes and hours in the input should come as integers. Otherwise, this becomes a chameleon challenge that appears to be about parsing relation words, but actually is about parsing English numbers. I think you can make the challenge more interesting by adding (D) it is H M. Please address 1) how to distinguish AM/PM or that we don't need to, 2) how to deal with roll-overs like "5 to 0", and 3) if H and M have upper and lower bounds. \$\endgroup\$
    – Adám
    Apr 1, 2020 at 6:29
  • \$\begingroup\$ I kid you not, I have never heard any one call it "H minus M". Still, I agree with @Adám that y'all need to ensure that input and output formats are what I like to call "reasonable and convenient", with extra emphasis on the "convenient" part. \$\endgroup\$
    – lyxal
    Apr 1, 2020 at 6:52
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    \$\begingroup\$ @Lyxal Me neither. But actually, that can be fixed by changing "minus" to "in", as in "4 in 20 [minutes]" \$\endgroup\$
    – Adám
    Apr 1, 2020 at 6:55
  • \$\begingroup\$ An alternative you might consider to checking if two sentences represent equal times, is to have code take just one and produce any "canonical form" of it, such that the canonical form can be anything where two inputs give the same canonical form if and only if they are equal. \$\endgroup\$
    – xnor
    Apr 1, 2020 at 9:15
  • \$\begingroup\$ @petStorm thanks for your edit but I would prefer if you did not edit any reference programs into my sandboxed posts (you may comment with a TIO link) nor edited the challenge to cope with the feedback I get from commenters. The feedback is very good and I will take care of it, but I prefer to do it myself so I can do the changes I see necessary: e.g. if I am accepting hours and minutes as integers, I no longer want the minutes to be in the set 5, 10, 15, ..., 55. \$\endgroup\$
    – RGS
    Apr 1, 2020 at 11:48
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\$\Theta(N\cdot\sqrt N)\$ sort

The challenge is to write a program that sorts an array of distinct positive integers in ascending order. You may input the array and output the result using the default IO methods.

However, the worst-case time complexity of the algorithm used must be \$\Theta(N \cdot \sqrt N)\$, where \$N\$ is the length of the input array.

You may not assume your built-in sorting functions to have any time complexity in particular. While you can implement a fast (e.g. \$O(N \log N)\$) sort and then perform pointless operations to increase the complexity, direct algorithms exist.

This question is tagged , so the shortest code wins!

Sandbox stuff

I have noticed that a possible solution is, for example, to create a sorted multiset from the array and read it back. I would probably like to disallow that. Is there a way to achieve that without making the validity criteria subjective?

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  • \$\begingroup\$ I feel like this will be answered by implementing sorting efficiently, then doing something pointless for the required number of steps. \$\endgroup\$
    – xnor
    Apr 1, 2020 at 8:55
  • \$\begingroup\$ @xnor That would involve implementing a O(n log n) sort or radix sort, which can be more complicated than a O(n*sqrt(n)) algorithm. There's, for example, a gap sequence that results in O(n * sqrt(n)) complexity for Shellsort. \$\endgroup\$ Apr 1, 2020 at 9:04
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Similar Numbers

posted

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Modify The Stack

Posted

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  • \$\begingroup\$ Specifying that the first element is the top of the stack could help understanding the challenge a lot. Can we use some other values instead of the stack elements a, b, c and/or the commands s, d, t? Also, the operation a b c -> b c a is often called rotate or roll. \$\endgroup\$
    – Bubbler
    Mar 30, 2020 at 2:38
  • \$\begingroup\$ For test cases: a c b is tts. a b a b c can be done with dtdtt or dtdts. \$\endgroup\$
    – Bubbler
    Mar 30, 2020 at 2:41
  • \$\begingroup\$ thanks, but dtdtt and dtdts doesn't work. \$\endgroup\$ Mar 30, 2020 at 5:29
  • \$\begingroup\$ Sorry, I had the t operation mistaken, but your tdtsdt doesn't work either. The first operation should be s. \$\endgroup\$
    – Bubbler
    Mar 30, 2020 at 5:39
  • \$\begingroup\$ right, I fixed that \$\endgroup\$ Mar 30, 2020 at 5:46
  • \$\begingroup\$ I don't think the test cases are very helpful here until they are actually proven optimal... Do you really want to require input validation? If so, it is probably a very bad idea to post this without writing a reference implementation to make sure it's possible and not too annoying. (besides: I silently downvoted before because I simply dislike the idea, and not because of some specification issues, so I had nothing to comment) \$\endgroup\$ Apr 5, 2020 at 16:05
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    \$\begingroup\$ @mypronounismonicareinstate Sandbox is all about feedback. Silent downvotes don't help the challenge writer and the community. If you don't like the whole idea, you could say so in the comments in the first place (preferably with why you think that way), and then the challenge writer could consider to rewrite it or abandon it and try out something different. \$\endgroup\$
    – Bubbler
    Apr 5, 2020 at 23:25
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Compactify the input

Posted

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  • \$\begingroup\$ Off topic: BASIC programmers were often recommended to name their variables this way. \$\endgroup\$
    – user92069
    Apr 8, 2020 at 14:26
  • \$\begingroup\$ I agree that it's better to compress a single word instead. \$\endgroup\$
    – user92069
    Apr 8, 2020 at 14:26
  • \$\begingroup\$ hmm ok, I'll do that \$\endgroup\$ Apr 8, 2020 at 17:42
  • \$\begingroup\$ I think the mention of compression and natural language is misleading, since it leads the reader to expect some compression based on the statistical properties of text. \$\endgroup\$
    – xnor
    Apr 8, 2020 at 18:36
  • \$\begingroup\$ hmm ok, do you have an idea for a better name? \$\endgroup\$ Apr 9, 2020 at 4:53
  • \$\begingroup\$ Do you think Compactify the name is a good idea? \$\endgroup\$
    – user92069
    Apr 9, 2020 at 8:44
  • \$\begingroup\$ Related. \$\endgroup\$
    – user92069
    Apr 9, 2020 at 8:46
  • \$\begingroup\$ yes, I like that name, maybe Compactify the input though? As it doesn't have to be a name \$\endgroup\$ Apr 9, 2020 at 9:02
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    \$\begingroup\$ I like Compactify the input \$\endgroup\$
    – xnor
    Apr 10, 2020 at 12:12
  • \$\begingroup\$ Just an FYI, the regex \B[aeiou] matches each character to be removed. You may receive a lot of answers that are basically just that. \$\endgroup\$ Apr 12, 2020 at 5:10
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How Many Ways To Empty The Glove Box?

Posted

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Compress Numbers

Write two programs, a compressor and a decompressor.

The compressor

  • The compressor will accept a sequence of integers of any value from 0 to 263-1, expressed in any convenient format.
  • You may specify the required format as long as any arbitrary sequence of integers in the required range may be expressed in this format.
  • Behaviour is undefined for any input that does not conform to your required format.
  • The output will be a self contained sequence of bytes.

The decompressor

  • The input will be an unmodified sequence of bytes produced by a valid input to the compressor.
  • Behaviour is undefined for any other sequences of bytes.
  • The output will be the same input to the compressor program that produced the provided sequence of bytes.

Judging

The winning entry will be the valid entry that produces the smallest intermediate sequence of bytes for a sequence of integers that will be produced by the question setter that will be revealed after some number of entries have been submitted and only entries submitted prior to that reveal will be eligible to win.

This sequence will be generated by joining these following sequences into a single sequence and then randomly shuffling that single sequence.

  • 1000 repetitions of the same randomly selected number from 0 to 9.
  • 1000 repetitions of the same randomly selected number from 262 to 263-1.
  • For each x in (8, 16, 32, 63):
    • 1000 random numbers from 0 to 2x-1.

The question setter will answer the challenge with GZIP/GUNZIP at the highest compression setting with no additional processing. If that entry wins, the glory of winning will belong to the authors of GZIP.

Tie-Breaker

If two or more entries produce produce byte sequences of the same size, the following criteria will decide the winner:

  1. If one of those entries is the GZIP entry posted by the question setter, that entry will win.
  2. The entry with the highest voting score wins.
  3. The entry posted first wins.
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Reconstruct an image from columns

You are given an image with all pixel-wide columns shuffled. The challenge is to attempt to reconstruct the image.

[image gallery of varying difficulties]

Sandbox stuff

or (probably asking for fewest inversions)?

Random thought: if rearranging the pixels was similar to the assignment problem, this seems to be similar to the traveling salesman problem.

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A065825

(This is A065825.) The defaults apply, so you can pick another format other than this one.

Given an input integer n, find the smallest number k so that there exists an n-item subset of {1,...,k} where no three items form an arithmetic progression.

Procedure

Here, we calculate A065825(9).

We assume you have already looped from 1 to 19, and k=20 (it's just an example).

1. Generate a range from 1 to k.

[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20]

2. Pick n items from that sequence, following the original order of the sequence.

[1 2 6 7 9 14 15 18 20]

3. No 3 items form an arithmetic progression.

If a sequence has arithmetic progression, it basically means the sequence has the same step between every two consecutive items.

For example, the sequence of positive even numbers ([2 4 6 8 ...]) has a consistent step (i.e. 4-2=2, and 6-4=2, etc.), so it has arithmetic progression.

The Fibonacci sequence ([1 1 2 3 5 8 13 21 ...]) does not have arithmetic progression, since it does not have a consistent step. (3-2=1, 5-3=2, 8-5=3, etc.)

As an example, let's pick 3 items from our generated sequence.

[1 2 6 [7 9 14] 15 18 20]

The picked 3-item sequence does not have arithmetic progression, since the differences are respectively 9-7=2 and 14-9=5.

This has to apply to every 3-item pair:

[[1 2 6] 7 9 14 15 18 20] (2 -1 =1, 6 -2 =4)
[1 [2 6 7] 9 14 15 18 20] (6 -2 =4, 7 -6 =1)
[1 2 [6 7 9] 14 15 18 20] (7 -6 =1, 9 -7 =2)
[1 2 6 [7 9 14] 15 18 20] (9 -7 =2, 14-9 =5)
[1 2 6 7 [9 14 15] 18 20] (14-9 =5, 15-14=1)
[1 2 6 7 9 [14 15 18] 20] (15-14=1, 18-15=3)
[1 2 6 7 9 14 [15 18 20]] (18-15=3, 20-18=2)

Here are some examples of picking non-consecutive items from the output sequence:

[1 [2] 6 [7] 9 [14] 15 18 20] (7-2=5,14-7=7)
[[1] 2 6 [7] [9] 14 15 18 20] (7-1=6,9 -7=2)

If the above is satisfied for k, then k is a valid output for A065825(9).

Meta

Do you think this challenge should be splitted into separate challenges? It seems that it is a single sequence on OEIS.

Test cases

Here is a reference program I use to check my test cases.

n       a(n)
1       1
2       2
3       4
4       5
5       9
6       11
7       13
8       14
9       20
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Are these two DFAs equivalent?

Two Deterministic Finite Automata or DFAs can be checked to see if they accept same set of strings in polynomial time. See section 3.3 of this for a long list of methods and this SO question/answer for a much shorter list.

Input

Your input will be two DFAs. In order to be able to test your code, it needs to be able to handle DFAs in the following format. This is taken directly from GAP (and slightly simplified).

Automaton( Type, Size, Alphabet, TransitionTable, Initial, Accepting )

For the input, Type will always be "det". Size is a positive integer representing the number of states of the automaton. Alphabet is the number of letters of the alphabet. TransitionTable is the transition matrix. The entries are non-negative integers not greater than the size of the automaton are also allowed. Initial and Accepting are, respectively, the lists of initial and accepting states.

For example:

Automaton("det",4,2,[ [ 1, 3, 4, 0 ], [ 1, 2, 3, 4 ] ],[ 3 ],[ 2, 3, 4 ])

This has transition table:

   |  1  2  3  4  
-----------------
 a |  1  3  4     
 b |  1  2  3  4  
Initial state:    [ 3 ]
Accepting states: [ 2, 3, 4 ]

And diagram:

enter image description here

It is equivalent to:

Automaton("det",3,2,[ [ 1, 3, 1 ], [ 1, 2, 3 ] ],[ 2 ],[ 2, 3 ])

which has diagram:

enter image description here

A more complicated example:

Automaton("det",6,4,[ [ 0, 2, 3, 5, 0, 0 ], [ 1, 3, 5, 0, 0, 0 ], [ 1, 3, 5, 6, 0, 0 ], [ 2, 3, 5, 0, 0, 0 ] ],[ 1 ],[ 1, 4, 5, 6 ])

has diagram:

enter image description here

It is equivalent to:

Automaton("det",5,4,[ [ 2, 2, 2, 4, 5 ], [ 2, 2, 3, 1, 4 ], [ 2, 2, 3, 1, 4 ], [ 2, 2, 5, 1, 4 ] ],[ 3 ],[ 1, 3 ])

with diagram:

enter image description here

More example of equivalent DFAs

1.

Automaton("det",18,4,[ [ 2, 2, 6, 10, 2, 6, 7, 16, 14, 10, 18, 14, 7, 14, 15, 16, 7, 18 ], [ 3, 3, 7, 11, 3, 7, 15, 11, 7, 17, 15, 18\
, 18, 7, 15, 17, 15, 15 ], [ 4, 4, 8, 7, 4, 13, 15, 15, 16, 7, 8, 7, 15, 7, 15, 15, 16, 13 ], [ 5, 5, 9, 12, 5, 14, 7, 13, 9, 14, 17, 12, \
13, 14, 15, 7, 17, 7 ] ],[ 1 ],[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18 ])
Automaton("det",16,"abcd",[ [ 1, 2, 15, 15, 5, 6, 7, 7, 6, 2, 16, 12, 12, 16, 15, 16 ], [ 1, 3, 1, 7, 9, 15, 1, 1, 15, 8, 7, 3, 8, 15, 1, \
15 ], [ 1, 1, 2, 1, 13, 4, 4, 10, 10, 1, 15, 15, 15, 2, 1, 15 ], [ 1, 15, 3, 4, 5, 16, 15, 3, 14, 4, 11, 16, 11, 14, 15, 16 ] ],[ 5 ],[ 2,\
 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ])
    2.
Automaton("det",50,4,[ [ 2, 2, 9, 13, 17, 9, 13, 17, 9, 24, 28, 30, 13, 33, 36, 30, 17, 9, 13, 9, 13, 39, 30, 24, 25, 44, 42, 28, 24, 30, 47, 39, 33, 50, 36, 36, 42, 46, 39, 25, 24, 42, 43, 44, 36, 46, 47, 42, 25, 50 ], [ 3, 6, 10, 14, 18, 10, 14, 20, 10, 25, 14, 10, 32, 34, 34, 38, 20, 10, 14, 10, 14, 38, 10, 25, 43, 34, 25, 45, 46, 10, 32, 49, 34, 43, 34, 49, 50, 50, 49, 50, 46, 25, 43, 49, 49, 50, 45, 50, 43, 43 ], [ 4, 7, 11, 15, 19, 11, 15, 21, 22, 26, 26, 31, 15, 11, 25, 15, 21, 11, 15, 11, 15, 40, 15, 40, 43, 43, 44, 26, 26, 15, 44, 31, 41, 26, 47, 25, 25, 22, 40, 43, 40, 25, 43, 43, 47, 41, 44, 44, 44, 40 ], [ 5, 8, 12, 16, 5, 12, 16, 8, 23, 27, 29, 12, 23, 35, 37, 16, 8, 12, 16, 12, 16, 41, 23, 42, 25, 40, 27, 27, 29, 23, 48, 45, 37, 49, 35, 42, 37, 48, 42, 40, 41, 42, 43, 25, 45, 37, 27, 48, 49, 25 ] ],[ 1 ],[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50 ])
Automaton("det",39,4,[ [ 1, 2, 3, 3, 5, 24, 7, 8, 22, 20, 8, 32, 18, 18, 3, 19, 25, 18, 19, 20, 25, 22, 23, 24, 25, 25, 24, 23, 5, 2, 35, 32, 19, 19, 35, 36, 36, 36, 36 ], [ 1, 38, 1, 23, 15, 9, 11, 26, 23, 28, 26, 10, 9, 26, 1, 3, 22, 26, 3, 28, 22, 23, 1, 15, 3, 3, 15, 1, 28, 27, 10, 27, 23, 23, 38, 15, 28, 15, 28 ], [ 1, 5, 1, 1, 1, 4, 12, 6, 6, 31, 31, 37, 37, 30, 5, 5, 29, 37, 3, 21, 4, 21, 4, 4, 4, 29, 30, 29, 1, 5, 29, 37, 5, 3, 29, 3, 3, 2, 2 ], [ 1, 16, 3, 4, 3, 21, 7, 18, 33, 39, 14, 13, 13, 14, 15, 16, 17, 18, 19, 34, 21, 34, 3, 19, 19, 16, 38, 15, 4, 33, 17, 18, 33, 34, 16, 19, 34, 38, 39 ] ],[ 7 ],[ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39 ])

3.

Automaton("det",288,4,[[2, 6, 10, 14, 18, 6, 10, 14, 18, 25, 29, 33, 36, 40, 43, 46, 36, 53, 10, 14, 18, 10, 14, 18, 25, 29, 60, 36, 29, 67, 71, 75, 77, 81, 83, 87, 88, 90, 94, 40, 98, 46, 104, 108, 111, 46, 116, 120, 75, 123, 127, 129, 53, 10, 14, 131, 129, 71, 75, 136, 140, 143, 146, 87, 149, 75, 67, 68, 155, 153, 156, 159, 161, 163, 75, 165, 77, 170, 81, 172, 81, 67, 88, 123, 156, 146, 87, 88, 156, 90, 183, 186, 188, 87, 90, 183, 94, 192, 143, 197, 199, 116, 75, 104, 108, 204, 172, 108, 208, 120, 127, 159, 90, 199, 163, 159, 215, 156, 149, 120, 153, 217, 123, 218, 131, 221, 127, 159, 87, 123, 225, 88, 155, 67, 165, 136, 227, 143, 221, 123, 218, 221, 143, 68, 67, 88, 123, 127, 143, 217, 68, 67, 153, 154, 155, 156, 234, 235, 159, 120, 161, 237, 143, 217, 165, 143, 241, 199, 188, 242, 197, 75, 67, 165, 241, 217, 248, 250, 172, 146, 221, 161, 225, 234, 111, 186, 153, 75, 217, 75, 188, 192, 257, 188, 68, 120, 90, 186, 127, 90, 208, 146, 221, 259, 140, 120, 235, 208, 165, 262, 199, 188, 68, 120, 215, 267, 217, 218, 250, 83, 75, 165, 75, 215, 225, 208, 234, 71, 149, 153, 75, 235, 208, 234, 67, 265, 272, 233, 241, 143, 120, 242, 257, 155, 153, 143, 153, 248, 267, 250, 116, 120, 75, 237, 71, 235, 250, 163, 259, 227, 153, 262, 67, 75, 155, 233, 272, 265, 116, 241, 281, 272, 68, 149, 120, 155, 283, 163, 67, 208, 285, 265, 287, 233, 285, 68, 287, 68], [3, 7, 11, 15, 19, 7, 11, 15, 22, 26, 30, 15, 37, 41, 44, 47, 50, 54, 11, 15, 19, 11, 15, 22, 26, 30, 61, 37, 30, 68, 72, 30, 78, 47, 84, 26, 30, 91, 37, 96, 99, 102, 105, 109, 112, 115, 117, 109, 122, 124, 128, 130, 54, 11, 15, 130, 132, 72, 30, 137, 141, 122, 147, 132, 150, 30, 68, 154, 109, 68, 157, 109, 162, 164, 30, 166, 168, 99, 102, 173, 175, 176, 177, 124, 128, 147, 132, 30, 72, 168, 184, 115, 189, 132, 96, 99, 37, 166, 195, 96, 99, 201, 150, 105, 109, 205, 164, 109, 154, 109, 157, 109, 211, 112, 213, 109, 154, 72, 109, 195, 208, 215, 124, 208, 130, 150, 166, 224, 26, 124, 157, 30, 226, 217, 166, 115, 213, 150, 30, 124, 208, 150, 195, 208, 176, 177, 124, 72, 224, 208, 233, 217, 68, 154, 195, 214, 195, 208, 109, 109, 236, 117, 195, 208, 214, 195, 201, 99, 173, 166, 168, 177, 68, 246, 213, 215, 68, 251, 173, 147, 150, 254, 166, 195, 99, 175, 208, 30, 215, 122, 164, 166, 251, 173, 154, 195, 78, 258, 166, 168, 154, 147, 150, 260, 141, 226, 217, 154, 214, 254, 184, 263, 154, 195, 154, 109, 208, 208, 269, 84, 177, 246, 150, 154, 166, 215, 195, 166, 150, 208, 150, 208, 215, 195, 215, 213, 195, 208, 213, 150, 195, 166, 254, 109, 68, 224, 233, 68, 109, 236, 201, 226, 150, 213, 166, 208, 277, 117, 278, 213, 233, 236, 215, 279, 195, 208, 224, 201, 117, 280, 254, 195, 208, 109, 109, 226, 213, 213, 215, 215, 277, 280, 195, 208, 236, 233, 195, 208], [4, 8, 12, 16, 20, 8, 12, 16, 23, 27, 31, 34, 38, 42, 12, 48, 51, 55, 12, 16, 20, 12, 16, 23, 56, 58, 62, 51, 65, 69, 73, 76, 79, 69, 85, 42, 89, 92, 95, 42, 100, 48, 106, 31, 113, 48, 118, 68, 48, 125, 48, 51, 55, 12, 16, 62, 51, 133, 135, 138, 56, 144, 62, 148, 151, 48, 144, 154, 154, 155, 69, 118, 154, 69, 48, 161, 79, 171, 69, 174, 69, 69, 178, 180, 69, 85, 148, 138, 182, 92, 95, 155, 135, 42, 92, 95, 148, 193, 76, 198, 200, 118, 48, 202, 58, 62, 206, 207, 69, 209, 210, 89, 92, 200, 135, 178, 216, 69, 174, 68, 68, 138, 202, 65, 219, 222, 48, 118, 148, 56, 138, 118, 154, 69, 155, 138, 228, 144, 206, 106, 229, 174, 144, 154, 144, 138, 202, 48, 144, 138, 154, 144, 68, 154, 154, 69, 228, 133, 152, 165, 154, 69, 182, 240, 155, 135, 155, 200, 135, 243, 198, 210, 244, 155, 165, 152, 249, 144, 206, 219, 252, 154, 178, 255, 113, 155, 155, 210, 240, 135, 135, 65, 151, 48, 155, 209, 92, 155, 210, 92, 244, 62, 206, 138, 202, 68, 151, 144, 161, 68, 200, 135, 265, 165, 266, 73, 152, 207, 144, 62, 48, 161, 76, 249, 138, 69, 271, 133, 73, 265, 135, 151, 144, 266, 144, 155, 182, 133, 155, 182, 161, 274, 151, 161, 265, 135, 155, 266, 151, 144, 138, 161, 275, 69, 73, 276, 144, 135, 138, 249, 68, 68, 244, 135, 161, 151, 144, 155, 138, 155, 151, 144, 155, 151, 161, 161, 249, 69, 69, 244, 144, 155, 271, 276, 144, 155, 266, 265], [5, 9, 13, 17, 21, 9, 13, 17, 24, 28, 32, 35, 39, 28, 45, 49, 52, 9, 13, 17, 21, 13, 17, 24, 57, 59, 63, 64, 66, 70, 74, 32, 80, 82, 86, 28, 32, 93, 39, 97, 101, 103, 107, 110, 114, 66, 119, 121, 49, 126, 49, 52, 9, 13, 17, 63, 64, 134, 59, 139, 142, 145, 63, 64, 152, 66, 153, 68, 144, 70, 158, 160, 151, 134, 66, 167, 169, 101, 134, 59, 70, 82, 179, 181, 82, 86, 64, 66, 74, 169, 185, 187, 190, 97, 191, 101, 64, 194, 196, 191, 101, 160, 103, 203, 160, 63, 103, 121, 195, 110, 179, 110, 212, 114, 214, 167, 213, 134, 160, 153, 121, 158, 203, 187, 220, 223, 66, 119, 57, 142, 139, 59, 151, 134, 187, 66, 214, 152, 66, 107, 230, 231, 153, 144, 145, 139, 203, 103, 232, 187, 151, 152, 153, 154, 68, 70, 214, 187, 121, 160, 68, 238, 239, 230, 70, 214, 187, 101, 59, 194, 169, 179, 245, 247, 214, 232, 70, 152, 66, 220, 253, 144, 194, 196, 101, 70, 187, 194, 256, 190, 231, 66, 152, 66, 195, 196, 80, 247, 194, 169, 213, 63, 103, 139, 203, 261, 152, 68, 239, 121, 185, 264, 213, 214, 68, 268, 121, 121, 145, 63, 139, 270, 223, 195, 66, 238, 239, 187, 74, 230, 231, 121, 266, 153, 232, 195, 236, 273, 70, 74, 239, 66, 121, 268, 245, 119, 247, 153, 144, 153, 187, 270, 253, 195, 167, 230, 232, 119, 66, 70, 261, 153, 256, 264, 236, 144, 266, 273, 158, 247, 144, 68, 273, 121, 167, 282, 195, 70, 158, 284, 266, 286, 236, 288, 68, 286, 68, 288]],[1],[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288])
Automaton("det",266,4,[[1, 127, 50, 50, 115, 249, 50, 8, 257, 10, 151, 12, 13, 14, 81, 78, 34, 106, 137, 107, 21, 22, 82, 89, 71, 43, 43, 62, 63, 63, 44, 10, 179, 171, 214, 265, 206, 38, 137, 152, 21, 151, 71, 22, 41, 41, 47, 13, 49, 50, 50, 210, 50, 210, 116, 90, 64, 49, 207, 207, 207, 62, 232, 64, 64, 89, 151, 236, 236, 70, 71, 236, 116, 260, 128, 75, 13, 38, 77, 133, 14, 82, 13, 13, 77, 235, 64, 64, 231, 206, 138, 91, 91, 206, 90, 264, 137, 169, 10, 10, 41, 71, 232, 228, 232, 21, 21, 107, 106, 110, 111, 266, 256, 114, 114, 116, 251, 251, 116, 114, 114, 111, 266, 260, 122, 182, 127, 128, 129, 213, 132, 132, 129, 49, 49, 138, 138, 138, 249, 71, 43, 43, 210, 235, 183, 214, 132, 265, 206, 138, 232, 64, 64, 153, 153, 64, 152, 152, 82, 236, 236, 82, 116, 116, 64, 207, 266, 64, 231, 169, 171, 250, 227, 70, 175, 175, 176, 10, 47, 178, 178, 110, 111, 266, 260, 122, 266, 127, 213, 49, 49, 152, 257, 153, 257, 90, 90, 183, 250, 264, 62, 228, 229, 82, 82, 206, 64, 266, 249, 249, 249, 242, 213, 214, 64, 116, 114, 114, 50, 50, 236, 236, 261, 115, 152, 251, 8, 228, 229, 229, 231, 232, 237, 235, 235, 236, 237, 235, 235, 235, 235, 235, 235, 242, 242, 242, 115, 251, 249, 250, 116, 116, 116, 207, 64, 265, 266, 257, 256, 266, 264, 261, 260, 264, 265, 266], [1, 125, 1, 114, 114, 121, 115, 3, 23, 19, 13, 15, 230, 28, 201, 202, 16, 84, 123, 103, 105, 208, 114, 84, 172, 199, 199, 119, 83, 83, 123, 170, 16, 31, 27, 26, 25, 104, 102, 23, 28, 13, 120, 208, 48, 103, 19, 230, 239, 1, 114, 218, 115, 219, 82, 140, 23, 208, 204, 216, 216, 119, 174, 119, 119, 84, 13, 115, 115, 50, 120, 50, 82, 204, 262, 79, 230, 104, 203, 85, 28, 114, 230, 230, 203, 3, 23, 119, 96, 96, 96, 123, 102, 140, 208, 3, 200, 200, 98, 97, 103, 120, 119, 120, 119, 28, 105, 103, 105, 54, 3, 23, 141, 1, 250, 50, 82, 114, 50, 1, 250, 3, 3, 219, 219, 125, 54, 263, 124, 124, 27, 124, 223, 208, 239, 25, 208, 208, 120, 120, 217, 217, 217, 120, 120, 142, 142, 141, 140, 140, 174, 174, 174, 204, 216, 23, 119, 23, 250, 114, 114, 250, 162, 162, 159, 205, 159, 159, 208, 123, 170, 1, 219, 50, 208, 208, 123, 177, 177, 19, 170, 173, 172, 172, 199, 199, 23, 186, 185, 184, 184, 23, 120, 216, 23, 140, 208, 120, 1, 3, 119, 120, 114, 114, 250, 239, 119, 3, 121, 3, 120, 219, 212, 212, 23, 50, 1, 250, 1, 114, 50, 114, 219, 114, 23, 114, 3, 120, 114, 114, 208, 119, 125, 121, 3, 50, 54, 120, 3, 120, 121, 3, 120, 218, 219, 217, 114, 114, 3, 1, 250, 250, 250, 253, 252, 173, 172, 120, 125, 3, 3, 219, 219, 3, 54, 3], [1, 1, 249, 249, 6, 1, 1, 247, 7, 130, 167, 17, 11, 66, 33, 33, 131, 136, 10, 32, 150, 9, 112, 36, 149, 112, 149, 56, 167, 37, 181, 130, 35, 147, 139, 51, 139, 11, 10, 234, 147, 37, 148, 113, 136, 136, 146, 24, 249, 1, 1, 249, 249, 249, 139, 6, 238, 127, 134, 238, 134, 9, 148, 238, 134, 167, 36, 50, 249, 247, 73, 249, 51, 139, 112, 167, 76, 76, 11, 167, 80, 73, 67, 66, 66, 135, 58, 58, 112, 139, 233, 100, 100, 2, 6, 95, 10, 32, 130, 130, 99, 94, 94, 56, 149, 150, 147, 150, 136, 51, 51, 51, 7, 51, 51, 51, 7, 6, 139, 139, 139, 2, 58, 134, 139, 7, 1, 112, 112, 249, 238, 238, 112, 249, 127, 238, 233, 238, 1, 149, 112, 149, 249, 135, 7, 139, 238, 51, 139, 238, 112, 238, 233, 234, 234, 134, 234, 190, 112, 50, 249, 73, 139, 51, 238, 134, 51, 134, 148, 32, 147, 145, 145, 145, 258, 259, 180, 130, 146, 189, 189, 51, 51, 134, 134, 139, 2, 1, 249, 127, 249, 191, 191, 191, 188, 188, 188, 188, 198, 197, 196, 196, 195, 187, 187, 139, 233, 134, 127, 127, 127, 49, 249, 139, 243, 211, 211, 211, 210, 210, 210, 210, 95, 209, 241, 209, 126, 117, 117, 9, 112, 112, 50, 50, 50, 50, 50, 50, 49, 49, 127, 127, 127, 249, 249, 249, 7, 7, 1, 247, 51, 139, 211, 134, 134, 51, 51, 7, 7, 2, 126, 145, 139, 247, 51, 51], [1, 51, 3, 4, 4, 7, 7, 50, 73, 61, 11, 12, 40, 109, 101, 93, 45, 18, 19, 20, 21, 64, 161, 29, 193, 118, 193, 65, 11, 42, 19, 59, 30, 46, 163, 164, 163, 40, 39, 57, 46, 42, 246, 60, 18, 21, 61, 158, 72, 50, 51, 53, 53, 3, 55, 55, 57, 246, 156, 64, 65, 64, 155, 64, 65, 11, 29, 68, 69, 236, 160, 72, 73, 55, 157, 11, 154, 154, 40, 11, 46, 160, 225, 192, 192, 86, 87, 88, 157, 118, 155, 19, 39, 74, 161, 239, 92, 92, 166, 254, 20, 144, 88, 240, 65, 109, 108, 21, 21, 50, 50, 73, 73, 50, 247, 236, 73, 161, 72, 3, 5, 54, 86, 239, 3, 51, 50, 64, 64, 161, 165, 64, 157, 161, 245, 165, 60, 64, 51, 240, 161, 240, 4, 144, 51, 55, 57, 73, 55, 57, 157, 157, 155, 57, 64, 156, 64, 87, 118, 160, 161, 248, 163, 164, 165, 168, 164, 168, 60, 19, 108, 3, 3, 72, 64, 60, 19, 194, 194, 61, 59, 247, 247, 193, 193, 5, 74, 7, 69, 244, 69, 156, 240, 65, 74, 74, 246, 143, 219, 86, 88, 144, 222, 222, 226, 72, 60, 239, 52, 54, 143, 239, 72, 72, 215, 221, 219, 224, 219, 220, 221, 222, 239, 220, 215, 222, 54, 160, 160, 161, 64, 64, 160, 68, 236, 236, 236, 160, 239, 240, 244, 245, 246, 69, 72, 161, 51, 160, 50, 50, 248, 118, 226, 255, 255, 248, 248, 160, 160, 245, 245, 72, 72, 236, 236, 236]],[12],[2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266])

4.

Automaton("det",9,4,[[1, 1, 2, 3, 1, 1, 2, 5, 2], [1, 1, 2, 8, 2, 2, 1, 6, 2], [1, 1, 2, 7, 2, 1, 2, 2, 2], [1, 1, 2, 9, 1, 1, 1, 1, 1]],[4],[2, 6])
Automaton("det",100,4,[[0, 1, 3, 7, 8, 9, 10, 11, 14, 15, 17, 18, 19, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 34, 36, 37, 40, 41, 42, 43, 44, 45, 46, 47, 48, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69, 71, 72, 73, 78, 79, 81, 84, 85, 86, 90, 93, 94, 95, 98, 99, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 4, 6, 7, 9, 10, 11, 12, 13, 15, 16, 19, 20, 21, 22, 23, 24, 25, 27, 28, 30, 31, 32, 35, 36, 37, 38, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 59, 60, 61, 64, 66, 67, 69, 70, 71, 75, 76, 78, 80, 81, 84, 85, 86, 87, 89, 92, 93, 95, 96, 97, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 15, 17, 19, 20, 22, 23, 26, 28, 29, 30, 32, 34, 35, 38, 40, 41, 45, 47, 49, 50, 53, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 76, 77, 79, 81, 82, 83, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 98, 99, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [ 0, 1, 3, 4, 5, 7, 8, 9, 10, 11, 12, 14, 15, 19, 21, 22, 23, 24, 26, 27, 28, 32, 33, 34, 35, 39, 40, 42, 43, 46, 47, 51, 54, 55, 59, 60, 61, 63, 64, 67, 71, 72, 73, 74, 75, 76, 77, 78, 79, 82, 84, 85, 89, 90, 91, 92, 93, 94, 96, 97, 98, 99, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]],[39],[1, 2, 5, 8, 10, 12, 13, 14, 15, 16, 17, 18, 19, 21, 24, 25, 28, 30, 31, 33, 35, 37, 41, 42, 43, 44, 49, 50, 52, 53, 57, 61, 63, 65, 66, 67, 69, 72, 73, 74, 75, 76, 77, 79, 80, 81, 82, 83, 85, 86, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 100])

5.

A pair of equivalent DFAs

Non-equivalent DFAs


Automaton("det",100,4,[[0, 1, 2, 3, 5, 7, 9, 12, 13, 15, 20, 21, 23, 24, 25, 27, 29, 30, 31, 33, 34, 35, 36, 37, 40, 41, 42, 45, 46, 47, 48, 56, 57, 60, 62, 64, 65, 69, 70, 73, 74, 76, 80, 81, 82, 84, 86, 87, 88, 89, 90, 92, 93, 94, 95, 97, 98, 99, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 2, 3, 9, 11, 12, 13, 16, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 36, 37, 38, 39, 40, 42, 47, 49, 52, 53, 54, 59, 60, 61, 62, 63, 64, 65, 68, 69, 71, 72, 75, 76, 78, 81, 82, 84, 86, 87, 88, 89, 90, 91, 92, 95, 96, 97, 98, 99, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 3, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 21, 24, 25, 26, 27, 28, 29, 30, 33, 35, 36, 37, 38, 39, 41, 43, 46, 50, 51, 53, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 70, 73, 74, 76, 77, 78, 80, 83, 86, 87, 89, 91, 92, 93, 95, 98, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 2, 3, 4, 6, 8, 13, 14, 15, 17, 19, 21, 22, 23, 25, 27, 28, 29, 30, 31, 32, 35, 36, 37, 40, 42, 46, 47, 48, 50, 51, 53, 54, 56, 58, 60, 61, 63, 64, 65, 66, 68, 70, 71, 72, 74, 75, 76, 79, 81, 82, 83, 84, 85, 86, 87, 89, 90, 91, 93, 94, 95, 96, 97, 99, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]],[52],[1, 5, 6, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 23, 24, 25, 26, 27, 28, 29, 30, 32, 34, 35, 36, 37, 39, 40, 41, 42, 44, 46, 47, 49, 51, 52, 53, 54, 55, 60, 61, 62, 66, 67, 70, 72, 73, 74, 75, 76, 77, 79, 80, 81, 82, 83, 84, 86, 87, 89, 90, 92, 94, 96, 97, 98, 99, 100])
Automaton("det",100,4,[[0, 2, 3, 4, 6, 7, 10, 11, 14, 15, 16, 17, 19, 20, 21, 22, 24, 25, 26, 27, 28, 31, 34, 35, 36, 37, 38, 40, 42, 43, 44, 46, 48, 49, 51, 55, 56, 57, 58, 59, 61, 62, 63, 64, 69, 71, 72, 73, 76, 78, 79, 80, 83, 86, 87, 88, 89, 90, 91, 95, 96, 99, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 17, 18, 19, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 34, 35, 36, 37, 40, 41, 42, 43, 45, 47, 48, 50, 51, 53, 56, 57, 59, 60, 62, 63, 64, 71, 72, 73, 75, 76, 77, 79, 80, 83, 85, 86, 87, 89, 90, 91, 92, 93, 96, 98, 99, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [ 0, 2, 3, 5, 6, 7, 8, 9, 10, 12, 13, 16, 18, 21, 23, 24, 26, 27, 28, 29, 30, 32, 34, 35, 36, 37, 39, 40, 41, 42, 45, 47, 48, 50, 51, 52, 53, 56, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 75, 76, 78, 79, 80, 82, 84, 85, 86, 89, 90, 93, 94, 97, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 6, 7, 8, 9, 10, 11, 12, 13, 16, 18, 21, 22, 23, 24, 28, 30, 31, 32, 34, 36, 37, 38, 39, 40, 42, 44, 45, 47, 48, 51, 52, 53, 56, 57, 59, 60, 61, 62, 63, 64, 65, 67, 70, 74, 76, 83, 84, 86, 88, 90, 91, 93, 94, 95, 96, 97, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]],[17],[1, 6, 7, 8, 9, 10, 11, 12, 13, 16, 18, 19, 22, 23, 27, 28, 29, 30, 32, 35, 36, 38, 40, 41, 42, 44, 46, 47, 48, 50, 51, 53, 54, 55, 62, 64, 66, 71, 72, 74, 75, 76, 79, 83, 86, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100])
Automaton("det",100,4,[[2, 3, 6, 7, 8, 9, 10, 12, 14, 15, 16, 20, 21, 25, 26, 28, 29, 30, 32, 35, 36, 37, 40, 42, 43, 44, 46, 47, 48, 50, 53, 54, 55, 57, 58, 59, 62, 63, 64, 65, 67, 68, 69, 72, 73, 75, 77, 79, 81, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 4, 5, 8, 13, 14, 15, 17, 18, 19, 20, 22, 23, 29, 30, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 58, 59, 60, 63, 64, 65, 66, 67, 68, 70, 71, 72, 74, 75, 77, 78, 79, 82, 83, 84, 85, 86, 87, 93, 95, 96, 97, 98, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 6, 7, 9, 10, 12, 13, 14, 15, 16, 17, 19, 20, 21, 23, 25, 27, 28, 30, 31, 32, 37, 38, 40, 41, 42, 45, 47, 49, 50, 51, 52, 56, 59, 61, 63, 64, 65, 68, 70, 72, 73, 74, 76, 77, 78, 80, 81, 85, 86, 87, 88, 92, 93, 94, 96, 98, 99, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 20, 21, 22, 23, 24, 26, 27, 28, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 48, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 62, 64, 65, 66, 68, 69, 70, 71, 72, 74, 75, 76, 77, 79, 84, 86, 91, 92, 93, 96, 97, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]],[46],[1, 2, 7, 8, 10, 12, 13, 15, 17, 18, 20, 22, 23, 24, 25, 27, 28, 29, 30, 32, 33, 35, 36, 37, 39, 41, 42, 44, 45, 47, 49, 50, 51, 52, 54, 55, 57, 59, 61, 63, 65, 66, 67, 68, 69, 70, 71, 73, 75, 76, 77, 79, 80, 81, 82, 85, 86, 88, 91, 92, 93, 94, 95, 96, 97, 98])
Automaton("det",100,4,[[0, 1, 4, 5, 7, 8, 9, 10, 11, 12, 15, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 33, 35, 36, 37, 39, 43, 44, 45, 46, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 62, 63, 67, 68, 70, 72, 73, 74, 76, 77, 78, 81, 82, 83, 85, 87, 93, 94, 95, 96, 97, 98, 99, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 3, 4, 5, 8, 10, 12, 15, 16, 17, 18, 19, 20, 21, 27, 29, 30, 31, 32, 34, 35, 36, 39, 40, 42, 45, 46, 47, 49, 50, 51, 52, 55, 58, 59, 60, 61, 62, 63, 64, 66, 67, 70, 71, 72, 73, 74, 75, 77, 79, 80, 81, 82, 83, 84, 86, 87, 88, 89, 92, 94, 96, 98, 99, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 3, 6, 7, 8, 9, 10, 11, 13, 15, 17, 19, 20, 21, 23, 30, 31, 33, 34, 35, 37, 38, 39, 42, 43, 44, 46, 47, 48, 50, 52, 53, 54, 55, 56, 58, 59, 60, 61, 63, 64, 65, 66, 67, 70, 71, 75, 76, 77, 80, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 94, 98, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 3, 4, 7, 8, 9, 10, 11, 12, 14, 16, 17, 18, 19, 20, 21, 22, 24, 26, 27, 28, 29, 31, 33, 34, 35, 37, 38, 40, 41, 43, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 62, 64, 65, 66, 67, 68, 69, 71, 72, 75, 76, 77, 80, 81, 82, 83, 86, 87, 88, 91, 93, 94, 95, 96, 97, 98, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]],[45],[2, 4, 6, 7, 11, 12, 14, 15, 16, 17, 19, 20, 24, 25, 27, 28, 29, 30, 37, 39, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 67, 71, 72, 76, 81, 82, 83, 84, 85, 86, 87, 88, 91, 92, 94, 95, 99, 100])

Score

This question is and . Your code must be able to run all the test cases in less than a minute on TIO.

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1
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Island Rose Breeder

Island Roses have an extremely simple genetic code, with just 4 genes: R, Y, W, and B, each with two alleles. This means their entire genome can be represented by four 2-bit gene pairs of the form: 00-00-00-00 (01 and 10 are equivalent)

Island Roses can be bred together. When two roses are bred, each parent flower donates one allele for each gene. This can be represented by Mendelian genetics via a Punnett square:

enter image description here

For instance, a 01-00-11-11 flower that is bred with a 01-00-11-11 flower will result in either:

  • a 00-00-11-11 flower (25% chance)
  • a 01-00-11-11 flower (50% chance)
  • a 11-00-11-11 flower (25% chance)

Based on their genes, Island Roses can display one of 8 phenotypes -- colors.

A list of the genotypes and their corresponding phenotypes can be found here.

Challenge

Given a starting stock of Roses, determine how many generations (and which Roses to use) it would take to breed a particular phenotype.

Because genetic testing is expensive, you can only identify the results of breeding by observing the phenotype of the offspring. For example, Breeding two 11-00-00-01 (Red) roses gives three distinct phenotypes, so any Black rose that results must have genotype of 11-00-00-11.

In the case of ambiguous phenotypes, subsequent generations of breeding can be done to disambiguate the specific phenotypes.

Example Input Roses:

  • 11-00-00-01
  • 00-00-01-00
  • 00-11-00-00

Target Phenotype:

  • 11-11-11-00
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1
  • \$\begingroup\$ Could you add some examples of what output should look like? Some test cases showing input -> output would also be helpful. Finally, make sure to mention the winning criteria (eg. if it's Code Golf, you should explicitly mention that) \$\endgroup\$ Apr 25, 2020 at 21:28
1
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Vampire Bats

TwilightSparkle needs help controlling COVID-19 in Equestria.

The bats are spreading the virus in the APL orchard. The orchard is an N×M rectangle of APL trees and the bats are on some of the trees.

The "Asdfjklio" spell can be casted to travel through a specified path starts on a bat and ends on a bat and destroy every bats it reaches. Asdfjklio can only move horizontally or vertically.

Your task is to output how many paths are there to destroy all of the bats.

They crossed the line, it's time to fight them back!

This is , so shortest code wins.

An example

Suppose there are two bats on respective grids, where X stands for the bats and . stands for empty spaces:

.X
X.

The Asdfjklio spell can travel in any path specified, although it has to start with a bat grid and end with a bat grid.

So there are 4 possible ways to destroy all the bats:

>>| ^| v|<<|
^ |>>|<<|v |

Sandbox

  • Is this task a dupe? If so I would change it to other (less interesting) candidates.
  • Input format?
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6
  • 2
    \$\begingroup\$ 0 paths, because there are no bats in Equestria! \$\endgroup\$
    – user92069
    Apr 28, 2020 at 2:36
  • \$\begingroup\$ @petStorm Okay. How do I clarify the question? \$\endgroup\$ Apr 28, 2020 at 2:38
  • \$\begingroup\$ So it is about counting all paths that starts and ends with a bat, and goes through every single bat on the grid, not visiting any grid cell twice, right? Do we count all paths regardless of the path lengths (e.g. if the grid is XX\n.., the U-shaped path does count too)? What if there is only one bat or no bats? \$\endgroup\$
    – Bubbler
    Apr 28, 2020 at 3:26
  • \$\begingroup\$ If you have problem describing the I/O format, look for existing challenges on main that have similar kind of I/O. As it involves a 2D grid, checking out grid will help. \$\endgroup\$
    – Bubbler
    Apr 28, 2020 at 3:28
  • \$\begingroup\$ @Bubbler Yep, regardless of the path length. \$\endgroup\$ Apr 28, 2020 at 3:58
  • \$\begingroup\$ I wonder whether is this NP-hard (and, if so, what related problems exist). \$\endgroup\$ May 1, 2020 at 2:27
1
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Linear recurrences

This is the fourth post for the second RGS's Golfing Showdown.

Rationale

Feel free to skip this, as I'm just sharing the train of thought that led me to creating this challenge.

The Fibonacci sequence we all know and love (?) is the sequence that whose first terms are

1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 121393 196418 317811 514229 832040

and starting from 1 1, each following number is obtained from the sum of the previous two. An interesting thing about the Fibonacci sequence is that it can be used to calculate the growth of a population of rabbits (see 4th, 5th, ... chapters of the linked section). Then I thought, what if I use it to calculate the number of people infected by COVID?

I tried reasoning to try and find sensible weights for a possible mock linear recursion to model the number of infected people, but I failed to do so. I need you to help me test my models.

Task

Code a function that takes a set of initial values and a set of weights (with the same length as the set of initial values) and then allows one to generate the sequence specified by the initial values and weights. Formally, if the \$k\$ initial values are \$T_1, T_2, \cdots, T_k\$ and the weights are \$w_1, w_2, ..., w_k\$ then the \$n\$th term of your sequence is given by \$T_n\$ if \$n \leq k\$, otherwise it is defined recursively by

$$T_{n} = \sum_{i=1}^k T_{n-i}w_{k-i+1} = T_{n-1}w_{k-1} + T_{n-2}w_{k-2} + \cdots + T_{n-k}w_{1}$$

Input

You must take two lists of numbers as input for the initial values and weights. Any sensible format is allowed. One or both lists can be reversed.

Additionally, you can

  • take no extra input and generate the sequence infinitely
  • take an extra integer n and generate the first n terms
  • take an extra integer n and generate the nth term (0- or 1- indexed)

Output

See input section above.

Test cases

Each 3 lines give the initial values, the weights, and then the first 10 terms of each sequence. Reference APL program.

Bonus imaginary internet points if your solution handles floating point initial values/weights.

1
2
1 2 4 8 16 32 64 128 256 512

1
3
1 3 9 27 81 243 729 2187 6561 19683

1 1
1 1
1 1 2 3 5 8 13 21 34 55

1 1
2 2
1 1 4 10 28 76 208 568 1552 4240

1 1
3 4
1 1 7 31 145 673 3127 14527 67489 313537


1 2
1 1
1 2 3 5 8 13 21 34 55 89

1 2
2 2
1 2 6 16 44 120 328 896 2448 6688

1 2
3 4
1 2 11 50 233 1082 5027 23354 108497 504050

2 2
1 1
2 2 4 6 10 16 26 42 68 110

2 2
2 2
2 2 8 20 56 152 416 1136 3104 8480

2 2
3 4
2 2 14 62 290 1346 6254 29054 134978 627074

1 6
1 1
1 6 7 13 20 33 53 86 139 225

1 6
2 2
1 6 14 40 108 296 808 2208 6032 16480

1 6
3 4
1 6 27 126 585 2718 12627 58662 272529 1266102

1 1 1
1 2 3
1 1 1 6 21 76 276 1001 3631 13171

1 2 1 1
1 1 1 10
1 2 1 1 14 144 1456 14719 148804 1504359
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4
  • 1
    \$\begingroup\$ Mathematica has LinearRecurrence (of course). \$\endgroup\$ Apr 28, 2020 at 16:03
  • \$\begingroup\$ @mypronounismonicareinstate that doesn't bother me; Mathematica's builtins tend to be long. I expect submissions shorter than that :) \$\endgroup\$
    – RGS
    Apr 28, 2020 at 16:06
  • 3
    \$\begingroup\$ How is this a reference program? I can't read it. \$\endgroup\$
    – S.S. Anne
    Apr 29, 2020 at 0:33
  • \$\begingroup\$ I don't see why this is -2. \$\endgroup\$ Apr 30, 2020 at 4:28
1
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Which anagram is the user trying to guess?

Input

  1. A list (in any form) of target words
  2. A guess word

You can take these in any form (eg, an array in which the first element is the guess word).

Output

  • If the letters of the guess word occur (in any order) in exactly one of the target words, output that target word.
  • Otherwise do something other than output letters. (Outputting nothing, or a number is fine. Throwing an error is fine. Infinite looping is not fine. :))

Assumptions

  • The members of the list, and the guess word, are each strings of 1-15 lowercase letters.
  • Members of the list might be anagrams of each other. (In this case, no guess word will ever succeed.)

Examples

  • list: fish, dog, cat, horse, porcupine:
  • guess: re -> (fail)
  • guess: so -> horse
  • guess: god -> dog
  • guess: kitten -> (fail)

Scoring and rules.

Code golf. Standard rules, no standard loopholes etc.

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3
  • \$\begingroup\$ "Don't assume that no two members of the list are anagrams of each other" The double negative is hard to read at first glance, consider changing it to "Members of the list may be anagrams of each other" \$\endgroup\$ Apr 29, 2020 at 16:50
  • \$\begingroup\$ Related: Determine whether strings are anagrams \$\endgroup\$ Apr 29, 2020 at 16:52
  • \$\begingroup\$ @mathjunkie Thanks, nice one. \$\endgroup\$ Apr 29, 2020 at 23:37
1
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Premise

I've crafted this zero-player game in an attempt to create a problem simple to explain but that would require an intricate implementation.
Sadly in the making of it, I realized that annoying conditions are required for safety (avoid to get stuck in loops) and non-ambiguity.

Ask me justifications for any rule that seems too arbitrary. Unfortunately it turned out to be 50% design and 50% precautions.

Turning Tiles game

The field of this game is a square toroidal grid (like that of Snake or Pacman) populated by dots. Each grid unit is one of the following:

  • tile (there are \$4\$ type of tile, indicating directions e.g.: ^ > v < or 1 2 3 4)
  • wormhole

The dot behaviour is very simple: it moves following the direction indicated by the tiles it walks on, and to wreak havoc after each step it rotates the left tile in a copycat fashion.
When two dots collide they will remain together forever and can be considered as one.
So the dots will either converge into one (wormholes facilitate this scenario) or remain stuck in a loop.

Detailed explanation:

One iteration of the game consists of three phases:

  • Move (M)
  • Peek (P)
  • Edit (E)

Phases are performed individually by each dot: next phase will begin only when every dot completed current phase.

At the beginning of iteration i there are ni distinct dots.
(when n>0) if ni < ni-1 then iteration i is a downgraded iteration.

Let x be a dot.

def tunnelling?:
- If x is on a tile do nothing.
- If x is on a wormhole it will immediately exit from the linked wormhole keeping the direction and tunnelling? is called.

def handle_overwrite_error:
- If multiple overwrite errors occurred in current iteration, x won't overwrite its starting tile.
- Else a wormhole will open in place of x's starting tile.

                                                                  begin iteration

M:
The tile x is on becomes its starting tile.
x moves one unit in the direction indicated by its starting tile and tunnelling? is called.
The tile x is on becomes its landing tile.
___

P:
x peeks at the landing tile of its closest dot(s) and plans its editing.
If the overwiting direction can't be uniquely determined (*) an overwrite error will rise for x.
___

E:
If x raised an overwrite error, handle_overwrite_error is now called.
Else x overwrites its starting tile with the direction decided in P.
___

If a wormhole appeared under someone's feet, that dot disappear (exiting direction couldn't be decided).
(This rule guaratees that tunnelling? will always terminate.)

                                                                    end iteration

Wormholes chain: since one single wormhole is allowed to open in each iteration, wormholes inherit their linkage order by the chronological order they popped-up. Last wormhole close the chain.

Metric: unsurprisingly taxicab metric applyied on a toroidal grid...

  • But here can enter the picture a devilish modification. What if the wormholes play a role in the metric? So that let's say x and y are 2 unit apart, with a wormhole in between they would be 4 unit apart instead. Also to find the closest dot would be totally trickier, cause the paths through any nearby wormhole have to be tried.

(*): For the overwriting direction not to be decidible the presence of multiple dots sharing the propriety "x doesn't have any dot closer than me" is necessary but not sufficient. Also their landing tiles have not to be the same.

What can be asked? (feedback)

Is this an interesting game?

Probably I've exaggerated it in the explanation but I cared to be as clear as possible and many requirements are conceivable to make it work.
Of course if that's too much I'd give up wormhole...

Rules in Shortest Game of Life inspires me

Of course the input would be the starting configuration, should wormholes be prohibited in input?

If simulation is not visually shown there would be an ITERATION_CAP
Fixed or passed in input as well?

Regarding output, the quirk of this game are the downgraded iterations. I thought that the sequence (or sum) of their indices can be returned along with last number of distinct dots...

This will be challenge, so the shortest code wins.
Default loopholes are forbidden.

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1
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Modular distance

You are given 3 non-negative integers: the domain d, the beginning index b, and the ending index e.

What is a modular distance?

Assume d=5 here. First, generate a range from 0 to 5-1:

0 1 2 3 4

We start from the beginning index. Assuming that is 3:

0 1 2 3 4
      ^

We continually go right, circling every number we've passed, until we met the ending index e.

0 1 2 O O
        ^

If the pointer is at the right end, it wraps around to the left.

Assuming e=0:

O 1 2 O O
^

We filter out every item we've circled:

0 3 4

Then, find how many items there are in this list:

3

Subtract it by 1 and it's our result:

2

Specification

  • You can always assume that b<d and e<d.

Test cases

6 2 5 -> 3
5 3 0 -> 2
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2
  • \$\begingroup\$ Do you mean to say "we filter out every item we haven't circled"? \$\endgroup\$
    – lyxal
    May 5, 2020 at 8:30
  • 2
    \$\begingroup\$ Is the modular distance just \$ (e - b) \bmod d\$ ? \$\endgroup\$ May 5, 2020 at 20:57
1
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Parse vietnamese infinite decimal notation

I wanted to express infinite decimals in text, but overlines are hard.

You need to take a decimal in vietnamese notation, and output the first 10 or more digits of the normal variant.

The notation

The way it works is that you have 0.ab(cd) and it means 0.abcdcdcd.... Of course, you can have any amount of digits in each spot, even zero. You can also omit the infinite part to represent finite decimals.

Notes

It's allowed to not accept 0.2 or 0.2() as input, and it's also allowed to output 0.2000000000 if you do accept them as input.

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5
  • 1
    \$\begingroup\$ Can we output the variant infinitely, instead of outputting the first 10 digits? \$\endgroup\$
    – user92069
    May 6, 2020 at 6:52
  • \$\begingroup\$ An existing keyboard-friendly notation is 0.ab(cd) (Wikipedia reference). \$\endgroup\$
    – Bubbler
    May 6, 2020 at 6:57
  • \$\begingroup\$ @Λ̸̸ Sure. I'll edit the question. \$\endgroup\$
    – PkmnQ
    May 6, 2020 at 8:22
  • \$\begingroup\$ So is the challenge just to split at the ( and then append the first part to the stuff in the brackets repeated 10 times? \$\endgroup\$ May 6, 2020 at 16:21
  • \$\begingroup\$ Is this a good time to post the question? \$\endgroup\$
    – PkmnQ
    May 10, 2020 at 9:22
1
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Arithmetic Square

Note: Credit goes to CCC 2019 S3 for the problem

You are given a \$ 3 \times 3 \$ grid which contains integers. Some of the \$ 9 \$ elements in the grid already have a value, and some of them remain unknown.

Your task is to fill in values for the unknown elements such that for each row, when read left-to-right, produces an arithmetic sequence, and that for each column, when read top-to-bottom, is also an arithmetic sequence.

Recall that an arithmetic sequence of length \$ 3 \$ is a sequence of integers in the form

$$ a, a + d, a + 2d $$

for integer values of \$ a \$ and \$ d \$. Note that \$ d \$ may be any integer, including zero and negatives.

Input Specification

  • You may input the \$ 3 \times 3 \$ grid in any sensible format
  • The unknown values may be represented by any character, so long that it is not a number (i.e. \$ 0-9 \$)

Output Specification

  • The output must be in the same format as the input, with the exception of unknown values becoming integers
  • All rows and columns must form arithmetic sequences
  • There is guaranteed to be at least one solution, and you may output any of them

Test Cases

(This is the only solution)
 8  9 10       8  9 10
16  X 20  ->  16 18 20
24  X 30      24 27 30

(This is one of many solutions)
14  X  X      14 20 26
 X  X 18  ->  18 18 18
 X 16  X      22 16 10

(This is the only solution)
 X -1 -2       0 -1 -2
 5  X  3  ->   5  4  3
 X  X  X      10  9  8

(This is one of many solutions)
 X  X  X       0  0  0
 X  X  X  ->   0  0  0
 X  X  X       0  0  0

This is , so the shortest code in bytes wins!

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Generate a "Poem"

Given a strictly positive integer, N, produce an output satisfying the following:

  • Produce an array of length N.
  • Every string (i.e. "word") in the array is of length N.
  • Every letter in the word is unique.
  • Every first letter of the words are unique between each other.
  • The remaining items of each word are equal to each other.

Example output

For an input of e.g. 3:

cba
dba
eba

Specification

  • Trailing whitespace is totally allowed.
  • The "letters" don't have to be from the lowercase alphabet, as long as they aren't whitespace.
  • The maximum N you need to support is 13, since there are 26 letters in the lowercase alphabet.
  • The separator of your array can be anything, as long as you will never involve that character for every possible input from 1 to 13. You can also just output a literal array.
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  • 1
    \$\begingroup\$ is there a maximum N we need to support? \$\endgroup\$
    – lyxal
    May 12, 2020 at 0:56
  • \$\begingroup\$ Yes, the maximum N here is 13. \$\endgroup\$
    – user92069
    May 15, 2020 at 10:15
1
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Is this a Freeman Dyson Number?

Background

From this Popular Mechanics article

One day, in a gathering of top scientists, one of them wondered out loud whether there exists an integer that you could exactly double by moving its last digit to its front. For instance, 265 would satisfy this if 526 were its exact double – which it isn’t. After apparently just five seconds, Dyson responded, “Of course there is, but the smallest such number has 18 digits.”

Challenge Write a program that, when given a base ten number that is at least 18 digits long, moves the last digit to the front and checks if it is doubled as a result.

I/O
Input can be any 18 (or longer) digit integer. Any leading digit must be larger than zero.

Output
The original number with the Dyson transform (last digit moved to the front) and any truthy/falsey value (if that's a digit, it must have a delimiter).

Test Cases/Sample I/O

111111111111111111 -> 111111111111111111,false
100000000000000002 -> 210000000000000000 **F**
123456789123456789 -> [912345678912345678,0]
42105263157894736842 -> 24210526315789473684👎
808080808080808080808080808016 - 680808080808080808080808080801-NO
246802468024680246802468024680246802 -> false224680246802468024680246802468024680
105263157894736842 -> true,210526315789473684
315789473684210526 -> (T:5315789473684210526)
26315789473684210526315789473684210 -> 52631578947368421052631578947368421👍

etc...

, so shortest answer in bytes (by language) wins.

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  • \$\begingroup\$ I would specify that you are talking about decimal digits. \$\endgroup\$ Mar 22, 2020 at 17:46
  • \$\begingroup\$ @JonathanFrech, Do you mean base 10? \$\endgroup\$
    – ouflak
    Mar 22, 2020 at 19:32
  • \$\begingroup\$ I think one issue here is how to verify that the specific action of moving the digit from back-to-front, and then subsequently checking for doubling, actually happened. Not sure how to get around that. \$\endgroup\$
    – ouflak
    Mar 22, 2020 at 20:10
  • \$\begingroup\$ Yes, you should specify that this is in base 10. \$\endgroup\$
    – S.S. Anne
    Mar 22, 2020 at 20:46
  • \$\begingroup\$ @ouflak Yes, I mean base ten. One often hears for example "binary digits", so the term "digits" is in my opinion not clearly defined to mean base ten. \$\endgroup\$ Mar 22, 2020 at 21:55
  • \$\begingroup\$ @JonathanFrech, @ S.S. Anne, The reason why I haven't immediately made the change is because I hadn't considered the idea of different number bases, and I'm really liking the idea of a challenge that in fact does include either various number bases, or a specific challenge for binary and this separate challenge for base ten. Mulling it over now. This would mean I'd have to figure out some binary test cases.... \$\endgroup\$
    – ouflak
    Mar 23, 2020 at 6:44
  • 1
    \$\begingroup\$ In binary doubling a number is adding 0 to the end of it, so unless you allow leading 0s it's not possible, otherwise it's correct iff the number starts with a 0 \$\endgroup\$ Mar 24, 2020 at 19:43
  • \$\begingroup\$ @CommandMaster, Yes! For binary, you would have to allow, even implicitly, a leading zero. The most obvious example is '1', which is really '01', which when the '1' is moved to the front becomes '10'. Don't see how you can get around that. It would be a different challenge. The number base thing has got me thinking. \$\endgroup\$
    – ouflak
    Mar 25, 2020 at 8:35
  • 2
    \$\begingroup\$ Here are some suggestions: Make it a decision-problem (e.g. returning the Dyson transform and the Truthy/Falsey value is a bit unnecessary). Keep the sample IO consistent (I get that you want to show the variation in possible output formats, but it would be easier to verify cases if the format were consistent). \$\endgroup\$ May 12, 2020 at 19:55
1
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Posted

Tile the plane with squashed hexagons

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1
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Compress a grandmaster chess position

Background

Compress a position from a grandmaster chess game to as few bits as possible on average. A strong submission will probably use that these positions come from real games by top players, and so will make chess sense and strategic sense, rather than just being random legal chess positions. As illustration, a study found that grandmasters do well at memorizing positions from real games using "chunking" but with only perform at novice level memorizing random boards.

The is related to but different from Smallest chess board compression, which scores on the worst-case scenario, and Smallest chess game compression, which compresses full games. (Sandbox: Let me know if this is too similar)

Task

You must write a compressor, which maps a chess position onto a sequence of bits, and a decompressor that returns its to the original position. You can vary the length of the bit sequence by position, and this will likely be important to getting a good score.

The position to compress will just be a the placement of pieces on the chess board. You do not to encode whose move it is, castling rights, or en-passant. It will be given in FEN string format with only the piece placement part, for example:

2krn2r/pppb4/4pq2/3pN2p/5P2/2PBP3/PP4P1/R2QK2R

The chess position for this FEN

Each letter corresponds to a piece (pawn="P", knight="N", bishop="B", rook="R", queen="Q", and king="K"). White's pieces use uppercase letters and Black's are lowercase. Slashes separate the descriptions of each of the rows from top to bottom, that is the 8 files doing from 8 (where black's pieces start) to down to 1. Numbers are used for blocks of that many empty spaces that are horizontally adjacent.

Scoring

You will be scored on the average length of your compressed bit sequence on 10,000 random game positions. They will chosen at random from games played by grandmasters, restricted to move 5 or later. [Will work out more details when generating this data.]

This Pastebin (TODO) contains 10,000 FEN strings to use as a training set that you can use to get a preliminary score. The final score will be based on a separate secret test set of 10,000 FEN strings.

Your code must correctly decode every game in the position. Be sure that it can handle all positions, such as ones with weird underpromotions, which might appear in the test set but not the training set. (Sandbox: How to handle submissions that break this? A default penalty score for games failed? Ask to resubmit?)

Your compression and decompression must complete within 5 minutes on all the games. (Sandbox: Allow to compress all games at once? Do one game at a time but store state to allow "learning"? Include a memory limit?)

The length of your code is immaterial to this challenge.

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5
  • \$\begingroup\$ How long (in number of positions) would a naive program that hardcodes all of the (recorded) existing grandmasters games be? (if that's not large enough, it would make the challenge trivial) \$\endgroup\$
    – DELETE_ME
    May 17, 2020 at 11:49
  • \$\begingroup\$ @user202729 That's a good question, I definitely don't want code to be use that the test set comes from an actual database, so I'd either needed to make that non-viable or ban it. \$\endgroup\$
    – xnor
    May 17, 2020 at 12:31
  • \$\begingroup\$ Does the time requirement have to be as strict as 30 games per second? (a certain question of the part also mentions "every game in the position", I assume that's a mistake) (I have no idea how to prevent storing a database of grandmaster games though) \$\endgroup\$ May 17, 2020 at 16:00
  • \$\begingroup\$ @myp I think that this requirement means that it can compress each game in 5 minutes. \$\endgroup\$
    – DELETE_ME
    May 18, 2020 at 0:50
  • \$\begingroup\$ @user202729 I had meant total for all the games, but I'll probably loosen it. \$\endgroup\$
    – xnor
    May 18, 2020 at 2:19
1
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Permutation primes

A permutation prime is a prime such that at least one of its uniquified permutations (not equal to itself) of its digits is a prime.

Given a number, check if this number is a permutation prime.

Reference program

Here is a reference program I made.

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1
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The golfing skills are strong with this one

Task

Consider the base string s = "The golfing skills are strong with this one", an adaptation of the quote "The force is strong with this one" by Darth Vader, an infamous character of the Star Wars saga (sandbox, am I correct?).

You have to output the string s with as many characters as there are bytes in your source code. If your code is longer than s, extend s by concatenating it repeatedly as many times as needed.

Your program must be non-empty.

Input

You may or may not take the string s as input for your program. (Sandbox, maybe it is more interesting to not allow the string as input?)

Output

A string as specified in the Task.

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5
  • 1
    \$\begingroup\$ Many languages, 0 bytes. PHP and /// polyglot, 1 byte: T. If the code is too long, is the string really intended to be The golfing skills are strong with this oneThe golfing skills are strong with this oneThe golfing skills are strong with this one? \$\endgroup\$ May 20, 2020 at 16:42
  • \$\begingroup\$ @mypronounismonicareinstate do you see a problem with the string being like that? What would you suggest? Also, probably should not allow the string to be used as input and require a non-empty program \$\endgroup\$
    – RGS
    May 20, 2020 at 16:46
  • 1
    \$\begingroup\$ That is perfectly acceptable, it's just that the transitions aren't very smooth (oneThe). If you can take the string as input, solutions won't have to depend on this specific string, so it would probably be a bad idea. (I mean, a[:5] isn't a very interesting answer) \$\endgroup\$ May 20, 2020 at 16:51
  • \$\begingroup\$ @mypronounismonicareinstate I failed to understand what variation you think is a bad idea. Do you think it is a bad idea to accept it as input or a bad idea to not accept it as input? \$\endgroup\$
    – RGS
    May 20, 2020 at 16:52
  • \$\begingroup\$ I think it is a bad idea to accept it as input. \$\endgroup\$ May 20, 2020 at 16:53
1
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Halting problem for simplified Brainfuck

Given a simplified Brainfuck program, you must determine whether it halts. Your program must always halt in finite time on valid inputs.

Simplified Brainfuck is a language that operates on a zero-initialized tape that is infinite in both directions. All cells contain integers from 0 to 255, and operations are performed modulo 256. There are the following instructions:

+ increment the current cell
- decrement the current cell
< move 1 cell to the left along the tape
> move 1 cell to the right along the tape
[ if the current cell is zero, skip past the next ]
] go to the previous [

Loops ([]) can't be nested.

This is tagged , so the shortest answer wins.

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9
  • \$\begingroup\$ Do you mean "Given a simplified Brainfuck program and an input of such program"? \$\endgroup\$
    – Domenico
    May 21, 2020 at 5:00
  • \$\begingroup\$ @DomenicoModica No, this language has no IO. Do you think I should mention that explicitly? \$\endgroup\$ May 21, 2020 at 5:02
  • \$\begingroup\$ Oh, I don't know, I was too hasty ahahah... Anyway If the tape was finite surely it would be solvable \$\endgroup\$
    – Domenico
    May 21, 2020 at 5:07
  • \$\begingroup\$ I think it is indeed solvable with doubly infinite tape, since the region that the pointer touches within an iteration of a loop is limited (which means we have finite number of states in that region). It's pretty hard to describe the algorithm though. \$\endgroup\$
    – Bubbler
    May 21, 2020 at 5:56
  • \$\begingroup\$ That is what I had in mind. Handling two loops in different directions is also non-trivial. \$\endgroup\$ May 21, 2020 at 6:00
  • \$\begingroup\$ I don't think handling multiple loops is that non-trivial. Consider first loop first, the answer is false if it is infinite loop, otherwise run it to the end and run all commands before the second loop. Then consider the second loop just like the first, etc. \$\endgroup\$
    – Bubbler
    May 21, 2020 at 6:49
  • 1
    \$\begingroup\$ Actually I think the challenge is not very interesting as[code-golf], because it's necessary to simulate the algorithm anyway and it can be proven (I think) that the number of steps the program takes (if it halts) is no more than \$2^{2^{2^{2^n}}}\$ (where n is the program length), so it will be no longer than an interpreter but takes impractically long to run. \$\endgroup\$
    – DELETE_ME
    May 22, 2020 at 8:48
  • \$\begingroup\$ @user202729 Is there proof of an upper bound of time? I feel it's unsolvable \$\endgroup\$
    – l4m2
    May 27, 2020 at 1:38
  • 1
    \$\begingroup\$ @l4m2 This is solvable because loops can't be nested. The body of each loops moves by a constant number of steps X, and if the program doesn't halt than it'll either repeat the same state twice (if X==0) or crosses the bound of the written tape part (because there's only a fixed number of written cells and then repeat states (there's only a finite number of cells touched by the loop body) \$\endgroup\$
    – DELETE_ME
    May 27, 2020 at 4:07
1
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Posted: Stepping Through Time

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69 70
71
72 73
150

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