# What is the Sandbox?

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

See the Sandbox FAQ for more information on how to use the Sandbox.

## Get the Sandbox Viewer to view the sandbox more easily

To add an inline tag to a proposal use shortcut link syntax with a prefix: [tag:king-of-the-hill]

• How are tags added to questions? – guest271314 Jan 9 at 7:51
• @guest271314 You can use this markup to create a tag in a draft: [tag:code-golf] – DJMcMayhem Aug 29 at 15:19
• Why no featured anymore? Can't we have it auto-added or something? – JL2210 Sep 26 at 15:57
• @JL2210 We now have a permanent info box that links to the Sandbox, so the featured tag isn't necessary – caird coinheringaahing Sep 29 at 13:43

# Number of all hyperrectangle-filling walks

• size of the hyperrectangle – generally an n-tuple
• eg. (s,s) in case of a square
• position in the hyperrectangle – generally 0 <= pos[i] < size[i] for i-th dimension
• eg. (x,y) where 0 <= x < s and 0 <= y < s in case of a (s,s) square.

Your task: Find the number of walks in the hyperrectangle, which start at the given position and visit each cell of the hyperrectangle exactly once.

In the context of this task, a walk is a sequence of positions, such that each position after the first differs from the previous one in exactly one dimension by amount of exactly 1. Eg. in the case of a 2x2 square, a possible walk would be (0,0) -> (0,1) -> (1,1) -> (1,0).

Note: It doesn't matter whether x is vertical position and y horizontal or vice versa. Neither it matters whether coordinates grow downwards / upwards or to the left / right (eg. vertical axis might grow downwards or upwards without any effect on the result). These statements extend to higher dimensions as well.

## Example

Given size = (3,3) and pos = (0,0), there are 8 solutions. These can be divided into four equivalence classes under the relation of transposition, viz. A == Transpose(A). Only one solution for each equivalence class needs to be found, the other one can be obtained by simply transposing the first one.

The four "canonical" solutions:

Output: 8.

## Possible specializations

Specialization 1: Support only hypercubes (hyperrectangles with equal sizes in each dimension). Specialization 2: Support only 2-dimensional hypercubes (squares).

## My questions

2. Is this task (in its general form) too difficult? Would it be more reasonable to restrict it to one of the specializations (or to a different specialization)?

• Have you made a reference implementation? It seems to me that it would be worth generating some sequences for the two specialisations and seeing whether they're in OEIS, and whether closed forms for the answers and known. – Peter Taylor Oct 1 '17 at 20:11
• @PeterTaylor Those were my thoughts, but I haven't yet gotten around to making an implementation. I suspect the sequences for specializations (especially Spec. 2) will be in OEIS and most likely will have a closed-form solution, but it's in the higher dimensions where it gets interesting, especially if you consider optimizations based on symmetries. – kyrill Oct 1 '17 at 20:31
• @PeterTaylor I have written a (hopefully correct) implementation in Python 2; though it being a brute-force algorithm, higher dimensional hypercuboids may require some time to be examined... – Jonathan Frech Oct 8 '17 at 12:52
• The relevant OEIS sequence for a hypercube of side lengths 2, starting at one corner, is A003043. – Jonathan Frech Oct 8 '17 at 14:48
• I for one really like this challenge and do not think any specialization which makes the task easier is required. – Jonathan Frech Oct 8 '17 at 20:36

# Detect Ambiguity in a Context-Free Grammar

Sandbox notes:

• Is the background too hard to understand? If so, should I clarify it further at the risk of making it unreasonably long, or simply delete it and state that the reader should have a knowledge of context-free grammars?
• Is there anything I should clarify in the specifications?
• Are there any other tags I should add? I couldn't find any better ones.
• Should I add more test cases?
• Apparently at the moment this problem is undecidable (which I found out way too late). Would this problem be decidable if I let solutions assume that ambiguous grammars will always have an unambiguous counterpart (in other words, the program will never be given an inherently ambiguous grammar?

## Background

A Context-Free Grammar (CFG) is a set of rules for constructing strings. For example, the following is a CFG describing BF:

progcommand | command prog
command+ | - | , | . | < | > | loop
loop[ prog ]

Let's see how the BF program ,[-] can be constructed using this grammar:

Wikipedia formally defines a grammar as a group of four items:

• A set of nonterminals, which are the "variables". In the example above, these are prog, command, and loop.
• A set of terminals, which are symbols in the alphabet that strings are composed of. In the example above, these are the BF program characters +-,.<>[].
• A set of production rules, which define what nonterminals are allowed to become. Each rule consists of a head, which is a nonterminal, and a body, which is a list of terminals and nonterminals. In the example above, these are the production rules:
• progcommand
• progcommand prog
• command+
• command-
• ...
• commandloop
• loop[ prog ]
• One nonterminal that serves as the starting point for the grammar (in other words, the root node in the parse tree). In the example above, this is prog.

Consider the following context-free grammar:

bitstringbit | bit bitstring
bit1 | 0

It may be tempting to collapse the two lines:

bitstring1 | 0 | bitstring bitstring

The disadvantage of this representation over the original is that it is ambiguous - that is, given a string, it is possible to deriving that string in multiple different ways. For example, in this grammar, the string 101 may be derived as ((10)1) or (1(01)).

The problem with ambiguity is that there is not a single way to create a representation of the generation process, which is useful for e.g. parse trees.

## A useful subset of CFGs

To make CFGs easier to manipulate, we will constrain them in this way:

• Restrict the alphabet of terminals to 0 and 1,
• Identify nonterminals by a number rather than a name (either 0- or 1-indexed),
• Assume the first nonterminal (0 or 1 depending on indexing scheme) to be the initial one.

In this way, we have reduced the description of a CFG down to two inputs:

• A number representing the quantity of nonterminals
• A list of production rules, which is a list of pairs (head, body), where head designates a nonterminal for the head, and body is a list of terms which can be terminals or nonterminals.

Given a representation of a context-free grammar as described above, output a truthy or falsey value representing whether the grammar is ambiguous.

This is , so the shortest valid submission (measured in bytes wins).

## Specifications

• You can use any two distinct non-empty strings instead of 1 and 0 for the terminals.
• You can assume the lists representing the bodies of the production rules are nonempty.
• You may take input in any reasonable format. If you are taking input as a number and a list and your language does not support mixed-type lists, you can assume the existence of two special nonterminals that represent the terminals 0 and 1. If this is done, please specify the two nonterminals in your answer.
• You can assume that every nonterminal can "halt", that is, be mapped to a finite string of nonterminals. This means that you will never get an input like:

string0 string | 1 string

This also means that every nonterminal must have at least one production rule.

• Keep in mind that production rules are technically a set. The order of the rules is not relevant, so your program should be able to handle them in any order.
• You can assume there will be less than 100 production rules, and therefore less than 100 distinct nonterminals.
• You can assume that the input will be a well-formed CFG in whatever input format you designate.

## Test Cases

In these examples, nonterminals are zero-indexed.

### Ambiguous (Truthy)

Only empty strings:

1, [
(0, []),
(0, [0])
]


string | string

Any string of bits:

1, [
(0, []),
(0, ["0"]),
(0, ["1"]),
(0, [0, 0])
]


string | 1 | 0 | string string

Nonempty strings of ones, separated by zeroes:

2, [
(1, ["1"]),
(1, ["1", 1]),
(0, [1]),
(0, [0, "0", 0])
]


stringones | string 0 string
ones1 | 1 ones

Odd-length strings of bits:

1, [
(0, ["0"]),
(0, ["1"]),
(0, [0, 0, 0])
]


string0 | 1 | string string string

1 and 0 balanced like parenthesis:

1, [
(0, []),
(0, ["1", 0, "0"]),
(0, [0, 0])
]


string | 1 string 0 | string string

### Unambiguous (Falsey)

Only empty strings:

1, [
(0, [])
]


string

Any string of bits:

1, [
(0, []),
(0, ["0", 0]),
(0, ["1", 0])
]


string | 0 string | 1 string

Nonempty strings of ones, separated by zeroes:

0, [
(0, [1]),
(0, [1, "0", 0]),
(1, ["1"]),
(1, ["1", 1])
]


stringones | ones 0 string
ones1 | 1 ones

Odd-length strings of bits:

2, [
(0, [1]),
(0, [1, 1, 0]),
(1, ["0"]),
(1, ["1"])
]


stringbit | bit bit string bit0 | 1

1 and 0 balanced like parenthesis:

1, [
(0, []),
(0, ["1", 0, "0", 0])
]


string | 1 string 0 string

• I think the CFG is described quite well, but the "useful subset" seems a little confusing - you restrict terminals to [0,1] and non-terminals to numbers and say "...body is a list of terms which can be terminals or nonterminals", but in the examples you have bodies containing quoted numbers. – Jonathan Allan Aug 24 '17 at 23:39
• @JonathanAllan Yes, the quoted ones are terminals, and the unquoted ones are indices of nonterminals. I might change that if it turns out to be too complicated. – Esolanging Fruit Sep 21 '17 at 2:24

# Is it Odd or Even

A group is an "Odd or Even group" if there is some member a such that every member in the group can be represented as either k • k or k • k • a.

For example the group Z4 is an even odd group if a = 1

0 = 2 • 2             Even
1 = 2 • 2 • 1         Odd
2 = 1 • 1             Even
3 = 1 • 1 • 1         Odd


The even and odd members can overlap, for example in Z5 if a =1 every member is both even and odd.

0 = 0 • 0 = 2 • 2 • 1 Even and Odd
1 = 3 • 3 = 0 • 0 • 1 Even and Odd
2 = 1 • 1 = 3 • 3 • 1 Even and Odd
3 = 4 • 4 = 1 • 1 • 1 Even and Odd
4 = 2 • 2 = 4 • 4 • 1 Even and Odd


An example of a group that is not an Even or Odd group is the Klein-4 group (Z2×Z2), because k + k = 0 for all k meaning there can be only one even member and one odd member despite there being 4 members of the group.

Given the Cayley table of a finite group determine if it is a Odd or Even group. You will be guaranteed that the input is a group, but you will not be guaranteed anything else. This is a so your code should output two distinct values one for accept and one for reject.

Answers will be scored in bytes with fewer bytes being better.

## Test cases

### True

0 1
1 0

0 1 2 3
1 2 3 0
2 3 0 1
3 0 1 2

0 1 2 3 4
1 2 3 4 0
2 3 4 0 1
3 4 0 1 2
4 0 1 2 3

0 1 2 3 4 5
1 0 4 5 2 3
2 5 0 4 3 1
3 4 5 0 1 2
4 3 1 2 5 0
5 2 3 1 0 4


### False

0 1 2 3
1 0 3 2
2 3 0 1
3 2 1 0

0 1 2 3 4 5 6 7
1 2 3 0 5 6 7 4
2 3 0 1 6 7 4 5
3 0 1 2 7 4 5 6
4 5 6 7 0 1 2 3
5 6 7 4 1 2 3 0
6 7 4 5 2 3 0 1
7 4 5 6 3 0 1 2

• The first paragraph is difficult to understand: It is not very clear that you define the terms "even" and "odd" and that the definition is dependent on a. Furthermore you first talk about numbers, but then talk about members of a group, so I'd avoid mentioning numbers, and perhaps link the wikipedia page about groups. The additive notation suggests you're only considering abelian groups, is that true? I'd also define first Z_n as the cyclic group of order n. – flawr Oct 5 '17 at 19:52
• Next question: The definition of "even" and "odd" seems to depend on a, so what is a then in your test cases? – flawr Oct 5 '17 at 19:55
• @flawr I'll try to clean up the first bit but addressing your second question. In the truthy examples a can be any member of the following sets {1}, {1,3}, {0,1,2,3,4}, {1,2,3} (same order as examples). – Wheat Wizard Oct 5 '17 at 20:02
• @flawr Is that a better explanation? – Wheat Wizard Oct 5 '17 at 20:04
• Yes now it is a lot clearer! One question remains, do you only consider abelian groups? – flawr Oct 5 '17 at 20:29
• @flawr No, the 4th test case is the dihedral 6 group which is not commutative. – Wheat Wizard Oct 5 '17 at 21:02
• In that case you'd probably be better off using multiplicative notation and explicitly saying that it is possible that the operation is noncommutative. – flawr Oct 5 '17 at 21:05
• I think you should add some more explanation about the input, without some knowledge of group theory one cannot understand what is a Cayley table or what to do with it. (You use just $Z4$ or $Z5$ in your explanation, but then there are tables in the test cases, which is confusing) – Leo Oct 6 '17 at 4:34
• Could use a test case where the number of distinct squares is at least half the size of the group but the group is not odd or even. – Peter Taylor Oct 6 '17 at 7:33
• @PeterTaylor I'd rather not. The test cases are already much larger than the rest of the question, and there are not a lot of falsy cases. If there is such a case then it would be enormous. – Wheat Wizard Oct 6 '17 at 13:04

# Evaluate a Starting Position in a Partitioning Game

Two players play a partitioning game. At the start of the game, there are n stones, all in a single heap. When a player takes a turn, they must divide an existing heap into two, ensuring that every heap still has a distinct size. The game is over when a player has no legal moves; that player loses.

For example, suppose that Max and Min are playing with n=6. Initially it is Max's turn, and he divides the starting heap into a heap of size one and a heap of size five. Min then divides the heap of size five into heaps of size two and three (her only option because she cannot make another heap of size one). Max, seeing heaps of size one, two, and three, has no legal move and loses.

Alternatively, Max could have split the size-six heap into heaps of size two and four. But then Min could not split the heap of size two (she would end up with both new heaps having size one), nor could she split the heap of size four evenly (for the same reason), so she would be forced to split the heap of size four into heaps of size one and three. Max would have lost anyway.

Since Max, the player to move first, has no winning strategy at n=6, call six a losing number. Similarly, call values of n for which Max can win (at least if he plays cleverly) winning numbers. Max wants a way to distinguish winning and losing numbers for his upcoming rematch against Min.

Write a program or function that, given an n, returns or outputs one value for losing numbers and a distinct value for winning numbers. For testing purposes, the first 50 winning numbers are:

3, 4, 5, 10, 11, 12, 13, 14, 21, 22, 23, 24, 25, 26, 27, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 78, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93


(This sequence is related to, but distinct from A161983.)

Rules and scoring are as usual for . The checkmark will go to an answer with well-explained and/or especially clever golfing, even if it doesn't compete with terser languages.

# Generate a program to output a string in yup

yup is an older language of mine with the following commands:

0   Pushes 0 to the stack.
e   Takes an argument N and pushes exp(N).
|   Takes an argument N and pushes ln(N).
~   Switches top two items on stack.
:   Duplicates the top item on the stack.
-   Subtracts the top of stack from the second-to-top of stack.
{   Begin while loop (while top of stack is positive and is defined).
}   End while loop.
$Reverse the stack. [ Moves the bottom of the stack to the top of the stack. ] Moves the top of the stack to the bottom of the stack. * Pushes an input item (char/number) to the stack. \ Terminates the program. @ Outputs top of stack as a character. (When used on a non-int, rounds the real portion.) # Outputs top of stack as a number.  For example, the program 00e pushes 0, then 0, then pops a 0, pushing exp(0), yielding the stack [0, 1]. ## Rules Your challenge, should you choose to accept it, is to create a program that, when given a string, outputs a short yup program that would output the given string. Your score is determined by the total number of bytes used to generate all test cases below. ## Test cases Formatted as a .JSON file (array of strings): ["Hello, World!", " !\"#$%&'()*+,-./0123456789:;<=>?", "ABCDEFGHIJKLMNOPQRSTUVWXYZ", "zyxwvutsrqponmlkjihgfedcba", "AaBbCcDdEeFfGgHhIiJjKkLlMmNnOoPpQqRrSsTtUuVvWwXxYyZz", "", "[[<<>>]]", "adksjf 9823-0 =-ao0sdf';zlx", "b662bf6c7a7cac66561025cf2509506f", "yup", " ~!}", "death surely will find us all", "NO_ONE_IS_HERE", "Ra Ra Rasputin", "hello\nWORLD", "*0e-{0e-}#", "            ", "go play nethack", "\ttabs\n vs spaces\r\n", ".", "~", "it is not necessarily unfair that we can single-handedly close challenges, --MrXcoder", "\nconst math = require(\"mathjs\");\nconst escape = require(\"escape-string-regexp\");\nconst Stack = require(\"./stack.js\");\nconst entries = require(\"./entries.js\");", "Never gonna give you up\nNever gonna let you down\nNever gonna turn around\nAnd outgolf you", "010100101000001000100111101010", "O0O0O0OOOO00O000O0OOOO0O00O0", "[0, [1, [2, 3], 4], 5]", "(()()()))))(()()))"]


If I feel submissions too heavily optimize for the given inputs, I will use a second set of words, with an md5hash of 30272eee598205bab2904e9768502517.

• Will you use the second set of words for all submission or only the one you feel like it's optimized? Also why not just combine both sets in any case? – ბიმო Oct 26 '17 at 16:55
• @BruceForte Once I feel that there are optimized answers, I will use the second list. (It's really just a variation of the first list with changed characters and similar, to ensure optimizing some constants but not others is prohibited) – Conor O'Brien Oct 26 '17 at 17:13

# The XOR Quines!

Your challenge is to make a program that outputs its source code but when each of its bytes are XORed with its answer number, it outputs the source code of the previous program.

For example, if the previous program was:

print 1


and your program is number #2, than your program could be this:

cngpv*%rpklv"3%+


cngpv*%rpklv"3%+


and when each byte is XORed with 2, you get:

alert('print 1')


which outputs the previous program:

print 1


Note that the first program doesn't have to do anything other than output its own source code.

The second-to last answer after a month of no answers posted wins.

• This is going to be too hardcore. – someone Oct 25 '17 at 12:21
• This is going to be way too hard except in certain esolangs. Since every answer builds off of the previous one, they are probably going to get bigger. I would recommend starting with a simple esolang that ignores most characters. – Esolanging Fruit Oct 25 '17 at 15:53

# Insertion sort counter

Calculate the number of moves necessary to do an insertion sort of an input vector containing positive integers.

Insertion sort iterates, consuming one input element each repetition, and growing a sorted output list. At each iteration, insertion sort removes one element from the input data, finds the location it belongs within the sorted list, and inserts it there. It repeats until no input elements remain.

You must count the number of times a number is moved from its original position. For instance, the vector [1,2,3,4] requires no moves, as it's already sorted, while the vector [1,3,4,2] requires one move, since the last 2 must be moved two places to the left.

### Example:

Input:
[6, 5, 3, 1, 8, 7, 2, 4]
Sorting:
0: [6, 5, 3, 1, 8, 7, 2, 4]
1: [5, 6, 3, 1, 8, 7, 2, 4]
2: [3, 5, 6, 1, 8, 7, 2, 4]
3: [1, 3, 5, 6, 8, 7, 2, 4]
4: [1, 3, 5, 6, 7, 8, 2, 4]
5: [1, 2, 3, 5, 6, 7, 8, 4]
6: [1, 2, 3, 4, 5, 6, 7, 8]
Output: 6


### Test cases:

• You should describe what an insertion sort is, for those who don't know. – Okx Oct 24 '17 at 9:13
• Will do :) Thanks. – Stewie Griffin Oct 24 '17 at 9:13
• As defined, the answer is always len(input). I've no idea what the example is supposed to show (or how it's counting). – Peter Taylor Oct 25 '17 at 7:27
• @PeterTaylor The number of insertions (maybe I should call it moves, or something else?) necessary for the array [1, 2, 3, 4] is zero. The number of moves for the array [1, 3, 4, 2] is one, since the only number that must be moved when using the insertion sort algorithm is the last 2, that must be moved two steps to the left, resulting in a sorted array. Placing a number back in its original position doesn't count as an insertion/move. Does that make sense? – Stewie Griffin Oct 25 '17 at 7:58
• So "Count the number of array elements a[i] which are not the greatest element in a[:i+1]"? – Peter Taylor Oct 25 '17 at 8:25
• I guess that's another way to put it, yes... – Stewie Griffin Oct 25 '17 at 8:53
• Maybe you could have it count the number of swaps assuming that you can only move a number by swapping it with one of its neighbors (and many implementations of insertion sort actually do this, especially those operating on arrays). For example, the number of moves for [1,3,4,2] would be 2, because the number 2 must be shifted twice to the left. – Leo Oct 26 '17 at 4:37
• That's actually a good idea. Thanks! :) I'll probably change it when I get the time. :) – Stewie Griffin Oct 26 '17 at 6:04

# Tear Down that Wall

Related (dupe?)

• This is my first time submitting a challenge.
• Suggestions and constructive criticism are always welcome.

### Cops:

As the cop, your task is to create a code that outputs this ASCII wall:

___|___|___|___|___|___|___|___|___|__
_|___|___|___|___|___|___|___|___|___|
___|___|___|___|___|___|___|___|___|__
_|___|___|___|___|___|___|___|___|___|
___|___|___|___|___|___|___|___|___|__
_|___|___|___|___|___|___|___|___|___|
___|___|___|___|___|___|___|___|___|__
_|___|___|___|___|___|___|___|___|___|
___|___|___|___|___|___|___|___|___|__
_|___|___|___|___|___|___|___|___|___|
___|___|___|___|___|___|___|___|___|__
_|___|___|___|___|___|___|___|___|___|
___|___|___|___|___|___|___|___|___|__


However, by deleting some part(s) of the code, it must also output a broken wall:

___|___|___|___|___|___|___|___|___|__
_|___|___|___|___|___|___|___|___|___|
___|___|___|___|___|___|___|___|___|__
_|___|___                    |___|___|
___|___|_                    __|___|__
_|___|___                    |___|___|
___|___|_                    __|___|__
_|___|___                    |___|___|
___|___|_                    __|___|__
_|___|___                    |___|___|
___|___|_                    __|___|__
_|___|___                    |___|___|
___|___|_                    __|___|__


## Rules:

1. Your code must terminate in a reasonable amount of time as long as it's correct. That means that the whole code and the correctly broken code must output the wall (broken or not) within 60 (too much or too little time? sugestions?) seconds. That doesn't apply if the code is incorrectly broken by the robber.
2. The broken wall needs to be output(ted? English is hard) without addition of code.
3. You may obfuscate the code as much as you see fit. (does hashing/encrypting count as obfuscating? if so, should it be allowed?)
5. Your wall will be safe if, after 1 week, it hasn't been broken. You must also reveal the answer. Your wall will not be safe until you have revealed the answer.
6. The outputs must match the exact ASCII walls provided. Leading/trailing newlines are allowed as long as the output matches the one provided. The walls consist of 13 lines and 38 columns of the characters | and _. The broken section of the wall is a block of 20 whitespace characters per line, beginning at the fourth line. The "padding" is of 9 characters (| or _) to either side of the whitespace block.
7. Preferably, include a link to an online interpreter for your chosen language.

(any other rules suggestions?)

## Rules:

1. You may not add any code to the answer, only delete.
2. The code is considered broken if and only if it outputs the entire broken wall.
3. The broken code must be a valid submission in the same language as the original code.

• Suggestions?

# Square-free Rock-Paper-Scissors tournament

On the day of the Codegolf Rock-Paper-Scissors tournament you hear through the grapevine that everybody else is going to play a fix square-free sequence (a sequence made of the letters R, P, S is square-free if it does not contain a subsequence that repeats twice. See Don't repeat yourself in Rock-Paper-Scissors for details.)

Write a program that for a game of N rounds, in each round n

1. prints one of R, P, S - its own nth hand (using all information gained so far)
2. receives an input of either R, P, S - the nth letter of the opponent's sequence

## Rules

• Rock beats scissors, scissors beats paper, paper beats rock.

• The "opponents" are all the square-free sequences of the given length.

• Your program may read the opponents moves at once and print its own moves - as long as it is functionally equivalent to a program reading the moves in the order specified in section "task".

• The program does not carry a state between playing against different opponents.

• Each entry should include a scoring script computing the score of the candidate against all square-free sequences of length N.

## Scoring

I am posting this to get some input about interesting scoring methods and a good choice of N.

Programs should score high if they win against a large fraction of square free sequences in an economic way. A possible criterium of "winning" against a single sequence is winning more hands against an opponent than losing. A possible criterium of scoring high is number of games won divided by the root of bytes.

• I'd say 16 could be a good choice for N, this would give 798 different opponents, which are still a manageable amount, and each game would probably be long enough to make the square-free analisys matter – Leo Oct 31 '17 at 3:39
• To win with a small margin it is enough to exploit that the sequence does not repeat. I think we need to put the winning margin into the score or put a threshold. – mschauer Oct 31 '17 at 7:58
• Maybe (rounds won - rounds lost)/bytes^2 , where rounds are counted from all the matches together – Leo Oct 31 '17 at 8:50

# Can You Catch the Robber?

This is not a cops and robbers type challenge, but a code-golf challenge based on the PBS Infinite Series video Cops and Robbers Theorem.

## Challenge

You will be given an undirected and connected graph. You may also assume the graph contains no self-loops; that is, the graph will not contain a vertex with an edge connecting to itself. You must determine if the graph is cop-win. That means that if a cop and robber start at any vertex, the cop will eventually land on the same vertex as the robber, with the cop and robber taking turns traversing one edge at a time, starting with the cop. Both the cop and the robber are playing optimally and have the option to not move on their turn.

If you haven't watched the video, let me explain how to simplify the problem. First, let's start with a definition. A pitfall is any vertex v whose neighbors are all a distance of 0 or 1 from a common vertex w, where v is not equal to w. To determine if a graph is cop-win, you must repeatedly remove pitfalls and the edges that connect to it until the graph is reduced to a single vertex or there are no more pitfalls to remove. If the graph can be reduced to a single vertex in this way, it is cop-win. A couple visual examples follow.

### Example 1

>o---o---o
\ / \ /
o---o
\ /
o

o---o<
/ \ /
o---o
\ /
o

>o
/ \
o---o
\ /
o

>o---o
\ /
o

>o
/
o

o


Result: Cop-win

### Example 2

  o---o---o<
/     \   \
o---o   o---o
\   \ /   /
o---o---o

o---o
/     \
o---o   o---o
\   \ /   /
o---o---o<

o---o
/     \
o---o<  o---o
\   \ /
o---o

o---o
/     \
o       o---o<
\     /
o---o

o---o
/     \
o       o
\     /
o---o


Result: Not cop-win

## Examples

Input: [[2,3],[2,4],[0,1,3,4,6],[0,2,5,6,8],[1,2,6,7,9],[3,8],[2,3,4,8,9,10],[4,9],[3,5,6,10],[4,6,7,10,11],[6,8,9,11],[9,10]]
Output: Truthy

Input: [[3],[4],[5],[0,5,6],[1,6],[2,3,7],[3,4,8],[5,9],[6,9,10],[7,8,11],[8],[9,12],[11]]
Output: Falsy

Input: [[1,2],[0,3],[0,3],[1,2]]
Output: Falsy

Input: [[1,2,3],[0,2,3],[0,1,3],[0,1,2]]
Output: Truthy

## Rules

You may take input as an adjacency list, adjacency matrix, or list of edges, whose vertices may be 0-indexed or 1-indexed. Your output must be a truthy or falsy value. This is , so the least number of bytes in each language wins.

### Notes

This is my first post; I could certainly benefit from some help in formulating and polishing my challenge. If anyone believes my language was ambiguous or contradictory to what was said in the video, please help me clarify.

• What is the input here? It looks a list of each vertex's neighbors, but could you clarify? – KSmarts Oct 3 '17 at 15:16
• Yes that's what I was going for, an adjacency list. A map of each vertex to a list of its neighbors. – kamoroso94 Oct 3 '17 at 16:34
• This looks like a good question: meaty enough that there's something to golf, but simple enough not to scare everyone away. What I would suggest is flexibility in the input: allow people to choose whether to take input as adjacency matrix, adjacency list in the format you've used for the test cases, or list of edges. Also, allow people to use 1-indexed vertices rather than 0-indexed if they prefer. – Peter Taylor Oct 10 '17 at 8:18
• I definitely agree with your suggestion of input leniency. I'll update the challenge. – kamoroso94 Oct 12 '17 at 8:57
• I'd suggest explaining what a cop-win graph is in full, including the start positions and that both players play an optimal strategy. A link to a non-video explanation would also be good for anyone who can't or doesn't want to watch a video. – xnor Oct 12 '17 at 21:06
• Thank you for the feedback, @xnor. I've worked it into the challenge. I feel it's an improvement. I think that the visual examples take up too much vertical space, so I'm not sure if I should include them or not. – kamoroso94 Oct 31 '17 at 2:17
• IIRC it shouldn't be "start at any vertex", but the selection of the start position is part of the game, also under condition of optimal play, with the cop selecting their position first. – Christian Sievers Oct 31 '17 at 13:00

# Polynomial Partition

META: Right now I'm wondering whether it would be a more interesting challenge to have two imput lists, and the program just needs to find a polynomial that separates the two lists (i.e. no connected component can contain points of both classes. Or altnernatively f(x,y)>0 for all (x,y) in list A, and f(x,y)<0 for all (x,y) in list B.

Given a finite list of at at least two points in the plane ℝ² (all points in the list are unique), your program should find a polynomial f in ℝ[x,y] whose zero locus Z(f) := {(x,y) ∊ ℝ² | f(x,y) = 0} partitions the plane such that each of the connected components of ℝ²\Z(f) contains at most one point of the input list. The goal is finding such an f of a low degree. (It does not have to be optimal.) Note that no point of the input list may be contained in Z(f).

### Scoring

The score for each test cases is the degree of the polynomial that your algorithm produces. The total score is the product of the scores of the testcases.

### Examples

The points {(0,0),(0,2)} can be separated by f(x,y) = y - 1 (degree 1) or f(x,y) = x² + y² - 1 (degree 2) or f(x,y) = x³ + 1 - y(degree 3) or (infinitely) many more.

The points {(1,1),(-1,1),(-1,-1),(1,-1)} can be separated by f(x,y) = xy (degree 2).

### Test Battery

to be included...

• (1) I presume that the words "a different" are missing from "each of the inputs is in ^one of the connected components". (2) Is the optimal solution not going to be one of the easiest approaches? – Peter Taylor Nov 3 '17 at 11:44
• Thanks for the feedback, I rewrote (1), regarding (2): One very easy not optimal solution would be making a a small enough circle around every point, so I guess it depends. – flawr Nov 3 '17 at 14:43

# Palindromic Collapse

Given a string s, traverse from left-to-right, finding the first prefix that is a palindrome. When you encounter the first prefix palindrome, remove the end-half of the palindrome. Insert it back into the original string, then restart again from the left side of the new word. Return the final result when no prefixes are palindromes.

Take for example "babble":

• First check would be [ba]bble, which is not a palindrome, move on.
• Second check would be [bab]ble, which is a palindrome (bab).
1. Compress the palindrome to the first "half", [bab] becomes [ba].
2. Reattach this in place of the original palindrome, resulting in [ba]ble
• Next we repeat, finding [bab]le again, and resulting in [ba]le after steps 1 and 2.
• We then iterate through the full word again, finding no palindromes, returning bale.

# More Examples (worked out)

moom

[mo]om (not a palindrome)
[moo]m (nont a palindrome)
[moom] (palindrome) -> [mo]
[mo]   (not a palindrome, done).


Final returned result: mo

abalbalba

[ab]albalba (not a palindrome)
[aba]lbalba (palindrome) -> [ab]lbalba
[ab]lbalba  (not a palindrome)
[abl]balba  (not a palindrome)
[ablb]alba  (not a palindrome)
[ablba]lba  (palindrome) -> [abl]lba
[ab]llba    (not a palindrome)
[abl]lba    (not a palindrome)
[abll]ba    (not a palindrome)
[abllb]a    (not a palindrome)
[abllba]    (palindrome) -> [abl]
[ab]l       (not a palindrome)
[abl]       (not a palindrome, done)


Final returned result: abl

# More 1-1 Examples

amanaplanacanalpanama -> amnaplanacanalpanama
1232132121            -> 123
1232132145            -> 12345
01001000123210        -> 01123210
01000000000000000001  -> 011
010101                -> 011
abbabababaa           -> ab
hellollehworld        -> helloworld
world                 -> world
<empty string>        -> <empty string>

• You like palindrome a lot, don't you? – Mr. Xcoder Nov 7 '17 at 20:00
• @Mr.Xcoder in all fairness it looks like Oliver Ni likes them more. – Magic Octopus Urn Nov 7 '17 at 22:06

# Explanation

You must decide whether the input represents a valid StarCraft II Build Order. Here is how you will decide:

1. Start with the first word (it will be the race, Zerg, Protoss, or Terran)
2. Set the list of valid units to just the ones from that race (explained later)
3. Loop through the input (split by space)
1. Check if the unit is in the list of valid items for the listed race
• Otherwise, output Invalid item + the listed item's name
2. Check that the player has enough supply to sustain that unit (if it's a unit) (explained later)
3. Check that the player has the prerequisites for that item

# Units and Structures

(will be listed in real question)

Example:

Terran:

• CommandCenter 0 supply, requires SCV gives +15 supply
• OrbitalCommand 0 supply, requires CommandCenter (consumes)

Zerg:

• Hatchery -1 supply, requires Drone (consumes) gives +6 supply
• Drone 1 supply, requires Hatchery
• SpawningPool -1 supply, requires Hatchery, Drone (consumes)

Protoss:

• Nexus 0 supply, requires Probe gives +15 supply

# StarCraft II Mechanics

At the beginning of the game, the player starts with a town hall (Nexus, CommandCenter, or Hatchery + Overlord) and 12 workers (Probe, SCV, or Drone).

Supply is the maximum number of units one can have. Supply Depots, Pylons, and Overlords give more supply.

The sum of the supply of all produced units can never exceed the current supply value (we ignore Zerg hacks).

The Supply cannot exceed 200.

# Input

You will receive an input in any valid way in this format:

Race <item> <item> .....


There will be at most 99 items, and they will be at most 30 chars long.

The race will be one of Zerg, Protoss, or Terran.

# Lines per file

Can't believe it was not questioned yet.

I want the shortest script you can supply to take on all files on a directory and output a list in the format

file number_of_lines

Every possibility should be accounted as a valid line terminator:

- <CR>
- <LF>
- <CR><LF>
- <LF><CR>


No winner, it is a per language basis. Still thinking if I should give some bonus for sorting by line count.

• Duplicate. Not the same but pretty much the same idea, would definitely get closed for dupeness. – Rɪᴋᴇʀ Nov 14 '17 at 18:58
• @Riker: Counting lines requires some more effort than the file's byte size! I had even posted an answer on that question! – sergiol Nov 14 '17 at 21:18
• It's literally just wc -l to count lines.. I'm not sure about most of the others, but I know at least my bash can be trivially modified to count lines. – Rɪᴋᴇʀ Nov 14 '17 at 21:33

# Prune my tree

Given a well-formed ASCII art tree and the name of a node, print or return a new, well-formed tree with that node and any children removed.

†Contains non-ASCII characters.

## Example

Given this input tree:

A
├ B
├ C
│ └ D
└ E


...and the node name E, the following should be returned:

A
├ B
└ C
└ D


## Well-formed trees

Rather than an exhaustive spec, I'll define well-formedness by example:

A
├ B
├ C
├ D
│ ├ E
│ └ F
├ G
│ └ H
│   ├ I
│   │ ├ J
│   │ └ K
│   └ L
└ M
├ N
│ └ O
│   └ P
├ Q
└ R


The above is the only valid way to represent this tree (rules above re: trailing spaces and newline apply here and henceforth). Note that:

1. The tree is rendered with some strict subset of the characters ├, │, └, AZ, space, and newline.
2. The tree has one root node (in this example A) with no characters to its left or right.
3. Each line has exactly one node.
4. Each └ and ├ is followed by a single space (required) and node name.

## Rules

• Standard loopholes are forbidden.
• This is an challenge; input and output must be a string or array of lines or equivalent, per standard rules.
• Trailing spaces and/or a single trailing newline are allowed in both input and output.
• You may use any character encoding, as long your solution prints or returns characters equivalent to ├, │, and └. (ASCII characters like +, | (pipe) and L (capital "l") are not equivalent.)

### Input

• The input tree will have at least one node.
• The given named node may or may not exist in the tree. If it does not exist, the original tree should be returned.
• Each node name will be a single character between A and Z inclusive. Node names will be unique and there will be no more than 26 nodes.
• Node names are not guaranteed to be contiguous nor in any particular order, e.g. the following is possible input:

Q
└ D


### Output

• The output tree may have zero nodes.
• The order of the remaining nodes in the output tree must be the same as the input tree.

## Scoring

This is . The shortest solution in bytes wins.

🌟Freebies🌟: If the literal characters ├, │, or └ appear in your source code, you may count them as one byte each, per occurrence.

## Test cases

I'll reuse a few trees for multiple test cases.

1. Input tree:

A

• Output if A removed:



• Output if B removed (B doesn't exist):

A

2. Input tree:

A
├ B
├ C
│ └ D
└ E

• Output if C removed:

A
├ B
└ E

• Output if D removed:

A
├ B
├ C
└ E

• Output if E removed:

A
├ B
└ C
└ D

3. Input tree:

A
├ B
├ C
├ D
│ ├ E
│ └ F
├ G
│ └ H
│   ├ I
│   │ ├ J
│   │ └ K
│   └ L
└ M
├ N
│ └ O
│   └ P
├ Q
└ R

• Output if H removed:

A
├ B
├ C
├ D
│ ├ E
│ └ F
├ G
└ M
├ N
│ └ O
│   └ P
├ Q
└ R

• Output if L removed:

A
├ B
├ C
├ D
│ ├ E
│ └ F
├ G
│ └ H
│   └ I
│     ├ J
│     └ K
└ M
├ N
│ └ O
│   └ P
├ Q
└ R

• Output if M removed:

A
├ B
├ C
├ D
│ ├ E
│ └ F
└ G
└ H
├ I
│ ├ J
│ └ K
└ L


# Questions for sandbox:

1. Enough/too many/missing test cases?
2. Enough/too many/missing details re: input/output?
• I would just make this an (actual) ASCII-art challenge. Up to you but meh – HyperNeutrino Nov 13 '17 at 19:24
• Given the proximity to Christmas, you could go for "trim the tree" as the title. – Nissa Nov 13 '17 at 21:47
• I think you should show the larger test case(s) with A removed. I know/guess it will be an empty output, but still, it's a corner case that will benefit from being properly shown. – Stewie Griffin Nov 15 '17 at 12:24
• I like the idea, but I too would prefer ASCII-only. Non-ascii adds a bunch of bytes without adding anything to the challenge itself. – Stewie Griffin Nov 15 '17 at 12:29

# Smallest Proth Prime Power

A Proth Prime is a prime number of the form (k*2^n)+1.

## The Challenge

Given a positive integer k, return the smallest non-negative integer n such that (k*2^n)+1 is a prime.

This is code-golf, so smallest answer in bytes will win!

OEIS link for sequence shifted by 1, with alternative calculation method

## Test cases:

Input Output
1     0
2     0
3     1
4     0
5     1
6     0
7     2
8     1
9     1
10    0
11    1
12    0
13    2
14    1
15    1
16    0
17    3
18    0
19    6
20    1
46    0
47    583
48    1


### TODO:

• Rework preamble
• More/better test cases?

# Make a program run infinitely code-golf

For this challenge, you will be given a program in a very simple stack-based 2D language (that will be specified by this challenge), and your task is to find an input that will make it run infinitely (i.e. make it have 0% probability of halting). For the sake of this challenge, it will be fully deterministic; that is, no random functions will exist.

# Language specifications

The program runs on a 2D cartesian grid and there is a single pointer with an (x, y) coordinate and a direction (up, down, left, or right). The memory is stack-based. The pointer starts in the top-left corner at (0, 0), moving to the right. After each command is finished executing, the pointer moves one space in the direction it is currently facing. The grid is cylindrical on both sides. The following commands exist:

## Movement

### Absolute

^ pointer direction becomes "up"
> pointer direction becomes "right"
v pointer direction becomes "down"
< pointer direction becomes "left"


### Relative

] rotate pointer direction right 90 degrees (up -> right -> down -> left ->)
[ rotate pointer direction left 90 degrees (up -> left -> down -> right ->)
# invert pointer direction (up -> down ->, left -> right ->)
| horizontally reflect pointer direction (left -> right ->)
_ vertically reflect pointer direction (up -> down ->)
\ diagonally reflect pointer direction (up -> left ->, down -> right ->)
/ diagonally reflect pointer direction (up -> right ->, down -> left ->)


## Operators

+ push pop + pop
- push pop - pop
* push pop * pop
: push pop / pop (integer/floor division)
% push pop % pop (modulo; the result is the same sign as the base)


## Stack Operations

. pop a value
, get a value from the input and push it to the stack
$swap the top two values of the stack & duplicate the top value of the stack  ## Conditionals ! if the top of the stack is falsy, move the pointer an extra step in its current direction (skip next command) ? if the top of the stack is truthy, rotate right, otherwise, rotate left  ## Other space: do nothing 0-9 : push the value of that digit ; : terminate  You will be given a 2D grid in any desired format (newline-delimited string, array of lines, array of arrays of character, etc). You may assume that all rows are of the same length. You can choose any set of characters to represent these; in other words, any bijection between a set of characters or a set of integers and the characters ^v<>[]#|_/\+-*:;%.,$&!? 0123456789 is valid.

You must return an array of numbers in any reasonable format where when these values are fed one-by-one into the program as inputs, the program will not terminate. There may be more than one such solution; if so, you must return at least one of them, and you do not have to be consistent in which ones you return, as long as at least one is returned. Note that the array must be finite; that is, if it keeps looping through a ,, then it does not count as a solution. There is always at least one solution.

After the program is run, no inputs should remain; that is, there must be exactly the right number of inputs in the array.

You may assume that there is at least one solution where all of the numbers are in the range [0, 256).

# Test Cases

,!v;
>v      =>  [1] (or any other single truthy value)
^<

,v>v;
>?>?v<
>v>>^  =>  [1, 0] or [0, 1] (or any other array of two values with opposite truthiness)
>?
;

,1-!;v<  =>  [-1] (only this value works)
>^


# Sandbox

• Is this too hard?
• Is there anything unclear or anything needing more clarification?
• Is this too easy?
• Is the language too complicated for a challenge like this?
• I don't really understand what 'push' and 'pop' mean thus the operator section is a little confusing to me. Also I think you need to include ; in the list of characters that one can make a bijection from. Also, would it make sense to swap the \  and / commands? If you do the characters would represent mirror planes (or plain mirrors) but now they seem a little counterintuitive to me. – dylnan Nov 16 '17 at 19:45
• @dylnan 1. push and pop are stack operations meaning put a value onto the top of the stack and remove the top of the stack and return its value, respectively. So for example, push pop + pop means pop a value off the top, pop another value off, add them, and push it onto the top of the stack. Also, yes, I missed ;, thanks for noticing. Also, I got confused by my own wording so yes, \/ should be swapped. Thanks for the comments! – HyperNeutrino Nov 16 '17 at 20:07
• So, if I understand, the submissions will take code in the 2D language as input, and the output will be values that, when fed into the input code, would cause it to run infinitely? – Kamil Drakari Nov 16 '17 at 20:30
• @KamilDrakari Yep. – HyperNeutrino Nov 16 '17 at 20:43
• How would the conditionals ! and ? deal with the stack? In your second test case, if the stack is 01 (say the right is the top) and the first ? sees the 1, wouldn't the stack have to be popped in order for the second ? to see the 0 and move into the infinite loop? – dylnan Nov 17 '17 at 1:21
• Also, I think is too hard due to the halting problem. Even with the busy beaver Turing machines it becomes very difficult to determine whether a machine will halt with machines of only a few states. Maybe if you somehow restrict the possible modes of running infinitely (e.g. program will only run infinitely if it gets into <^>v or <v>^ loops) and restrict the length of the program but even then I think it might be too hard but I'm not sure – dylnan Nov 17 '17 at 1:44
• @dylnan It theoretically shouldn't be too impossible because you can just go through all possible states and if it ends up in the same state as before, it will loop infinitely (because there are no non-deterministic commands). It will be horribly inefficient, but eh, it's code-golf, efficiency is not the priority :P – HyperNeutrino Nov 17 '17 at 1:59

# Packing Density of Polyline Defined Shapes

So... I was making bacon this morning and I couldn't fit all of my bacon into my pan. However I oriented the strips, there was always one or two pieces that didn't fit. Culinary endeavors aside, here's my challenge:

## Input:

pan and bacon

Each of these inputs is a list of (X,Y) coordinates that define a closed shape. The very first index and the very last index are different, but the shape is closed. It not guaranteed that the shape is convex, but it is guaranteed that the path doesn't cross itself. Further, for simplicity, you may expect all the (x,y) coordinates to be integers.

Your program must find the most occurences of bacon that can fit into the pan, allowing rotation and flipping.

## Output:

An integer that represents how much bacon can fit in the pan.

## Scoring and rules:

For proper cooking:

• A bacon may touch another bacon or the edge of the pan.
• bacon may not overlap, nor may it go off the pan.
• The first index of both pan and bacon is always (0,0).
• If there is a tie in number of bytes, the user whose code is formatted to look like ASCII bacon wins.
• If two users tie and both have ascii bacon, upvotes wins. Standard rules apply. This is code golf, so the standard rules apply.

# Sample input and output:

## Test Case 1:

Bacon directly overlaps the pan, and is the same size.

pan: [(0,0),(0,1),(1,1),(1,0)]
bacon: [(0,0),(0,1),(1,1),(1,0)]
Output: 1

## Test Case 2:

When bacon is bigger than pan

pan: [(0,0),(0,1),(1,1),(1,0)]
bacon: [(0,0),(0,2),(2,2),(2,0)]
Output: either 0 or an error.

## Test Case 3:

What happens when bacon crosses itself?

pan: [(0,0),(0,1),(1,1),(1,0)]
bacon:[(0,0),(1,1),(0,1),(1,0)]
Output: just error here. Any way you feel like. If you manage to report an http 418 error, you get bonus points, redeemable for nothing.

## Test Case 4:

What happens if the bacon doesn't exactly overlap the pan?

pan: [(0,0),(0,3),(5,3),(3,0)]
bacon: [(0,0),(0,2),(2,2),(2,0)]
Output: 2

• This looks like a tough question, but I like it. 1.) Are the coordinates integers or can they be floats? 2.) Is the shape guaranteed to be convex and contain more than two coordinates? 3.) Because this is a code golf challenge, it's unlikely anyone will go for the second output, so you should probably stick with just one of the two output methods. 4.) Example inputs and outputs would be great. – Laikoni Nov 16 '17 at 21:15
• Having arbitrary polygons make this tough, even just to figure out if one shape fits inside another. I think you'll do well to have extensive test cases that probe at the possibilities and defy heuristics. – xnor Nov 16 '17 at 21:42
• I've added quite a few test cases using minimal pans and bacon. @xnor, what do you mean by 'defy heuristics'? – Jakob Lovern Nov 16 '17 at 21:57
• @JakobLovern Like, for example, making it so that code that just outputs the ratio of the areas doesn't happen to pass all test cases. Other examples could be making sure the code allows bacon to be rotated by non-multiples of 90 degrees, doesn't just try to do some greedy fill from one corner, considers reflecting the bacon, etc. The idea is that someone whose code meets all the tail cases should be reasonably certain it meets the problem conditions. – xnor Nov 16 '17 at 22:36
• @JakobLovern My experience has been that writing the code to do the task has been very helpful to think of edge cases and to generate test cases. You can then post it as (ungolfed) reference code, which is often appreciated by solvers. – xnor Nov 16 '17 at 22:43

# Implement a basic two-dimensional esolang code-golf

There are hundreds of two-dimensional stack-based esoteric programming languages out there, and lots of them follow a very similar syntax:

v redirect instruction pointer down
> redirect instruction pointer right
^ redirect instruction pointer up
< redirect instruction pointer left
/ redirect instruction pointer: up -> right, right -> up, left -> down, down -> left
\ redirect instruction pointer: up -> left, left -> up, right -> down, down -> right
0 push 0 to the stack. 1 pushes 1, ... 9 pushes 9.
A push 10 to the stack. B pushes 11, ... F pushes 15.
: duplicate the top stack value
~ swap top two stack values (all languages implement this as a different character)
i read input as a ASCII character and push to stack
o print the top of stack as an ASCII character
n read input as integer and push to stack
u print the top of stack as an integer
+ increment the top of stack
- decrement the top of stack
! jump over the next command
; stop execution


Almost all two-dimensional esolangs contain more commands, but for the sake of simplicity, the one we're writing will contain only the above.

# Specification

The stack should be able to hold at least 30,000 values. You may pick any integer size (e.g. 32-bit, 64-bit, unbounded, etc) for stack values.

The instruction pointer should start moving right from the top left corner of the source code, and should wrap upon exiting the playing field, meaning that this code will be an infinite loop:

<^
v>


First, < will be reached, pointing the IP off to the left.
The IP will wrap around to the right, continuing left, and hit the ^, directing it up.
Then it will wrap, hit the > and travel right, wrap, hit the v and travel down, wrap, hit the <, and start over.

# Squaring the circle

## Background

This is a generalization of this question on puzzling.SE. Essentially, it asks you to generate a circular array of integers such that any two adjacent integers add to a perfect square, and that the integers are a permutation of those from 1 to 50. The original question gave you a part of the array, and asked you to solve it. I wish to generalize this problem.

## Problem Description

Given an integer n, generate a circular array of numbers from 1 to n such that any two adjacent integers sum to a perfect square, without repeats of any number.

## Input

Input is limited to positive integers greater than or equal to two.

## Output

If there is no possible array (as can be manually proven to be the case for n=4), then your function should gracefully handle the error and exit.

Otherwise, it should output a representation of that array for that n as a string of delimited integers, such that, if the string were concatenated into a long integer, it would be the minimum possible string. To illustrate:

1 2 3
1 3 2
2 1 3
2 3 1
3 1 2
3 2 1


Of these six representations, only 1 2 3 is in minimal form.

You may delimit your string in any consistent, parsable way you choose.

## Example I/O

For n<32, there are no valid arrays (And I can prove it, if necessary.) The smallest n with a valid array is n=32, and it is structured:

=>01 08 28 21 04 32 17 19
15                       30
10                       06
26                       03
23                       13
02                       12
14                       24
22                       25
27                       11
09 16 20 29 07 18 31 05


The output to n=32, would therefore be 1 8 28 21 4 32 17 19 30 6 3 13 12 24 25 11 5 31 18 7 29 20 16 9 27 22 14 2 23 26 10 15

## Example code

Because code is clearer than words, here's a (purposefully) very naive and inefficient routine for this in Python (2.7):

import math, itertools
def main(n):
def test_if_a_given_list_is_a_ring(input_list):
is_a_square = lambda value: math.sqrt(value).is_integer()
output_flag = True
for index in range(len(input_list)):
if is_a_square(input_list[index]+input_list[index-1]):
continue
else:
output_flag = False
#end if
#end for
return output_flag
#end test_if_a_given_list_is_correct
def turn_it_into_a_string(input_list):
temp_list = []
for i in input_list:
temp_list.append(str(i))
#end for
output_string = ''
for i in temp_list:
output_list += ' '+ i
#end for
return output_list[1:]
#end turn_it_into_a_string
lowest = string(n)*n

for perm in itertools.permutations(range(n,0,-1)):
if test_if_a_given_list_is_correct(perm):
flag = True
for perm_character,lowest_character in zip(turn_it_into_a_string(perm),lowest):
if int(lowest_character) < int(perm_character):
flag = False
break
#end if
#end for
if flag:
lowest = turn_it_into_a_string(perm)
#end if
#end if
#end for
return lowest
#end main


If you're gonna golf this code... I'd highly recommend optimizing it first.

## Scoring

Programs will be scored based on: 1. Asymptotic complexity 2. Average runtime 3. Byte count 4. Runtime when the byte count is fed into the program as input

(I can't decide which of these scoring systems to use. Note that I've manually worked out that when n<=31, there are no arrays. At n=31, there is a valid double loop system, but no valid single loops.)

• your example is not a valid ring, is it? I only see two perfect squares, 11+5=16 and 1+8=9 – Luca H Dec 1 '17 at 9:18
• No, it isn't. As of ten minutes ago, I constructed (By hand) the ring for n=32, so I'll post that. – Jakob Lovern Dec 1 '17 at 18:56
• (1) "ring" has a specific meaning (an algebraic structure with multiplication and addition subject to certain rules), which is distracting. How about changing it to circular array? (2) In my opinion, "generate a [circular array] of numbers from 1 to n" does not impose a restriction on the length of the array or on the impossibility of repeats. For me the clearest way to add the restrictions which I infer from the linked question would be to say that it's a permutation of the numbers from 1 to n. – Peter Taylor Dec 1 '17 at 21:02
• (3) "This is a two part question": I only see one part. If you intend a follow-up, maybe worth including it so that you can get opinions on whether it would be closed as a dupe of the first part. – Peter Taylor Dec 1 '17 at 21:03
• @PeterTaylor I was originally intending to ask the question twice, but score using different conditions. I expect that code which would minimize asymptotic complexity wouldn't look at all similar to code which minimizes size. I wanted to see the difference. You made a good point on the dupe problem, though, as the two questions are essentially similar to each other. – Jakob Lovern Dec 1 '17 at 21:44
• So what's the scoring? If byte-count gets fed to the program no solutions that are < 31 bytes & if it's gonna be an average runtime based scoring you should choose large enough values such that it becomes about complexity and include how you measure. – ბიმო Dec 3 '17 at 3:10
• That's exactly why I was asking for input on my various ideas for scoring. I don't expect that there's going to be any programs that small that can successfully answer the question, but it could happen. I'm leaning towards asymptotic complexity or byte count. – Jakob Lovern Dec 5 '17 at 18:01

k-combinations for a set of size n represent in what different ways one can pick k elements out of a set of n elements. There is a natural representation of such a pick as an integer with n bits, of which exactly k are set.

Define next[n, k] :: Pick(n, k) -> Pick(n, k) to be the group action that takes each pick to the next one, wrapping around. More formally: Let r be an n-bit integer with k bits set. Then next[n, k](r) will return the smallest integer > r that also has k bits set. If there exists no such integer, the smallest integer with k bits is returned. Example: next[4, 2](0b0011) = 0b0101, next[4, 2](0b1100) = 0b0011.

[- Annotation: if k = 0, then there is only one unique integer with zero bits set. next[n, 0](r) = 0. -]

You will be given a pick r and a positive integer step. Output (next[n, k]^step)(r), that is, apply next[n, k] step times to r.

### Rules

• You will be given 4 integers n k r step. Output (next[n, k]^step)(r)
• 1 <= n can be assumed to be small enough to represent picks as integers naturally in your language
• 0 <= k <= n
• r will always be a valid pick of k out of n.
• 0 <= step <= C(n, k) can be relatively large. As an example, C(32, 12) = 225,792,840

### Criteria

Return the correct output for all valid inputs.

This is code-golf, shortest code wins.

### Examples

4   2 0b1001 2  => 0b1100
16 10 0xF11F 10 => 0bF15E
4   2 0b1100 2  => 0b0101

• Nice challenge! But what if k = n = 0? And maybe specify formally how next works. – ბიმო Dec 3 '17 at 5:38

# Best Yahtzee score

Yahtzee is a game played with five six-sided dice and a score sheet with thirteen different boxes to fill a score in. Each box has its own scoring rules:

• 1s, 2s, 3s, 4s, 5s, 6s all score points equal to the sum of the respective dice (that is, a roll of [3, 2, 3, 1, 5] scored as 3s would be awarded 6 points - 3 for each 3).
• 3-of-a-kind and 4-of-a-kind (as they sound, three or four dice rolled the same) score points equal to the sum of all five dice.
• Full house (two dice show one value, the other three show another) scores 25 points
• Small straight (four consecutive values) scores 30 points
• Large straight (all consecutive values) scores 40 points
• Yahtzee (all dice show the same value) scores 50 points

The thirteenth (chance) makes sense in-game, but not so much for this challenge; additionally the game has bonuses for extra Yahtzees which make no sense here. Because the challenge is...

Given five dice as input (five integers 1-6, input however is convenient), output the highest score that roll can score as well as what box it's being score under. The score should be output as its decimal numeric value, whether that's an integer or a string representation thereof, whatever. It should be immediately recognizable as a number. How you identify boxes is up to you so long as they are all unique and any given roll that will be scored in a given box always returns the same value. Please specify in your answer how boxes are identified. Order ([score, box] or [box, score]) does not matter. If you're outputting to STDOUT or otherwise not returning two values from a function, please separate score and box with at least one non-alphanumeric character of your choosing.

Code golf, so shortest answer in a given language wins. Standard loopholes apply.

Test cases, using , as separator, and 123456kKfsly for the box names (respective of their order above):

in: 1 5 4 3 2
out: 40
in: 1 1 4 3 1
out: 10
in: 1 1 6 5 3
out: 6


## Sandbox/meta

• I saw one existing Yahtzee challenge, but IIRC it boiled down to scoring a whole game. I did the 'given five dice, what is the best score' exercise once and felt like there were some interesting challenges to be found in optimizing it.
• Better ways to express I/O? I want it to be flexible but relatively readable...
• My first potential submission, I'm sure I'm forgetting something...
• IMO, multi parts output is pretty much a party killer. In that specific question, I think the score itself is enough to constitute a nice challenge. The box value is drived by conditional programming, which (of the challenge goes well) might not be present in some answers. – Uriel Dec 6 '17 at 22:58
• Anyway, for that wide range of possibilities, you should add at least one test case to cover collisions, multiple scorings and at least one of each box type (again, as I see challenges here) – Uriel Dec 6 '17 at 23:00
• @Uriel Thanks for the input — I planned to fill in more test cases, I guess I could've mentioned that in the meta section. I'm not trying to be difficult, but I'm curious if you could expand on your other point w/ the score itself being enough. The score is (I believe?) entirely dependent on the box being determined, and spitting something box-related out seems programmatically like a small challenge vs. the 'reward' of the output. This was why I wanted that output to be very flexible. Part of me thinks you're right, part of me thinks I'm right… so if you have more to say, please do… – brhfl Dec 7 '17 at 2:37
• my point is, in order to get the right score the user necessarily went through the right box (and not even print it, but also did a somewhat-more-complex calculation with it) - so it's kinda like letting them output twice. – Uriel Dec 7 '17 at 10:02
• @Uriel Makes sense, and I was leaning that way the more I thought about it last night. Cutting it also eliminates the need to address collisions. I think it's out... Thanks! – brhfl Dec 7 '17 at 13:35

# Google Doodle Kids Coding-style simulator

One input is a list of commands. There are three action commands and a loop construct. There is some flexibility as to the command format:

• As a string or equivalent: The loop construct should use a pair of matching brackets. The direction commands should be < and > or L and R (either case). The motion command should be ^ or F.
• As a list of characters: The loop construct should be a sublist. The other commands should be individual characters in the list, specified as above.
• As a list of integers: The direction commands should be -1 and 1 while the motion command should be 0.

The other input is the starting position. This consists of an two-dimensional array in any suitable format (including a newline-separated string). Background values should be represented using 0 or spaces. Carrots should be represented using -1, ^ or V (either case). The starting square should be represented using 1, @, or R (either case).

Optionally, the starting direction can be an input (one of <>V^ or an angle in degrees or turns), or it can be hard-coded (please specify the default starting direction in this case).

Command rules:

• Loops always execute four times
• The direction commands rotate the rabbit in place
• The motion command moves the rabbit one square in the current direction

The rabbit wins if it eats all of the carrots.

The rabbit dies if:

• It runs out of commands
• It walks out of bounds
• It walks onto the background

The starting square and carrot squares are all safe.

Your output should be a consistent truthy value if the rabbit wins, and a consistent falsy value if it dies. This can also be achieved by exception or error exit.

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

• Related – Emigna Dec 8 '17 at 11:51
• What's the background? – user202729 Dec 8 '17 at 12:07
• 1) exception exit is already a standard way to output a falsey value, and 2) in the actual Google doodle you don't lose if you try to walk off the edge of the map, it just does nothing. – Nissa Dec 8 '17 at 14:02
• @StephenLeppik It's not meant to exactly simulate the Doodle. – Neil Dec 8 '17 at 14:32
• By "background" I means as in "It walks onto the background". – user202729 Dec 9 '17 at 10:04
• @user202729 The background is any square whose value is 0 or space depending on your input format. – Neil Dec 9 '17 at 10:55
• Ready to post to main? – user202729 Dec 11 '17 at 5:48
• Don't abandon this... :( – user202729 Dec 18 '17 at 15:43

# Background

Many people visit webpages, which require special browsers because of lack of compatibility. So you have to write a script (client sided or server sided), which just prints the name of the browser. Because not everyone has fast internet, the script has to be as short as possible.

# Rules

1. You have to print the name of the browser loading the page without any version number etc. to STDOUT or equivalent. Leading or trailing spaces are allowed.
2. You can assume the browser is Firefox, Chrome, Edge, Safari or Opera, so only those browsers will be tested. Don't print "Chromium", this does NOT count.
3. The script may be server sided with CGI (in any language), ruby on rails, jsp and similar. Client sided scripts may be written in JavaScript, TypeScript, and any other versions of ECMAScript, it just has to run in all five browsers.
4. If your language has no offline interpreter for CGI, assume it's saved in /usr/bin/i, the shebang at the beginning does not add bytes to the count.
5. this is a , so the shortest answer wins!

# Meta

• Does this question have important loopholes?
• Is there any language which cannot be programmed in? (CGI should work always, even Java or bf could be done with a shebang, lol)
• About the "Is there any language which cannot be programmed in?" --- that's actually a very good question. Let me try. – user202729 Dec 10 '17 at 14:37
• About the background... "fast internet" doesn't matter if the script is server-side. – user202729 Dec 10 '17 at 14:38
• @user202729 This is a joke, lol, just like those other joke reasons the program has to be short. Is it a good question though? – Mega Man Dec 10 '17 at 14:49
• Probably. But the fact is, not everyone is familiar with writing a server, so you may not get a lot of answers. – user202729 Dec 11 '17 at 6:03

# Coin Game: Shoot It Out!

In Shoot It Out, we will play with coins on a table.

# Basic Idea

Shoot It Out is a 6-player game. The players will be split into two teams of 3 players, one offensive, and one defensive.

Initially, every player has a coin on the table. Additionally, there is a target coin. Players take turns to shoot their coin. However, the shots will not be very accurate.

The offensive team will try to shoot the target coin out of the table, while the defensive team tries to prevent the target coin from being shot out. You should make a bot that can play as both offensive and defensive team, and try to maximize the winning rate.

# Rules

### Playing Order

• Every player has its player ID. ID 1, 3, 5 are on the offensive team; ID 0, 2, 4 are on the defensive team.

• Playing order is the same as ID. After the turn of ID 5 is ID 0's turn. If a player is removed, simply go to the next player.

• When it is a player's turn, they will shoot their coin once. After every coin stopped moving, the turn ends.

### Elimination in a Game

• If a player shoots their own coin out of the table, the player is removed from the game. If the target coin moves out of the table in the same turn, it will be placed back to the previous position.

• If a player shoots another player's coin out of the table, both players are removed from the game.

(Note that these two can occur in the same turn.)

### Winning Conditions

• Defensive team wins when both conditions below are satisfied:

• The target coin is in the table area.
• All players on the offensive team are removed, or 18 turns have been played (skipped turn is not counted).
• Offensive team wins when one of the conditions below are satisfied:

• The target coin is out of the table area.
• All players on the defensive team are removed.
• There is one exception: if all players are removed at the end of a turn, the defensive team wins.

### Table Settings / Parameters

• The table is a circular area of radius 100 cm. The radius of every coin is 1 cm. A coin is out of table iff its center is out of the circular area.

• For convenience, we set the coordinate of the center of the table to (0, 0), and denote the position of a coin by the coordinate of its center.

• The coefficient of restitution between coins is 0.9.

• The maximum intended speed of a shot is 240 cm/s.

• When a coin is moving, it will have an acceleration of -240 cm/s^2 (due to friction).

• When the game starts, the target coin is located at (0, 0), while the coin of ID x is located at (2.5 cos(f(x)*pi/3), 2.5 sin(f(x)*pi/3)). The values of f(x) are:

x f(x)
0 0
1 3
2 1
3 4
4 5
5 2


Here is a picture of initial positions.

# Errors

Each player's shot has two parameters: angle and initial speed. Programs will output the two parameters representing its intended shot. However, the actual shot won't be the same of what is intended: errors will be added into parameters.

Specifically, if the angle (in radians) and initial speed (in cm/s) of the intended shot are θ, v, then:

• The actual angle will be θ+R(pi/70).

• The actual initial speed will be v*exp(R(1/12)). (Note that it may exceed the maximum speed.)

Where R(x) is a random variable with Gaussian distribution of standard deviation x and average 0.

# Scoring

Since only 6 players can play in one game, the controller will randomly assign players to a game.

Lots of games will be held until each player has played both defensive and offensive team in more than 10000 games.

The final score of your program will be y/x+z/(1-x), where:

• x is the average winning rate of offensive team in all games.

• y is the winning rate of your program when on the offensive team.

• z is the winning rate of your program when on the defensive team.

# Input / Output

Your program will be run once per game. It should receive inputs from stdin and output to stdout.

At the beginning of a game, it will receive a line of input a, where a is the player ID (thus indicating which team you should play in).

When a turn starts, you will receive input like this:

3
0 3.798 3.332
1 12.656 3.666
3 18.652 7.913
4 8.004 7.132
6 -3.187 -9.553


The first line indicates the player of this turn. Each remaining line contains information of a coin: The first number is the player ID of the coin's owner (or 6 if it is the target coin). The remaining two numbers are x and y coordinates of the center of the coin.

If it is your turn, you should output two numbers, separated by a newline or space, representing the intended angle (in radians, 0 is +x, pi/2 is +y) and initial speed (in cm/s). You should flush stdout after output. (If it is not your turn, you should not output anything.)

You needn't to handle the termination of your program. When the game ends (or you are removed), the controller will send SIGKILL to your program to terminate it.

# Specifications

• Your program should be able to be compiled into an executable, or be executed like an executable (for example, add shebang if you use interpreted languages). If your program need to be compiled to run, you should also specify how to compile your program.

• Your program should not access files, or anything that stores information between games.

• Your program should be deterministic. You can use random number generators, but you should make sure that the generator you use is based on a fixed seed, and will not use random devices (such as RDRAND or /dev/random), system time, etc.

• All "random" numbers (while generating errors and assigning players) used by the controller are generated in a deterministic way. However, your program should not take any advantage of it.

• The total response time of your program in a game should not exceed 0.1 second.

• You can submit multiple programs, but they should not team up against the others.

# Controller & Sample Bots

(Still working on them...)

# The 64 | 64 Color Selector

All colour selector tools suck. Let us make another one that sucks also, but in a different way.

• two squares, of 64x64 "pixels" each one. Pixels do not need to be strictly pixels, but anything where the user can have 64 possible selections in each direction, vertical or horizontal, representing all the possible different RGB colors.

• a third element of the interface that will represent the color selected with user has selected based picked on squares.

• a fourth element which represents the 6 digit hexadecimal RGB hex-code (example: #FFBF32). You can divide it in three elements, but you have to make clear which component is what from RGB.

• a fifth element which represent the decimal RGB code (example RGB(127,33,43)). You can also divide it in three elements, but you have to make clear which component is what from RGB.

When the two squares are at the top left corner, selected color must be RGB(0,0,0); and when the two squares at the bottom right corner must be RGB(255,255,255).

You must have the the pixels in the square sorted by increasing order; I don't care what direction, vertical or horizontal, you choose for increasing one-by-one, but the two squares must have the same pattern.

When the user picks a "pixel" in the first square, the colours of the second must be updated and reflect all possible values under the second pixel.

When the user picks a "pixel" in the second square, 3rd, 4th and 5th elements must be updated to reflect new color selection.

• Your specifications seem a bit too loosely-defined to me, though unfortunately I don't have any suggestions for improvement at the current moment – HyperNeutrino Dec 11 '17 at 15:32
• I assume that your first requirement should state 'Pixels do not need to be strictly pixels...' – brhfl Dec 11 '17 at 18:34
• @brhfl Yes. Thanks. Fixed. – sergiol Dec 11 '17 at 18:50
• Is there any requirement on the ordering of selections in the first two elements, or is it fine as long as every RGB color could be expressed as a coordinate pair on the first element plus a coordinate pair on the second element? – Kamil Drakari Dec 11 '17 at 19:21
• @KamilDrakari: Yes. Thanks. Updated. – sergiol Dec 12 '17 at 11:09
• @HyperNeutrino: better now? – sergiol Dec 12 '17 at 11:10
• It looks good, you may want to point out that you want a 1:1 color conversion. I was looking at it and I think that's what you want since 64^4 = 256^3. – Neil Dec 13 '17 at 4:03
• "You must have the the pixels in the square sorted by increasing order" is nonsense unless you address the issue that HyperNeutrino raised about the specifications not truly being specifications. – Peter Taylor Dec 13 '17 at 9:41

## Sheet music exact transposition

As we're limited to ASCII here, I'll just refer to the notes by name A-G, although obviously real sheet music has a range of about an octave and a half even before you take ledger lines into account.

Notes are written on sheet music in two ways. Most of the time, notes have their own position on the stave, but no accidental is indicated; this means that the note gains the accidental corresponding to the key signature. For example, the scale of A is ABCDEFGA; the C, F and G are played sharp because of the key signature. These notes are easy to transpose, because you simply need to shift them by the appropriate number of note names; the accidental is taken care of by the key signature. For example, the scale of A is simply ABCDEFGA; if you transpose down two notes, you get the scale of F, FGABCDEF; in this case the C, F and G become natural and the B becomes flat, but there's nothing extra for you to do here because the key signature takes care of it. This works even if the key itself contains accidentals; transposing the scale DEFGABCD from D♭ to D♯ simply results in DEFGABCD again.

For notes that are not available in the key signature, an accidental needs to be applied. This is either the ♮, indicating that an accidental in the key signature (or previously used for that note, but that's not relevant here) should be ignored, or one or more of either ♭ or ♯, indicating how many semitones the note should be adjusted. (Although an accidental exists for ♯♯, we will ignore this to simplify the challenge).

You can't just throw accidentals around, otherwise you end up with the scale of E written as F♭E♯♯A♭A♮C♭B♯♯F♭♭E which is ridiculous. It is therefore essential when you transpose a note that the note name is transposed identically no matter how many accidentals the note may have.

However, there is a caveat: the named intervals are not regular. The interval between B and C and that between E and F are just one semitone, while the other intervals are two. This means that you might have to adjust the accidental if the number of semitones between your original and transposed note differ from that of the original and transposed key. The number of accidentals in the key must also be taken into account, of course.

Take the example of transposing the note D from the key of A to the key of F. Because F is five notes above A, the note D transposes to the note B; the key signature takes care of making the B flat. However, if we were transposing the note D♯, we would have to calculate that the final note needs to be B♮ in order for the number of semitones to be correct (F - A = 8, B♮ - D♯ = 9 - 1 = 8; the ♯ increase the number of semitones while the ♭ decreases it, but of course subtracting a ♯ results in a decrease too).

Conveniently, the output has an accidental of some sort (including ♮) if and only if the input note does, which should simplify the challenge.

Your challenge is to write a program which will accept three notes as arguments. Two of the notes will represent the original and transposition key of the transposition, while one of the notes will represent the note to be transposed. You must then output the result of the transposition. Examples:

Note    From    To      Result
G♮      A♭      B♭      A♮ (not A)
C♯      B       D       E♮ (not E)
B       F       D       G
B♭      C       G       F♮
B       B       A       A
B       E       B       F (not F♯)
D♭      E       G♭      F♭♭ (not E♭ or D♯)
G♭      E       G       B♭♭ (not A or A♮)
E♭      G♭      C♯      A♮ (not A)
C       F       D       A
G♯      C       G       D♯ (not E♭)


This is , so the shortest program wins. However, since there does not appear to be an ASCII character that can represent ♮, I will allow any of the three UTF-8 characters ♭, ♮ or ♯ to count as a single byte.

# Simultaneous Selection

In the game Risk of Rain there is a game mode where you can select which items you want out of dropped boxes. The only problem is that when you open two boxes at the same time your movements in one box effect your movements in another. Now this can be a problem since you may want to retrieve a particular item from one of the boxes. However there is a solution.

Since the boxes have different shapes and you are not permitted to move your cursor outside of the box you can desynchronize the two cursors.

For example if we have the two boxes

S.F...    S.....
......    ...F..
....      .....


Where F is the goal and S is the starting location, we can get the cursor to the goal by moving the cursor

Right 4 times
Down 3 times
Up 1 time
Left 1 time


Still working on it ...

## Input

As input you will receive two 2 dimensional boolean containers, representing the shapes of the boxes. In these boolean arrays true means that square exists in the box false means square does not exist. You may assume that your input will be padded with false values such that no true values touches the edge of the array.

You will also receive two coordinate pairs representing the start and end locations.

## Output

You should output a ordered container of "moves" such that when performed on both boxes the cursor will arrive at the end point. A "move" may be one of 4 chosen values each representing one of the 4 cardinal directions. For example you might choose: [N,S,E,W], [1,2,3,4] or [(1,0),(0,1),(-1,0),(0,-1)]. Your program must be self consistent in these values across multiple sessions.

If no solution is possible for the given boxes you must output a value that is distinct from any possible sequence of moves, for example a list containing a 5th value that cannot represent a move, or a non list item.

Still working on it ...

• How do we take input? As two separate strings or can it be arrays, etc... – Neil Dec 17 '17 at 5:20
• @Neil Its going to be boolean arrays, true means square exists false means square does not exist, and coordinates for start and end locations. I've been a little lazy in finishing this question. – Wheat Wizard Dec 17 '17 at 5:22

# Demolish a string! v2

A modified version of Demolish a String; since the original question involved randomness, the challenge was too complex and there were not many answers. This challenge removes the criterion and allows flexibility by the answerer, which should invite responses in languages without randomness built-ins.

# Challenge

Given a string input, output the demolished version of it.

# The Process

P
r      Pr       r
o       o       o
g       g       g
r       r       r      rogr         r
a  ->   a  ->   a  ->     a  ->     a  ->           ->           ->           ->           ->
m       m       m         m         m
m       m       m         m         m         mmar         m
i       i       i         i         i         i            i           mi           m
n       n       n         n        gn        gn           gn           gn           gni         mgni
g       g      Pg        Pg      roPg      roPg         roPgmar      roPgmar      roPgmar      roPgmar


Place the string vertically. Repeat the following steps until they are impossible:

1. Take any column of characters that can be demolished (explained below)
2. Select some integer between 1 and (height of the column of characters) - 1 and some direction (left or right).
3. Rotate that number of characters in that direction (only if those spaces are unoccupied; if not, go back to step 3).
4. Let those characters fall due to gravity.

At the end, the output should be a string whose heights of consecutive columns differ by at most one.

Note: the choice of integers and the direction is up to the answerer

If there are space characters in the input, demolish those first, all at once.

C
o

d
e  ->     oC  ->         ->  ...
de
G        G          G
o        o          o
l        l          l
f        f        defoC


## Rules

• Standard loopholes are forbidden.
• Trailing and leading newlines are allowed.
• Your program may either print or return a string/equivalent.
• Please explain the demolition algorithm (# of characters and direction) in your answer.

## Some test cases to try

A
Programming
Code Golf
The quick brown fox jumps over the lazy dog


This is , so the submissions with the smallest byte counts in their languages win!

# Program an Uncircularness Score

derivative of this challenge

## Meta:

This is just a rough idea for a slightly different challenge. I have no idea how successfull it would be in the current state, so feel free to share your opinions and suggestions.

Your task is to program a mathematical function s, that takes a finite set A of points in the 2D plane, and outputs an uncircularity score s(A) that satisfies following properties:

1. positive definiteness: If there is a circle or a straight line that contains all points of A, then s(A) = 0. Otherwise s(A) > 0
2. It is surjective to the nonnegative real numbers, that means for every nonnegative real number r there is a finite subset A of the plane such that s(A) = r.

### Scoring

You get one point for every of the following properties that your function (provably) has.

• Translation Invariance: s is translation invariant if s(A) = s(A + v) for every vector v and for all A.
• Scale Invariance: s is scale invariant, if s(A) = s(A * t) for every t≠0 and for all A.
• Monotony: s is monotonous if s(A) ≤ s(B) for all A,B where A ⊆ B.
• Circle Inversion Invariance: s is circle inversion invariant, if s(A) = s(f(A)) for all A with 0 ∉ A, where f(x,y) = (x/(x^2+y^2), y/(x^2+y^2)) is the circle inversion. (Here (x,y) represent the cartesian coordinates of a point in the plane.)
• Triangle inequality: s satisfies the "triangle inequality" if s(A ∩ B) ≤ s(A) + s(B) for all A,B. (This is implied by Monotony.)
• Reverse triangle inequality: s satisfies the "reverse triangle inequality" if s(A) + s(B) ≤ s(A ∪ B) for all A,B.
• Continuity. s is said to be continuous if the function f(p) := s(A ∪ {p}) (mapping the a point p to a real number) is continuous using the standard absolute value on the real numbers, and the standard euclidean norm on the points of the plane.
• More to come...
• Perhaps you should change the "non-negative real number" to "non-negative rational number" or "non-negative algebraic number" in part 2. If these functions are being produced by code it seems quite unreasonable to expect numbers that cannot be represented in computer memory to be output. – Wheat Wizard Aug 26 '17 at 17:13
• @WheatWizard That's an interesting thought. Personally I quite like the idea of these properties working over the real numbers in theory, and the code implementing it to a desired accuracy of approximation, but I'm not sure if that's easier or harder to score/judge valid. – trichoplax Aug 26 '17 at 17:18
• @trichoplax I will admit I am opposed to any "code must work in theory" rules in challenges. However any code that works in theory must also work on the reals or algebraics which allows us to have code that works not just in theory. – Wheat Wizard Aug 26 '17 at 17:22
• @WheatWizard I agree that asking for testable solutions is much more satisfactory than "works in theory". – trichoplax Aug 26 '17 at 17:30
• I guess "provably" needs to be defined in the context of the challenge. Will there be a defined method of testing or does this require a mathematical proof (in which case it leans more towards puzzling's scope). – trichoplax Aug 26 '17 at 17:32
• @WheatWizard That is a good point that I did not think about. But I'd allow for limited precision implementations (i.e. floating point), because everything else would probably almost make the challenge impossible. – flawr Aug 26 '17 at 18:58
• @trichoplax You'd need a lot of testcases to be convincing, but I think the participants should be able (they don't have to write down proofs) to provide good arguments for why a certain property is satisfied, just as we require any program to be actually doing what it is supposed to do. (we don't require proof of correctness either) – flawr Aug 26 '17 at 19:01
• I think trichoplax makes a good point. I'm not sure how much this is really about code. It might be a better idea to post this on puzzling as a math puzzle where you need only define a function rather than some code. – Wheat Wizard Aug 26 '17 at 19:03
• @WheatWizard Thanks. I think this could be made into a code-challenge (or code-golf), but it could also be made into a mathematical function challenge like you suggest. I can't guess which would be more interesting (or easier to define objectively) though. I suppose there's nothing stopping it being two challenges, one on each site... – trichoplax Aug 26 '17 at 20:18
• Translation and scale invariance are easily added: translate to put the centroid at the origin and then if there's more than two points scale so that the furthest point from the origin is at distance 1 from the origin; then apply the original function. It might be possible to deliberately construct a noncircularity function such that this would destroy the surjectivity, but in practice I don't think the question would be harmed by assuming that all answers will be affine-invariant and simplifying the scoring system appropriately. – Peter Taylor Aug 27 '17 at 17:09