Sandbox for Proposed Challenges

Question

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

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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
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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.

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Other

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Answer 1

Softcode, take 2

Softcoding is an anti-pattern defined by “the practice of removing ‘things that should be in source code’ from source code and placing them in some external resource”, which usually are config files, database entries, or both. “At the extreme end, soft-coded programs develop their own poorly designed and implemented scripting languages”, as can be seen by one of the most egregious examples of the practice, the Enterprise Rules Engine.

Thus, programmers who fall to the habit of softcoding, after tons of work, find themselves at the very point they were starting from: they have developed “some sort of COmmon Business-Oriented Language that’s generic enough to code any rule”. But unfortunately for them, there already is such a thing. “It’s called C++. And Java. And C#. And Basic. And, dare I say, COBOL.”

For the sources of the above quotations are more information of the practise, see: Soft Coding on The Daily WTF, Softcoding on Wikipedia and The Enterprise Rules Engine on The Daily WTF.

The Challenge

Softcode! Make an actual, Turing-complete language that will reside in config files!

More specifically, you should write a compiler / interpreter / anything in between that will define a Turing-complete programming language, whose every valid source code will also be a valid JSON file. ^{(The reason why JSON has been chosen is the simplicity of syntax and wide avalability of JSON parsers, so that you won't have to write a parser yourself.)}

Input/output format of your JSON language is up to you.

Shortest interpreter / compiler code wins, as long as it implements a Turing-complete language.

Technical details

Unfortunately, given how this challenge is defined, I must put one arbitrary restriction: If your language of choice supports calling a compiler or interpreter of any Turing-complete language, I must disallow doing that. Otherwise, this challenge would likely degrade to calling eval on a single property name of your JSON input file.

However, not to burden you with writing JSON parsers, you may use third-party libraries, as long as they're freely available. (Otherwise, good ol' C++ would be a nightmare without Boost.)

Be creative.

Example interpreter

For reference, below is a simple JS interpreter of a Turing-complete JSON programming language. Of course, this code is ungolfed. ^{(I hope there are no bugs in this interpreter, but I don't feel like testing it now.)}

importPackage(java.io);
importPackage(java.lang);

// This interpreter implements GOTO-programs, which are Turing-complete.

var stdin = new BufferedReader( new InputStreamReader(System['in']) );
var progsrc = stdin.readLine();
var prog = JSON.parse(progsrc).prog;

var vars = {};
vars.in = Number(stdin.readLine());

for(var i = 0; i < prog.length; i++) {
    switch(prog[i].command) {
        case 'ADD':
            vars[prog[i].varname] = vars[prog[i].varname] || 0;
            vars[prog[i].varname] += prog[i].constant;
            break;
        case 'SUBSTRACT':
            vars[prog[i].varname] = vars[prog[i].varname] || 0;
            vars[prog[i].varname] -= prog[i].constant;
            break;
        case 'GOTO':
            i = prog[i].index-1;
            break;
        case 'IF':
            vars[prog[i].varname] = vars[prog[i].varname] || 0;
            if(vars[prog[i].varname] == prog[i].constant) {
                i = prog[i].index-1;
            }
            break;
        case 'HALT':
            i = prog.length;
            break;
    }
}

vars.out = vars.out || 0;
print(vars.out);

Answer 2

Othello Greedy Strategy

The rules for Othello can be found here.

In a greedy strategy, in each go, you just choose a square in which to place your counter such that there are no other places that could allow you to flip more counters. However, there is still often a choice where you need to decide where to put your counter.

Given an integer N as input, when black goes first and both players follow a greedy strategy, output a possible configuration of counters at the end of the game where there are N black counters. Assume that there exists a configuration for N.

Output should be a 64-character string, where the (r-1)*8+1th to r*8th characters (inclusive) represent the rth row from left to right.

I'll add test cases if people think that this is a good challenge.

Answer 3

Array-of-arrays string conversion

Matrix challenges are popular. There's an issue of how to provide test cases. A common method is the row-wise array-of-arrays representation, such as:

[[1,2],[3,4],[5,6]] -> a 3 by 2 matrix

This is good with vertical space, but there's always the task of converting the test cases into something your language can use, and vice versa for producing test cases to this format.

So this is a code-golf challenge and also a repository of conversion functions that people can use when trying or composing matrix challenges.

Defining the format

A row string of length m is a comma-separated list of m ≥ 1 numbers, enclosed in square brackets.

A row-wise n×m array-of-arrays string is a comma-separated list of n ≥ 1 row strings of length m enclosed in square brackets.

There can be no leading whitespace. One trailing newline immediately after the final ] is optional. Otherwise any whitespace in the string is optional.

The challenge

Produce two* programs/functions in your language:

1. one which takes a rowwise n×m array-of-arrays string as an input, and outputs the matrix (as implemented in the language.)

2. another one which takes an n×m matrix (as implemented in the language) as an input and outputs the rowwise n×m array-of-arrays string.

*It is allowed for one program/function to perform both tasks and you can have helper code used by both conversion functions.

Rules

• To be clear: the language must support matrices (or something equivalent like 2D arrays - the name is not important) because the output/input of the two tasks needs to be an actual matrix in the language.
• This is code-golf.
• Fewest total number of bytes (from all functions and any helper code) in each language wins.
• If one program or function does both conversions, only count those bytes once.
• Standard rules apply/loopholes forbidden.

Here's the Sandbox and a related question.

Answer 4

code-golf quine string sorting

A sort of cyclic program to string together

Write a program that sorts a string.

However, it does some other things too:

1. When given a non-sorted string (that is not your source code), outputs the string in non-descending ASCII code order, as expected.
2. When given a sorted string, outputs your program's source code but sorted.
3. When given your source code but sorted, outputs the original source code.
4. When given your source code (not sorted), outputs any nonempty string that is none of the above outputs
   • i.e. Your program cannot output a sorted string and therefore must be at least two characters, and it cannot output your original source code

---

As a result, consider input string -> output string. If you're starting with any non source code unsorted string:

• The program will start with given unsorted string -> given string sorted. This sorted string can then be input to your program again resulting in given string sorted -> source code sorted
• If you continue to inputting what the program produced as output, it will then cycle through source code sorted -> source code -> chosen unsorted string -> chosen string sorted -> source code sorted.

---

Example

Let your program be foobar. Consider the following examples:

-- Case 1 (unsorted string -> sorted string) --

Input:  Programming Puzzles & Code Golf
Output:     &CGPPadeefggillmmnooorrsuzz

Input:  
This is an unsorted string
Hey look a newline
Output: 

       HTaadeeeeghiiiikllnnnnnooorrssssttuwy

-- Case 2 (sorted string -> sorted source code) --

Input:  123ABCDabcd
Output: abfoor

Input:      &CGPPadeefggillmmnooorrsuzz
Output: abfoor

Input:  a
Output: abfoor

-- Case 3 (sorted source code -> unsorted source code) --

Input:  abfoor
Output: foobar

-- Case 4 (unsorted source code -> unsorted string) --

Input:  foobar
Output: a1

Using the last example, if your program outputs a1 as your chosen string, then it will continue to cycle through a1 -> 1a -> abfoor -> foobar -> a1.

---

Specifications

• Input and output are both strings
• Your source code can't already be in sorted order since there are two different actions depending on whether or not it is sorted
• Standard I/O methods apply and standard loopholes forbidden
• This is code golf so shortest answer in bytes wins

---

Sandbox

Usually I have some sort of solution for a challenge but I have absolutely no idea how to go about doing this. I liked the idea though and wanted to know if it's original and if it's clear enough.

Answer 5

Reverse Engineering RNG

cops-and-robbers random-number-generator

---

Intro to both

Pseudorandom number generators are used for simulation and security. While most are appropriate for games and simulations (appropriateness depends on statistical properties), only a select few algorithms are appropriate for security because most of the others are too predictable and can introduce severe vulnerabilities. This challenge should (hopefully) demonstrate how easily some algorithms can be cracked and why the choice of RNG algorithm matters for security.

---

Cops

Choose/implement/create a pseudorandom number generator, seed it with a constant state, generate the first 10,000 32-bit unsigned integers, and link to it from your post. The robbers will be trying to make a program that generates the same sequence.

Your post should include:

• The total number of bits of state used by the generator. For example the well-known Mersenne Twister has 19,937 bits of state.
  • Note that if you're using multiple RNG algorithms together, you will have to show the combined count of bits of state.
  • Any randomness used to seed the generator does not count toward this value, though the seed must be constant.
• A link to the generated sequence of 32-bit unsigned integers

DO NOT post the source code of your generator. That's what the robbers are trying to figure out.

A submission is considered "cracked" if a robber has made a program that generates the exact same sequence. Therefore it is necessary that a robber determine not only the algorithm, but also the initial state of your generator

"Bits of State" Explanation

Every random number generator has a state that is used to determine the next number in the sequence and every number thereafter. Each time a number is used, the state is convoluted in some way and a random number is emitted. The minimum number of binary bits required to store this state will be your "bits of state" count. If you were using a 32-bit linear congruential generator, you would have 32 bits of state. If you were using an LCG with a modulus of 123,456,789, you would have 27 bits of state because 27 bits is the minimum number of bits required to represent every integer between 0 and 123,456,788, inclusive, even if such a state would actually be stored on a 32-bit integer.

Rules and Scoring

• All state must be self-contained within your generator and your program should generate the exact same sequence every time it is run.
• You may not use any external sources of entropy, including uninitialized memory, wall time, input, atmospheric noise, network latency, etc...
• If using an existing algorithm, you will need to make sure to do your research to ensure that the generator meets the above requirements. You may need to seed it manually to ensure that.
• There are no statistical restrictions on your sequence: it does not have to pass any statistical tests and can fit any distribution you would like, so long as it fits within the range of an unsigned 32-bit integer.
• The source code to the program used to generate your sequence cannot be larger than 4 KB.
• A submission that has not been cracked in 168 hours (1 week) will be considered "safe".
• The "safe" submission with the fewest number of bits of state is the winner.

---

Robbers

Choose a Cop submission from the other thread (link) and crack its random number generator. It will be considered cracked if you can recreate the sequence exactly.

Rules and Scoring

• Hard-coding the sequence is not allowed.
• Your program is limited to 4KB
• Your generator does not need to have the same state size as long as it generates the same sequence. In practice, this will be necessary unless the RNG used is a really bad algorithm.
• For each successful crack of a not-yet-safe random number sequence, you will score points according to the number of bits of state used by the generator:
  • 1-32 bits: 1 point
  • 33-128 bits: 2 points
  • 129-1024 bits: 3 points
  • 1025-8192 bits: 5 points
  • 8193-65536 bits: 8 points
  • More than 65536 bits: 13 points

Answer 6

^Asked

Answer 7

Add least char to match

Given a string, add at least chars to make the whole string match the given regexp. You can assume it's possible. If there are more than one solution, output a (not necessary uniform) random one.

Here regexp may contain:

|  or
() group
?  possibly not appear
*  may appear for any times. Maybe different in each match
0  
1

Samples

0100      (01)*         010101
0         (0|1)(0|1)    00; 01; 10 (any should possibly appear)
1010      ((0|1)(0|1))* 1010
101       ((0|1)(0|1))* 1010; 1011; 1001; 0101; 1101

code-golf random regex

Answer 8

Draw the Recamán's Sequence

graphical-output animation kolmogorov-complexity

Recamán's sequence (A005132) is a mathematical sequence, defined as such:

A(0) = 0
A(n) = A(n-1) - n if A(n-1) - n > 0 and is new, else
A(n) = A(n-1) + n

A pretty LaTex version of the above (might be more readable):

The first few terms are 0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11

(Description of the sequence borrowed from this older question).

Your task is to animate the drawing this sequence as a series of semi-circles:

Where each entry above is a keyframe in the animation. Tween frames should draw the circle segment, and if necessary, scale the image down when the new locus would be out of frame.

After 600 terms of the sequence you should have something like this: (Image from this Numberphile video)

Your choice whether to draw horizontally, vertically, or diagonally, provided that the entire image fits within the image boundary. Line color can be any value, background can be any value (values must be distinct).

Winner

• The program to generate the most terms of the sequence wins (before the program terminates, crashes, or otherwise corrupts the output--eg by exceeding file size limitations¹).
• Tie will go to the shorter program.

Rules

• Output image size shall be no smaller than 2048x2048, compiled as a gif, apng, common video format (e.g. mp4), or as an HTML or Javascript canvas (in-place animation).
• Segments should be drawn over 0.5 second intervals
• Frame Rate should be no slower than 24 frames/second
• (That is, each term of the sequence will take at least 12 frames to draw)
• You need not embed the entire output in your answer, although some means of showing off the results of your work is expected (sped up version, choice stills, etc).

1 _{If your program will happily produce files in excess of 128 MB (the 64 bit NTFS file system will allow up to 16 TB files), post an altered version of your program that terminates after approximately 128 MB to avoid trashing people's hard drives. You may score based on the unaltered bytecount. Do please post a still image of the final frame your program could otherwise produce (within reason: you not required to generate the entire animation in order to determine true termination). You may use a modified / separate program to produce this still, as it is purely for aesthetic and curiosity purposes.}

Answer 9

American Checkers AKA English Draughts

king-of-the-hill

This is a king of the hill challenge for checkers/draughts enthusiasts.

_{Note: All code below is written in F#}

Rules

For this game, I am using the rules from The American Checker Federation (Note: it tries to download a .doc file). The relevant rules are listed below.

Moving

Checkers move forward diagonally one square.
Kings move diagonally one square in any direction.

Capturing

Capturing is required in this variant.
Checkers jump forward diagonally two squares; they may only jump over an opponent's piece onto a blank square and continue jumping until there are no more pieces to jump, or until they reach the king row.

King jumps follow the same pattern as checkers jumps, but do not have the restriction on moving forward.

Winning

The game is won when one player has no more pieces or cannot make any more moves.

Draws

A draw is declared when the same position is reached three times or when neither player moves an unkinged checker for 40 moves and there are no captures in those forty moves.

Play

Each program will take a list of the game history in the form of a PdnTurn list (Read about PDN notation here):

type PieceType = Checker | King
type PdnMove = { Move :int list; ResultingFen :string; DisplayString :string; PieceTypeMoved :PieceType Option }
type PdnTurn = { MoveNumber :int; BlackMove :PdnMove; WhiteMove :PdnMove Option }

It will return the data in the form of a list of ints, where each int represents a square on the board. That is, if you have a piece on square 1 and intend to jump to square 10 over a piece on square 6, your program will return [1; 10] (notation as an F# list). If any player returns an invalid move, they forfeit the game.

Scoring

Each player will play three games against each opponent; each win will be scored as 1, each loss as 0, and each draw as 1/2. The loser of the match will be disqualified. At the end of the tournament, the player(s) with the highest score win.

The Tournament (incomplete):

I set up a website at checkerstreasury.azurewebsites.net. Communication from the server to the player is done with SignalR preferring websockets (you can probably just use websockets without SignalR, but I don't know how). Communication from the player to the server is done with POST requests. I am at work now, but I will post the API and finalize this later.

This challenge feels incomplete; am I missing something?

Question: I have my own AI implemented alongside my controller. I intend on submitting this as a base submission, but will not award it the win even if it is the king of the hill. Should I include it in the question, or as an answer? If an answer, should I post it with the question, or wait a while?

Answer 10

Execute a Subpar Shuffle™

Inspired by the Execute a Superb Shuffle™ challenge, and a shuffling method I used as a young child before I realised how bad (and time consuming) it is.

In a Subpar Shuffle, you take the deck of cards, and perform the following actions:

1. Take the top card of the deck and deal it out into a pile.
2. Take the next card of the deck and place it underneath the deck.
3. Repeat steps 1 & 2 until you've dealt out the whole deck.

If your deck is represented as a list, then it looks something like this:

1. Set up an empty list to hold the shuffled list.
2. Put the first item of the old list at the start of the new list.
3. Put the first item of the old list at the end of the old list.
4. Repeat 2 & 3 until the old list is empty, then return the new list.

So, for example, the input list [1, 2, 3, 4] would result in the following:

Old list     | New list
[1, 2, 3, 4] | []
[2, 3, 4]    | [1]          Put the 1 at the start of the new list
[3, 4, 2]    | [1]          Put the 2 at the end of the old list
[4, 2]       | [3, 1]       Put the 3 at the start of the new list
[2, 4]       | [3, 1]       Put the 4 at the end of the old list
[4]          | [2, 3, 1]    Put the 2 at the start of the new list
[4]          | [2, 3, 1]    Put the 4 at the end of the old list
[]           | [4, 2, 3, 1] Put the 4 at the start of the new list

So the final Subpar Shuffled list is [4, 2, 3, 1].

Here are a few more test results for Subpar Shuffling of various lists:

Input                     | Output
[]                        | []
["Ace of Spades"]         | ["Ace of Spades"]
["A","c","e","o","f","S"] | ["o","S","c","f","e","A"]
[1,2,3,4,5,6,7,8,9,0]     | [4,8,0,6,2,9,7,5,3,1]

Answer 11

Binary Positional Average

Introduction

(This challenge is from work today) This challenge seems relevant for actual use in the real world, it's a (as far as i know) not yet dealt with kind of integer sequences.

Challenge

• Inputs: A Integer between 1 and 64 representing the amount of bits to iterate through
• Output: An Array or a delimiter separated sequence of arrays or sequences of 0s and 1s

The algorithm has to take the input and generate all binary sequences up to the given number ordered by the position of the average 1 bit in the binary representation of the current number. The direction of the sorting is irrelevant. 0 can be ignored.

The solution must terminate, otherwise this is code golf, tiebreaker is performance in program steps.

Example Input and Output

Input:

4

Has (among others) the following possible outputs:

0001,0011,0101,0010,0111,1011,0110,1111,0000,1001,1101,1110,1010,0100,1100,1000

Or:

0001,0011,0111,0010,0101,1011,0110,1111,1001,1101,1010,1110,0100,1100,1000

Example Implementation

(Javascript - modified sketch from work)

function binaryPositionalAverage(size) {

    let srMap = [];

    for (let i = 2**size -1; i > 0; i--) {

        let inp = (i).toString(2);
        let out = "";
        // pad with 0s
        for (let i = 0; i < (size - inp.length); i++) {
            out += "0";
        }
        out += inp;
        out = out.split("").map(s => parseInt(s));
        // out format: [1,1,1,1];

        let rating = 0;
        let divisor = 0; // we ignore 0 by loop condition
        for (let k = 0; k < out.length; k++) {
            if (out[k]) {
                rating += k+1;
                divisor++;
            }
        }
        rating /= divisor;

        srMap.push({
            rating: rating,
            binary: out,
        });
    }
    return srMap.sort((a, b) => a.rating - b.rating).map(e => e.binary);
}

Answer 12

A fast-growing evaluator

math code-challenge

Introduction

The fast-growing hierarchy is a hierarchy of, well, fast-growing functions, with a one-to-one correspondence to ordinals. If you did some busy-beaver challenges, you may have worked with them, since it's a systematic means of defining functions with extremely fast growth rates.

Here, you are defining as many of them as you can. Of course, because of obvious problems with enumerating them sequentially, the challenge is to yield any particular one given the ordinal, up to as far an upper limit as possible.

The fast-growing hierarchy

If you are lost on some of the jargon here, I recommend a read about ordinals: https://en.wikipedia.org/wiki/Ordinal_number

The fast growing hierarchy is defined for each ordinal in a recursive manner as follows:

• The lowest and slowest function, corresponding to 0, is f₀(n) = n+1.

  • f₀(3) = 3+1 = 4

• For succeeding ordinals and functions in the hierarchy, f_a+1(n) = f_aⁿ(n).

  • f₁(2) = f₀²(2) = f₀(f₀(2)) = f₀(3) = 4

• For functions in the hierarchy corresponding to limit ordinals, first determine a fundamental sequence that approaches the ordinal in question. Then, f_a(n) = f_a[n](n), where a[n] is the nth ordinal in the fundamental sequence.

  • The fundamental sequence of ω is {0, 1, 2, 3...}, indexing from zero. So f_ω(2) = f₂(2) = f₁(f₁(2)) = f₁(4) = 8

As can be seen, for infinite-ordinal entries of the fast-growing hierarchy, the value of the function is dependent on the choice of fundamental sequences. Most ordinal notations specify fundamental sequences with the ordinals that they define notations for.

Here are some typical choices of ordinal notations and fundamental sequences, arranged in increasing ordinal-notating capability:

• Cantor normal form, for which The Wainer hierarchy defines fundamental sequences
• The Veblen functions
• Madore's ordinal collapsing function
• Buchholz's ordinal collapsing functions
• Jager's ordinal collapsing functions

The challenge

Within 1024 bytes, write a program that takes the string representation of an ordinal A in some ordinal interval starting at 0, and a number B of arbitrary size, and prints the fast-growing function corresponding to A, applied to B.

• Choices of domain of representation, ordinal domain, ordinal notation, and ordinal fundamental sequences must be specified. The choice of fundamental sequences must actually approach the ordinals they define fundamental sequences to, such that logically, the ωth ordinal of that sequence would be the ordinal of that fundamental sequence.
• The program must provably halt for any input, given sufficient resources, even for invalid inputs or inputs corresponding to ordinals beyond the program's capability. In particular, raw eval() of the input is forbidden, and entries are disqualified if they permit arbitrary code execution.
• For all given ordinals with the program's capability, the program must print the value as described above for all numbers, deterministically, given enough resources.
• Standard restrictions on running time and resource usage of programs are relaxed.
• Competing entries must be able to handle at least A=0.

Scoring

Take C to be the first ordinal for which the program fails to satisfy the requirements above, and D to be the difference between your program byte length and 1024, the maximum byte length of submissions. Then your score is C+D.

Sample scores:

• Alice, in 200 bytes, writes a program for which A can be any natural number. Her score is ω+824.
• Bob, in 220 bytes, writes a program for which A can be ω or any natural number. His score is (ω+1)+804 = ω+805.
• Carol, in 400 bytes, writes a program for which A can be any ordinal purely in Cantor normal form. Her score is ε₀+624.
• Dave, in 700 bytes, writes a program for which A can be a natural number or any epsilon number. His score is ω+324.
• Eve, in 300 bytes, writes a program which segfaults if A is represented by a decimal string longer than 65536 bytes. Her score is 10⁶⁵⁵³⁶+724.

Answer 13

Assign tasks to processors code-golf^{anything better to put here?}

Given a list of processor speeds \$S\$, where each element denotes how many ticks the processor at its index takes to complete a task, and a number of tasks \$N\$, replace every element in \$S\$ with the number of tasks the processor at its index should perform. The order of completion doesn't matter, and the tasks aren't enumerated anyway. The processors you pick don't matter either. The only thing that matters is that the ticks needed to complete all the tasks are the least possible. If there are multiple solutions, choose one with the lowest sum of the ticks each processor spends working (less man-hours means happier workers). This is a simple version of such a challenge, so you can assume that every task takes the same amount of time to be completed. You can assume that \$S\$ only consists of positive integers and that its length is at least \$1\$, and \$N\$ is a non-negative integer. ^{What a blob of text...}

Examples (test cases)

\$S=[4,1,3,1,2,2,1,1]\\N=13\\\text{Example output: }[0,3,0,3,1,0,3,3]\$

\$S=[8]\\N=28\\\text{Example output: }[28]\$

\$S=[1,1,1,1,1,1,1,1,2]\\N=5\\\text{Example output: }[1,1,1,1,1,0,0,0,0]\$

\$S=[1,28]\\N=28\\\text{Example output: }[28,0]\$
Note that \$[27,1]\$ is an invalid output, since \$1\times27+28\times1>1\times28\$.

Answer 14

Integers in increasing order of width when printed in Helvetica

According to Explain XKCD, Helvetica kerns adjacent 1s together slightly. This means that the sequence of integers in increasing order of width is (0, ) 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 10, 12 ... 99, 111, 110, 112 ... 119, 211, 311, 411, 511, 611, 711, 811, 911, 100 ... 109, 120 ... 210, etc.

For the purposes of this question you can assume that repunits will always print wider than numbers with fewer digits. Note that the adjacent pairs may overlap e.g. 11011 has the same width as 11100.

Given an integer n, either return the nth integer in the sequence (you may but do not need to support the 0th integer as 0) or the first n integers (starting at either 0 or 1). Alternatively, print the sequence indefinitely or return a generator or equivalent lazy list.

This is code-golf, so the shortest program or function that breaks no standard loopholes wins!

(Should I include negative integers? They could be assumed to be longer than all positive integers with the same number of digits, but shorted than those with more digits.)

Answer 15

Play a Game of Balls Bounce

code-golfgame

The game Balls Bounce consists of the following:

• a number of blocks, each containing a \$durability\$ number \$\geq 1\$
• a field of dimension \$h \times w\$, partially filled with blocks (field is \$9\times 7\$ in the example)
• a number of \$balls\$, positioned in one location at the bottom of the field

Rules of the game:

• The player chooses a direction in which all the balls will be shot sequentially.
• Each time a ball hits a block, that block's \$durability\$ decreases by \$1\$.
• A block that has its \$durability\$ decreased below \$1\$ is removed from the field.
• Balls that hit a block are deflected and continue to fly. Note that one ball may be deflected multiple times and hit the same block more than once.
• Balls do not interact with each other directly. They may be in the same place at the same time.
• If a ball touches the top, left, or right side of the field, it gets deflected in a similar manner.
• If a ball touches the bottom of the field, it gets stuck there and won't continue to fly this round.
• A round ends once there are no more balls flying around.
• After a round ends, all blocks on the field move one row downwards, and new blocks spawn in the top row.
• The player loses if any block goes past the bottom line.

Note that \$balls\$ might be higher than \$durability\$ of the first block that is hit. In that case, the player now has to keep to paths in mind: the first, a \$durability\$ amount of balls, is deflected by the block, while the second, a \$durability - balls\$ amount passes through the position where the now destroyed block once was.

In the mobile game, the player can choose some angle for the shot. Because I want to make this challenge not bigger than it already is, there is only three possible angles to choose from: 45° to the left, denoted by \$L\$, straight upwards, denoted by \$U\$, and 45° to the right, denoted by \$R\$. Also, the first ball to touch the bottom line marks the position from which the nex round's shot will be taken. For simplicity's sake, all shots will be taken from the middle of the baseline. If a grid has even \$w\$, left of the middle is chosen. If an ambiguity would be created by two balls interacting with the same block at once, the ball that was shot first interacts first.

Input

• The Field with Blocks

  You may take this as a \$h \times w\$ 2D array of integers or strings. Each value represents the \$durability\$ of the block at that position. You may choose something other than \$0\$ to represent an empty space.

• The Amount of Balls

  Quite self-explanatory. Integer (or any convenient format).

• The Direction

  One of \$\{L, U, R\}\$. You may choose the three strings "L", "U" ,"R" to represent this, but any three distinct and consistent values will suffice.

Output

• Is the game over?

  Output a truthy value if the game is lost after this round, and a falsy one if the game can go on. Any two distinct and consitent values will suffice.

This is code-golf, so shortest code in bytes for each language wins.

---

Example:

Input:

Field

[0][0][0][0][0]
[0][9][0][0][0]
[0][0][1][0][1]
[0][0][0][2][0]

Balls 3

Direction "R"

Output:

False

Step-by-step:

-----------------------
          (1)
-----------------------
#######################   #  border of field
#+---+---+---+---+---+#   
#|   |   |   |   |   |#   +  corner of block/empty cell
#+---+---+---+---+---+#   -  horizontal border of block/empty cell
#|   | 9 |   |   |   |#   |  vertical border of block/empty cell
#+---+---+---+---+---+#   
#|   |   | 1 |   | 1 |#
#+---+---+---+---+---+#
#|   |   |   | 2 |   |#   2  durability
#+---+---+---+---+---+#
###########o###########   o  ball
           3              3  number of balls remaining to be shot

-----------------------
          (2)
-----------------------
#######################
#+---+---+---+---+---+#
#|   |   |   |   |   |#
#+---+---+---+---+---+#
#|   | 9 |   |   |   |#
#+---+---+---+---+---+#
#|   |   | 1 |   | 1 |#
#+---+---+---+---+---+#
#|   |   |   o 1 |   |#      the first block is hit, durability decreased to 1
#+---+---+--/+---+---+#   /  "tail" to show the direction of the ball
###########o###########
           2

-----------------------
          (3)
-----------------------
#######################
#+---+---+---+---+---+#
#|   |   |   |   |   |#
#+---+---+---+---+---+#
#|   | 9 |   |   |   |#
#+---+---+---+---+---+#
#|   |   | 0 |   | 1 |#      second block decreased to 0, ball that hit it is deflected
#+---+---+-o-+---+---+#
#|   |   |   o 0 |   |#      same for the first block
#+---+---+--/+---+---+#
###########o###########
           1

-----------------------
          (3)
-----------------------
#######################
#+---+---+---+---+---+#
#|   |   |   |   |   |#
#+---+---+---+---+---+#
#|   | 9 |   |   |   |#
#+---+---+---+---+---+#
#|   |   |   |   | 1 |#       
#+---+---+-o-+---+---+#
#|   |   o   o   |   |# 
#+---+---+---+---+---+#
###########-###########
           0

-----------------------
          (4)
-----------------------
#######################
#+---+---+---+---+---+#
#|   |   |   |   |   |#
#+---+---+---+---+---+#
#|   | 9 |   |   |   |#
#+---+---+---+---+---+#
#|   |   o   |   | 1 |#       
#+---+---+---+-o-+---+#
#|   |   |   |   |   |# 
#+---+-o-+---+---+---+#      first ball hit the bottom line...
###########-###########
           0

-----------------------
          (5)
-----------------------
#######################
#+---+---+---+---+---+#
#|   |   |   |   |   |#
#+---+---+---+---+---+#
#|   | 8 |   |   |   |#
#+---+-o-+---+---+---+#
#|   |   |   |   o 0 |#       
#+---+---+---+---+---+#
#|   |   |   |   |   |# 
#+---+---+---+---+---+#      ... and is removed subsequently
###########-###########
           0

-----------------------
       (6 to 19)
-----------------------
#######################
#+---+-*-+---+---+---+#      *  path of the right ball
#|   *   *   |   |   |#
#+-*-+---+-*-+---+---+#
#*   | 8 |   *   |   |#
#+-*-+---+---+-o-+---+#
#|   o   |   |   |   |#      °  path of the left ball
#+-°-+-*-+---+---+---+#
#°   |   *   |   |   |# 
#+-°-+---+-*-+---+---+#
###########-###########
           0

-----------------------
          (20)
-----------------------
#######################
#+---+---+---+---+---+#
#|   |   |   |   |   |#
#+---+---+---+---+---+#
#|   |   |   |   |   |#      all balls are gone, blocks are shifted down
#+---+-V-+---+---+---+#      no block reaches the bottom line, so no game over
#|   | 8 |   |   |   |#       
#+---+---+---+---+---+#      Return false
#|   |   |   |   |   |# 
#+---+---+---+---+---+#      
###########-###########
           0

The step-by-step diagram is just for illustrative purposes. You are not required to print any of the above.

---

Sandbox Questions

As this is my first challenge on here, I need some guidance. What examples should be added to clarify the task? What corner cases hould I take into consideration? And most importantly, is it clear what my challenge will be?

Answer 16

Drawing a convex polyiamond code-golf ascii-art polyomino

A subtask of Drawing convex polyiamonds. I consider the drawing part hard enough on itself.

A polyiamond is a polygon made from equilateral triangles. For example: (example in ASCII art)

  *
 / \
*---*

Or:

  *---*
 / \ / \
*---*---*
 \ /
  *

(with lines drawn between the triangles for clarity)

While the first polyiamond is convex, the second one is not.

---

Consider a convex polyiamond. All of its internal angles must be less than 180°. Also, the internal angle of a triangle is 60°, so each vertex must be 60° or 120°.

Assume a polyiamond has all 120° angles. It must have 6 edges.

Given the length of those 6 edges, it's either possible to reconstruct the polyiamond uniquely, or there are no such polyiamond. For example:

(1,1,1,1,1,1) ->

  *---*
 / \ / \
*---*---*
 \ / \ /
  *---*

(1,2,1,2,1,2) ->

  *---*---*
 / \ / \ / \
*---*---*---*
 \ / \ / \ /
  *---*---*
   \ / \ /
    *---*

---

Now consider a 60° internal angle. It can be assumed to be two consecutive 120° angle with the intermediate edge have length 0. For example:

(0,1,0,1,0,1) ->

  *
 / \
*---*

---

Your program should take a list of 6 non-negative integers (in any convenient format such as: tuples, string of comma-separated integers, \$2^a 3^b 5^c 7^d 11^e 13^f\$ (for Fractran?)) which represents a valid convex polyiamond, and output the polyiamond as ASCII art.

It's guaranteed that:

• No numbers in the list will exceed 12.
• It's guaranteed that there is at least 1 cell in the output. (so (0,0,1,0,0,1) is not a valid input) Equivalently, no two consecutive 0's can appear in the input list.

Answer 17

Given a list of variable names and a list of monomials, output a string representation of the name of the polynomial. The monomials should be represented as pairs [coefficient, vector of exponents] where the vector of exponents has the same length as the list of variable names.

Combine like terms, omit terms that have coefficient zero, and output the resulting polynomial.

If the list of variables is ["x", "y", "z"] then [c, [i,j,k]] represents the monomial c*x^iy^jz^k, so for example [2, [1,2,3]] should be printed as 2xy^2z^3 and [-1, [0,1,2]] should be printed as -yz^2.

A worked example:

Input ["x","y"], [[4,[2,1]], [1,[0,0]], [-1,[1,1]],[-2,[2,1]]]: The monomial [2,1] which corresponds to x^2y is repeated twice, [4,[2,1]] with coefficient 4 and [-2,[2,1]] with coefficient -2 so we add those two coefficients together to get 2x^2y.

[1,[0,0]] corresponds to 1x^0y^0 which should be displayed as 1 and [-1,[1,1]] corresponds to -1x^1y^1 which should be displayed as -xy. The polynomial is the sum of these three, so all together the output should be 2x^2y - xy + 1 or some reordering of these terms.

Requirements:

• Operators can be surrounded in spaces
• Like terms should be combined.
• If the exponent is 1 it should be omitted: x, not x^1. If the exponent is zero, the variable should be omitted entirely: y not x^0y and 1 not x^0y^0.
• Empty polynomials should be represented as 0.
• Terms with coefficient zero should be dropped. A coefficient of 1 should be omitted unless all exponents are zero.
• A negative coefficient should be written with a minus sign. If the first monomial has a positive coefficient, it should not be preceded by a +.
• Terms can be output in any order

Test Cases

Input: ["x"], [] ==> "0"
Input: [], [[3,[]], [-7,[]]] ==> "- 4"
Input: ["x"], [[0,[5]]] ==> "0"
Input: ["x"], [[1,[5]]] ==> "x^5"
Input: ["x"], [[-1,[5]]] ==> "- x^5"
Input: ["x"], [[1,[5]], [1,[5]]] ==> "2x^5"
Input: ["x"], [[1,[5]], [-1,[5]]] ==> "0"
Input: ["x"], [[1,[2]], [2,[1]], [3,[0]]] ==> "3 + 2x + x^2"
Input: ["x"], [[3,[0]], [2,[1]], [1,[2]]] ==> "3 + 2x + x^2"
Input: ["x", "y", "z"], [[1,[0,0,1]], [1,[1,0,0]], [-1,[0,1,0]]] ==> "x - y + z"
Input: ["x_1", "x_2"], [[1,[1,1]],[1,[2,2]]] ==> "x_1x_2 + x_1^{2}x_2^{2}"
Input: ["x", "y"], [[2,[2,2]], [3,[2,1]], [4,[2,0]], [1,[0,0]], [-1,[1,0]],[-2,[2,0]]] ==> 
        "1 - x + 2x^2 + 3x^2y + 2x^2y^2"

Answer 18

Lord Vetinari's Clock

Someone very clever — certainly someone much cleverer than whoever had trained that imp — must have made the clock for the Patrician’s waiting room. It went tick-tock like any other clock. But somehow, and against all usual horological practice, the tick and the tock were irregular. Tick tock tick ... and then the merest fraction of a second longer before ... tock tick tock ... and then a tick a fraction of a second earlier than the mind’s ear was now prepared for. The effect was enough, after ten minutes, to reduce the thinking processes of even the best-prepared to a sort of porridge. The Patrician must have paid the clockmaker quite highly.

-- Feet of Clay, by Terry Pratchett

The challenge

Write a function or a program that alternatively outputs "tick" and "tock" every second. There is a 1/5 chance that the tick or tock should be slightly faster or slightly later than expected, with a 50/50 chance between it being early or late. The time difference should be 0.2 seconds.

The clock should still keep accurate time: that is, if a tick or a tock is early or late, the next tick or tock should still be on-time. The clock itself should not "drift" because of the displaced ticks or tocks.

Rules

The usual rules and loopholes apply.

This is code golf: shortest code wins.

code-golf

Answer 19

Looking for feedback on my first question.

Title: Largest Left-Truncatable Prime in Base \$b\$ (A103443)

Introduction

Numberphile recently posted a video about truncatable primes, and the concept seems like it would make a good base for a number of good code golf exercises. I explain the concepts below, but watch the video only if you want ideas about an algorithmic process for finding them.

A left-truncatable prime in base \$b\$ is a prime \$p\$ such that

• all the digits of \$p\$ in base \$b\$ are nonzero, and
• when any number of leading digits of \$p\$ when written in base \$b\$ are removed, the result is still a prime. (That is, every suffix of \$p\$ when written in base \$b\$ is a prime, when still interpreted in base \$b\$).

For example, \$1223\$ is a left-truncatable prime in base \$10\$, since \$1223\$, \$223\$, \$23\$, and \$3\$ are all prime; \$1223\$ is also a left-truncatable prime in base \$4\$, since \$1223\$, \$223\$, \$23\$, and \$3\$ are all prime when considered in base \$4\$ (in base \$10\$ they are \$107\$, \$43\$, \$11\$, and \$3\$, respectively). OEIS sequence A024785 is a list of all left-truncatable primes in base \$10\$.

There are many variants on this concept, but this is all you need for this challenge. This concept also appeared in this challenge from two years ago.

Challenge

Your challenge is to find the largest left-truncatable prime in base \$b\$. You can show (from this paper I believe) that there are only finitely many left-truncatable primes for a given base, so the largest one exists. Here it is instrumental that we require these primes to have all nonzero digits; otherwise, there would be no largest one.

For example, the largest left-truncatable prime in base \$10\$ is 357686312646216567629137, as mentioned in the above video. These are found in A103443.

Your program must input an integer \$b \geq 3\$, and output an integer written in base \$10\$ which is the largest left-truncatable prime in base \$b\$ (indeed, one must always exist as well). Your program/function should work for any input \$b\$ your language supports.

This is code-golf, so the shortest answer wins! No standard loopholes, but built-in primality testing is allowed.

_{If your program fails because it would require integers that exceed your language's max integer, then state so in your solution; these solutions are still allowed, but solutions that aren't limited by the language's max integer are better. Alternatively, if you are restricted by a max integer, give the largest left-truncatable prime base \$b\$ that is smaller than this max integer.}

Example Input and Output

Input:

10

Output:

357686312646216567629137

See A103443 for more test cases.

Remember that \$1\$ is not a prime.

Answer 20

Locate Substring

This is not a challenge yet, just a place to write down an idea.

Given some finite binary string \$S\$, we can try to find the minimal length \$n \in \mathbb N\$ such that we can uniquely locate each contiguous substring \$ T \$ of \$ S \$ that has length \$ n \$.

Example

Let \$ S = 01000110 \$. Then surely \$ n > 1\$. But we also immediately see that \$ n > 2\$ because for instance the substring \$T = 01\$ appears twice in \$ S = \color{red}{01}00\color{red}{01}10\$. But all substrings of length \$ n=3 \$ are distinct, these are in fact (in the order they apppear from left to right) \$ \{ 010, 100, 000, 001, 011, 110 \} \$. This means that \$ n=3 \$ is minimal. [end of example]

Alternatively given some \$ n \$ one might ask to find the longest sequence \$ S \$ such that all substrings \$ T \$ of length \$ n \$ are uniquely locatable.

Answer 21

Order times fully written out in English, alphabetically

A 12h format time of day can be fully written out in English according to the following rules:

1. a word from one to twelve;

2. a space;

3. optionally a word from one to fifty-nine followed by a space;

4. the "word" AM or PM.

Examples:

 1:31 AM  => "one thirty-one AM"
11:12 PM  => "eleven twelve PM"
 4:00 AM  => "four AM"

Challenge

The challenge is to take a list of 12h format times and order them alphabetically by the way they are fully written out in English.

Input and output format is flexible. Output can either be the times themselves or their fully written out in English versions.

This is code-golf. Shortest in bytes for each language wins. Standard loopholes forbidden.

Test cases

[ "1:31 AM", "11:12 PM", "4:00 AM" ]   =>   [ "11:12 PM", "4:00 AM", "1:31 AM" ]

More test cases can be added if there is interest.

I'm mainly concerned this might be a dupe. I couldn't find one.

Answer 22

Edit distance for sparse strings

The input to this challenge will be two strings of length one million each. Each string contains only zeros and ones. However each string will contain at most 100 ones and so will be represented by a sorted list of integers. The integers will indicate where the ones are.

Example of input

[ 42394, 108181, 154190, 217161, 301607, 379951, 412651, 623862, 624712, 783863]
[ 42393, 108181, 154189, 267161, 301608, 379951, 412651, 623862, 624713, 783863]

We want to compute the Levenshtein distance between these two strings. However, the standard algorithm will take around 10^12 time which is too slow.

Task

Your code should take in the two inputs and output the edit distance between the two strings. The only restriction is that your code must be fast enough (and not use too much memory) so that it will complete in less than a minute on a standard desktop PC. In case of doubt, I will test the code on my 8GB AMD processer PC using test inputs that I will create.

Small test cases

To test your code here are some small inputs for strings of length 100 with up to 10 ones.

This pair gives edit distance 8.

[18, 23, 30, 40, 47, 53, 60, 73, 89, 94]
[21, 23, 39, 48, 53, 59, 60, 89]

This pair gives edit distance 8

[19, 25, 26, 40, 43, 62, 74, 75, 85, 89]
[10, 26, 27, 28, 44, 70, 74, 75, 76, 86]

This pair gives edit distance 7

[ 9, 17, 18, 29, 45, 50, 57, 64, 80]
[ 2, 16, 23, 27, 32, 43, 49, 56, 63, 79]

This pair gives edit distance 6

[ 3,  9, 12, 33, 39, 49, 55, 72, 84, 94]   
[ 3,  9, 29, 40, 41, 72, 84, 94]

code-golf

Answer 23

Make a reversible formula

For the purposes of this question:

1. a basic formula \$ y = f(x) \$ takes one of the following forms:

$$ x \\ g(x) + c \\ c + g(x) \\ g(x) - c \\ c - g(x) \\ g(x) c \\ c g(x) \\ \frac {g(x)} c \\ \frac c {g(x)} $$

where \$ g(x) \$ is a basic formula;

2. a reversible formula \$ y = f(x) \$ takes one of the following three forms:

$$ \begin{align} y = x & \implies x = y \\ y = c - g(x) & \implies x = g^{-1}(c - y) \\ y = \frac c {g(x)} & \implies x = g^{-1} \left ( \frac c y \right ) \end{align} $$

where \$ g(x) \$ is a reversible formula whose reverse is \$ g^{-1}(x) \$ according to the above rules and \$ c \$ is a non-negative integer. A simple example of a reversible formula would be the expression \$ y = \frac 1 {1 - x} \$ whose reverse is \$ x = 1 - \frac 1 y \$.

Your challenge is to take a basic formula and express it as a reversible formula. The following transformations are allowed:

$$ \begin{align} \left . \begin{array}r x + c \\ c + x \end{array} \right \} & \implies c - (0 - x) \\ x - c & \implies 0 - (c - x) \\ \left . \begin{array}r x c \\ c x \end{array} \right \} & \implies \frac c {\frac 1 x} \\ \frac x c & \implies \frac 1 {\frac c x} \end {align} $$

(Note that the strict domain of the resulting formula may exclude some values not excluded in the original formula, but the limit of the formula should be equivalent to the original formula.)

Of course we're dealing in string equations so you'll be using * and / instead. Examples:

(x + 1) * 2 => 2 / (1 / (1 - (0 - x)))

x * 2 + 1 => 1 - (0 - 2 / (1 / x))

Do not include extraneous parentheses in your result.

This is code-golf, so the shortest submission that breaks no standard loopholes wins!

Answer 24

Should I index like this or like that? code-golf integer decision-problem

Challenge

Let's take a 0-indexed array of length \$l\$. You can index into it with \$i\$, where \$-l\le i<l\$, and the returned element is the element in position \$[i<0]\times l+i\$ (\$[\dots]\$ is the Iverson bracket).

In some cases, it's shorter to use a negative index instead of a positive one, counting the minus sign and the digits as bytes. For example, if we want the \$102\$th element of an array with \$104\$ elements, indexing with \$101\$ and \$-3\$ will both give the same result. However, if we write the numbers in code, 101 is 3 bytes long, while -3 is 2 bytes long, so we prefer -4. In other cases, using a negative index is counterproductive (for a code golfer). Such an example is the will to obtain the \$4\$th element of a \$10\$-element array. In this case, we can use \$3\$ and \$-7\$, but -7 is longer than 3, so we'll choose 3 instead.

Given two inputs \$l\$ and \$i\$, where \$l>0\$ (it doesn't make sense to index into an empty array) and \$0\le i<l\$ (or \$-l\le i<0\$, be consistent), your job is to determine whether positive or negative indexing is better for code golfing purposes. In case both are of the same length, you may return either decision, even inconsistently. The returned value must be one of two distinct and consistent values, defined by the answerer.

Of course, using standard loopholes isn't fun, so, if you do use any, then, sorry, your answer isn't valid. ;-)

Test cases

Here, 1 is used for negative indexing and 0 for positive. I also always prefer using positive indices, but you may prefer otherwise.

l     i           (actual index)
----- ----- ----- -----
    1     0     0     0
   10     9     0     9
 1000   999     1    -1
10000  9755     1  -245
  101   100     1    -1
  150   141     1    -9
  150   140     0   140

Answer 25

Fuzzy Circles

Edit

I don't actually like this challenge all that much. Anyone who wants it can have it, else I'll get rid of it.

Background

For a real number x, let ⌊x⌋ be the greatest integer less than or equal to x.

Challenge

Given an input n, find the minimum radius of the circle such that all points that satisfy the following equation are on its interior or border.

⌊x⌋^2+⌊y⌋^2 = n

Input: A real number n

Output: A real number representing the radius of the smallest circle that contains in its interior or border all points that satisfy ⌊x⌋^2+⌊y⌋^2 = n.

Note: The precision expected in this challenge is two decimal places, both for the input and output.

This is a code-golf challenge.

Test Cases (More to be added):

25->5.70

Answer 26

Knightmare in 1024 bytes of (JavaScript?)

king-of-the-hill javascript grid board-game

---

Board

The board is a 16x16 grid of squares. It does not wrap, so the outer edges are an impassable boundary.

Pieces

Each piece is like a Chess knight, and will be referred to as a knight. It moves to a square that is two squares away horizontally and one square vertically, or two squares vertically and one square horizontally.

A knight can move to any of these squares, regardless of whether it is occupied. There is no limit to how many knights may occupy the same square at the same time.

Players

This is a 2 player game. Each player has 16 knights. Knights cannot be removed from the board so there will still be 16 knights per player at the end of the game.

Turns

Each turn both players move all 16 of their knights simultaneously (that is, all 32 knights move at the same time).

Costs

Each square has a cost, which is a non-negative integer, initially set to zero. Each time a knight visits a square, the cost of that square is increased by 1. To be explicit, if N knights land on a square in the same turn, that square's cost is increased by N.

Penalties

After each turn, each knight incurs a penalty, which is the cost of the square it occupies, plus the number of other knights occupying the same square (regardless of whether they are friend or foe).

The player's cumulative penalty is zero at the start of a game, and is increased by each knight's penalty each turn (for all 16 of its knights).

Winning

A game ends after 1024 turns. The winner is the player with the lowest cumulative penalty.

Input

The player is supplied with:

• an array showing the cost for each square
• an array showing the number of its own knights for each square
• an array showing the number of its opponent's knights for each square
• an array showing the total knights for each square
• an array of coordinates for its own knights
• an array of coordinates for its opponent's knights
• its own cumulative penalty
• its opponent's cumulative penalty
• the turn number

Output

The player responds with a move for each of its 16 knights. Each move is a number from 0 to 7, indicating the direction to move, numbered clockwise from the top. The response must be received within 5ms.

Invalid moves

Since the edge of the board is impassable, sometimes there will be fewer than 8 valid moves available for a given knight. If an invalid move is given, it will be reflected vertically and/or horizontally to give a valid move, and that move will be made instead. This means every knight will move every turn - none will ever stand still.

Code

Each entry provides the body of a JavaScript function that is no more than 1024 bytes.

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Sandbox questions

• I'm not settled on which language to use yet. I like the idea of using a different language for each KotH. I'm considering maybe Japt or APL for this one. Ideally something terse since golfing is part of the challenge here.
• Fixed starting configuration (for example, players in a line along opposite edges of the board), or random initial placement?
• Leaning towards a board that does not wrap. Any reasons to avoid this?
• I've put placeholder values for the number of bytes, the size of the board, and the number of knights per player. Any feedback on how to improve these values welcome.
• I'm not sure whether to make staying still a valid move. I'd prefer to keep it simple and have 8 possible moves with no possibility of staying still.
• I'm currently deciding between the penalty being the cost plus the number of other knights on the same square, or the cost times the number of knights on the square.
• I need to settle on input and output that are suitable for both golfing the contestant code and keeping things running reasonably quickly.

Answer 27

Golf me some Golf

code-challenge game

Write a program to play Golf solitaire!
(I'm somewhat surprised that I haven't seen this pun yet.)

How to play

Golf uses a standard 52 card deck. Play begins with 7 stacks of 5 cards each, one card forming the foundation, and the remaining 16 cards forming the stock. There are two legal moves:

• Move a card from the top of a stack to the foundation (must be one rank higher or lower)
• Draw the top card of the stock and place it on the foundation

The number of cards remaining in the tableau when you run out of moves is your score, with zero being a perfect game.

To make things easier, queens may be played on kings, and aces and kings can be played on each other. Also, while the stock is normally face-down, you will be able to read it all at once.

Rules

The input to your program will be 7 lists of 5 cards representing the tableau (with the last cards on top) plus 1 list of 17 representing the stock (the last card being the foundation). These lists can be flattened as desired (you can take 1 list of 35 and 1 list of 17, or just 1 list of 52). Cards are represented as numbers 0-12.

Your program should output a list (or string) of numbers 0-7 representing the moves in a game of Golf. The numbers 0-6 represent playing a card from a column to the foundation, and 7 represents drawing a card from the stock. Any illegal moves (including playing from an empty column or stock) will disqualify your program.

Your score is the number of bytes in your program plus 2 bytes per card left on the stock after running through the 18 games in the scoring set. The program with the lowest score wins.

Test cases

Example output: (coming soon)

Scoring set: (coming soon)

All games in the scoring set are solvable.

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Sandbox questions:

• Is code-golf appropriate for this scoring metric, or would code-challenge be more appropriate?

• Should I do away with the scoring metric, and just require the games to be solved completely?

• Would it be more interesting to include some unsolvable games in the scoring set to make programs handle that case gracefully?

Answer 28

Permutation Encoding

Now posted to the main site. Check the revisions log if you want to see the WIP versions.

Answer 29

Distinct Dice Sum Algorithm

From a puzzle on Brainden. Paraphrasing,

What is the best set of 8 sided dice, each identical, such that 3 dice can generate 120 distinct sums? "Best" means the minimum highest sided die configuration.

With 7 sided dice, the best possible sides for each (identical) die is: 1, 2, 8, 51, 60, 79, 83.

For the sake of discussion, use sides=s, and dice=d.

Note1: 120 is the maximum number of distinct sums with s=8, d=3. The formula is:

$$ \frac{(s+d-1!)}{(s-1)!(d)!} $$

Similarly, for s=7, d=3, the formula gives 84. And brute force shows that a side of at least 83 is required for this easier problem.

Note2: The lowest numbered side is always 1 for an optimal solution to the original question. (See comments.)

My question is, "What's the fastest algorithm to discover the minimum highest sided die for maximum distinct sums?".

Specifically, is there some existing algorithm, or better yet, formula, for the minimum highest sided die? For determining all sides?

While there are obvious choices for languages, I'm not interested in that. I'm interested in the best algorithm possible in general. A sketch of the algorithm with the best (smallest) Big-O score wins.

Complexity of answers should be expressed by Big-O notation, e.g., M(s) = O(???), with d=3. Ties will be broken according to number of dice, i.e., M(s,d) = O(???).

As a puzzle toy to idle time some years ago, I wrote a brute force solver. Unfortunately, for (s=8, d=3), and even knowing an upper limit, my program never completed the search (uptime was an issue).

Answer 30

What is the simplest reversible circuit that computes conjugacy of transpositions?

math,permutations,logic-gates

Motivation

Reversible computation refers to computation in which little or no information is deleted. Reversible computation a major component of quantum computation, and reversible computation is potentially many times more energy efficient than conventional computation. I want to know how easy it is to compute the conjugacy of transpositions reversibly?

Challenge

Let T5 be the set of all transpositions on the set {1,2,3,4,5}. Let * be the conjugacy operation on T5 defined by x * y=xyx^(-1) (here concatenation denotes the group operation). In other words, the underlying set of T5 consists of all 10 pairs (a,b) of distinct numbers from {1,2,3,4,5} and where we declare (a,b)=(b,a). The operation * is the unique operation on the underlying set that satisfies

• (a,b) * (c,d)=(c,d),
• (a,b) * (b,c)=(a,c),
• (a,b) * (a,b)=(a,b)

whenever a,b,c,d are distinct.

What is the simplest n bit input reversible circuit C along with an injective function R:T5->{0,1}^n such that C(R(x),R(y))=(R(x),R(x*y)) for all x,y in T5?

The gate cost of a reversible circuit shall be the sum of the costs of every individual logic gate in the reversible circuit.

Here is the price chart per logic gate (see this link for a description of the logic gates) along with a description of the reversible gates.

Each SWAP gate (x,y)->(y,x) will have a cost of 0.

Each NOT gate x-> NOT x shall have a cost of 1.

Each CNOT gate (x,y)->(x,x XOR y) shall have a cost of 2.

Each Fredkin gate (x,y,z)->(x,(NOT x AND y) OR (x AND z),(x AND y) OR (NOT x AND z)) shall have a cost of 4 (the Fredkin gate can also be described as the reversible logic gate where (0,x,y)->(0,x,y) and (1,x,y)->(1,y,x)).

Each Toffoli gate (x,y,z)->(x,y,(x AND y) XOR z) shall have a cost of 5.

No other gates are allowed.

Observe that each reversible gate has the same number of inputs as it has outputs (this feature is required for all reversible gates).

The complexity of your circuit will be the product of the gate cost or your circuit with the number n which you choose. The goal of this challenge will be to minimize this measure of complexity.

Format

Complexity: This is your final score. The complexity is the product of the number n with your total gate cost.

Space: State the number n of bits that your circuit C acts on.

Total gate cost: State the sum of the costs of each of the individual gates in your circuit C.

NOT gate count: State the number of NOT gates.

CNOT gate count: State the number of CNOT gates.

Toffoli gate count: How many Toffoli gates are there?

Fredkin gate count: How many Fredkin gates are there?

Legend: Give a description of the function R. For example, you may write

(1,2)->0000,(1,3)->0001,(1,4)->0010,(1,5)->0011,(2,3)->0100, (2,4)->0101,(2,5)->0110,(3,4)->0111,(3,5)->1000,(4,5)->1001.

Gate list: Here list the gates in the circuit C from first to last. Each gate shall be written in the form [Gate type abbreviation,lines where the gates come from]. For this problem, we shall start with the 0th bit. The following list specifies the abbreviations for the type of gates.

T-Toffoli gate S-Swap gate C-CNOT gate F-Fredkin gate N-Not gate.

For example, [T,1,5,3] would denote a Toffoli gate acting on the 1st bit, the 5th bit, and the 3rd bit. For example, [T,2,4,6] produces the transformation 01101010->01101000 and [C,2,1] produces 011->001,010->010 and [N,3] produces 0101->0100. For example, one could write [S,7,3],[N,2],[T,1,2,3],[F,1,2,5],[C,7,5] for the gate list.

The gates act on the bit string from left to right. For example, the gate list [C,0,1],[C,1,0] will produce the transformation 01->11.

Sample answer

Complexity: 80

Space: 5

Total gate cost: 16

NOT gate count: 3

CNOT gate count: 2

Toffoli gate count: 1

Fredkin gate count: 1

Legend: (1,2)->00001,(1,3)->00011,(1,4)->00101,(1,5)->00110,(2,3)->01000,(2,4)->01011,(2,5)->01100,(3,4)->01110,(3,5)->10001,(4,5)->10011

Gate list: [N,1],[N,0],[N,4],[S,1,2],[S,2,3],[C,0,1],[C,2,3],[T,3,2,1],[F,4,3,2,1]

Sandbox