Sandbox for Proposed Challenges

Question

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.

To post to the Sandbox, scroll to the bottom of this page or click on the "Add Proposal" link below, and click "Answer This Question". Click "OK" when it asks if you really want to add another answer. Write your challenge just as you would when actually posting it. You may also add some notes about specific things you would like to clarify before posting it. Other users will help you improve your challenge by rating and discussing it. When you think your challenge is ready for the public, go ahead and post it, replace the post here with a link to the challenge and delete it.

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

The Sandbox works best if you sort posts by "active".

Add Proposal

Search the Sandbox

• Most people include applicable tags in their proposal, so for instance you can search for all king-of-the-hill proposals by merely adding the tag name in quotes to the search query.

Browse your pending proposals

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]

Answer 1

This puzzle is based on this Math.SE post.

Assume I have some number of black shirts and some number of white shirts, both at least 1. Both colors of shirt have a non-zero durability. All shirts of a given color start with the same durability.

Every day, I pick out a clean shirt to wear, and it becomes dirty. Once I run out of all clean black shirts or all clean white shirts, I wash all my dirty shirts of both colors and start over. Clean shirts do not get washed. Whenever a shirt gets washed, its durability goes down by one. Immediately after washing, if the durability of a shirt reaches 0, it must be thrown out.

When picking which shirt to wear of a particular color, I always choose a shirt with the highest durability of that color to ensure even wear and tear among shirts.

Challenge:

Take in a sequence of two characters of arbitrary length (eg. b b b w b w w b...) representing my choice of shirt to wear on that day. Continue execution until either my last black shirt or my last white shirt is thrown out. Once this occurs, stop consuming input and halt execution immediately. Note that the program must not consume any more input than is required before halting.

Inputs:

Number of black shirts, number of white shirts, durability of black shirts, durability of white shirts, and an arbitrary number of two single characters, your choice (eg. b and w)

Output

None. The program must simply halt when the last shirt of either color is thrown away.

Test cases

1 1 1 1 b

1 999 1 999 b

1 999 1 999 w w w w w w w w b

2 999 1 999 b w w w b

2 999 2 999 b w w w b w b w w w b

5 3 6 1 w w w w w b b b b b b b b b b b b b b w

General rules:

• This is code-golf, so shortest answer in bytes wins.
• Default input rules apply for the first four arguments. For the arbitrarily long input sequence after the first four arguments, input must come from a source which can provide input one character or byte at a time, of theoretically infinite length, such as STDIN or some other stream.

Answer 2

Calculate mobile data coverage

Background

You've been hired by the HQ of Vodafizon - a relatively new mobile network provider interested in spreading to the global market. In particular, your job description involves working as a marketing rep to produce ads for each country, where you give a figure of the data coverage, as a percentage, in that country. You get this data from the data scientists, but you've started to notice a pattern: the number always seems to be 98%, 99% or 100% (which, in your experience, seems to be far too high). Despite your trust in Vodafizon, you seem to find this suspicious, so you write your own program to investigate, ensuring maximum precision, even implementing your own floating-point and circle rasterization algorithm to minimize error. You end up making a 112KB monster of a program, but the result confirms your suspicions: these figures are, for the most part, made up by the data scientists, to try and exaggerate their claims.

When you mention this discovery to a coworker, they act surprised at first, but later tell you to keep quiet: upper management probably know about the forgery, and in fact endorse it. Telling them that you know their dirty secret could will result in losing your job.

But here's the thing: you know that advertising these fake numbers could result in massive lawsuits to Vodafizon, the effects of which could result in you getting laid off. You know you can't risk getting fired, but just using the data scientists' figures could be disastrous in the long term.

After consulting Workplace SE, you come up with a plan: keep using your program, but hide it from your superiors. The only issue is, that the data scientists responsible for providing you the data also happen to be the makeshift sysadmins in Vodafizon HQ, so your program can't attract too much attention to itself. 112KB is far more than Vodafizon uses on average (they prefer to split code into lots of tiny files), so when filtering through by file type, the sysadmins will easily see this file as potentially twenty times larger than all the others. So clearly, you need to compress it, without sacrificing the accuracy.

Input

The input will consist of a nested array of form [[x, y], [x, y]] (or alternatively an object of form [{"x":x, "y":y}, {"x":x, "y":y}]) of line segments, in clockwise order, defining the border of a country.

The input will also contain a nested array of form [[x, y, strength], [x, y, strength]] (or an object of form [{"x":x, "y":y, "s":strength}, {"x":x, "y":y, "s":strength}]), which will describe the location of the mobile data towers, and the strength: the radius (or diameter, you can request either in your answer (but not both)) of the circle in which that given tower provides mobile data.

Output

Your program should output an approximation of the mobile data coverage of the input given. Of course, this is impossible to get perfect (unless you live in Indiana, that is), so you need to provide an approximation, but while reducing your byte count as much as possible. Note that your program must halt by itself before 5 seconds of runtime (for any test where the number of towers is less than or equal to 500, and the number of edges is less than 100), or alternatively continuously provide output such that once it is stopped after 5 seconds, the last output will be taken as the result.

Scoring

Like I mentioned, my program also needs to be small, therefore size will factor into the equation. So, to score your program:

• Get the number of bytes, B
• Run your code with the randomly-generated test cases provided by tests.py in this repo, and save the ref outputted.
• Run your outputs through score.py, providing the ref at the start. The last input you will be asked for will be B.

Get the score outputted by score.py, and post it in your answer.

Sandbox

• Is my background too long?
• Is my scoring system too long-winded? I intend to use a complex algorithm (which I have mentally worked out, but not coded yet) which essentially creates a weighted average of all of the scores as a percentage of a value which is correct to 16 decimal places. Is referring people to some code, instead of telling them the algorithm, standard practice? I don't want to spend ages describing a confusing algorithm, when I could just write a program to do it.
• Is this challenge not a duplicate? Is is unclear in any way?

Answer 3

Broken mouse

This is just an idea, I have not elaborated it.

My mouse accidentally fell to the ground, and now there is a double click for each of my single click(which makes window-closing very hard to do). :(

Most computer screens have a higher resolution ratio than 16x12, but let's assume that my computer screen has a 16x12 resolution ratio.

Example: A Window looks like this:

0-----OX
|      |
--------

The number 0 is the indicator of the window. O is a dragging button that allows windows to be moved. X is a closing button that closes the window. (You can not resize windows.) Assume that there is a window below that window looking like this:

1-----OX
|      |
--------

If I click X, I will close both windows. However, what should(or must, if appropriate) I do if I only want to close the first window?

I can move my mouse to the O tab and drag the window around by using mousedown. After 1 drag to the right:

10-----OX
||      |
---------

Now I can click the X to close the window 0 after I click the O button again to remove the dragging effect. (Note that there is the window "1" below that window.)

Wait, I changed my mind and wanted to close the window 1. What should I do?

I should click the number 1; then, the window 1 goes to the top and the X button shows. Now I can click the X button to close the 1 window.

For reference, this is the TUI commands I used(when the mouse starts at 0x0):

0-----O
>>>>>>.>.<<<<<<<.>>>>>>.

What should I do if I want to close the windows that I specified? (Output the TUI instructions.) (Your score is -(code length + output); you want to keep your score as high as possible.)

TUI Instructions

• ^v<>: Move the mouse up, down, left, or right
• .: Mouse down+mouse up (i.e. click)

Answer 4

tags: "code-golf", "ellipse", "geometry"

Sandbox Questions

Is this a proper code-golf question?

A major challenge is: How to verify the computed shape? Numerical verification is impossible, since there are infinitely many possible solutions. Is there an easy way to plot xy-data online, or should I provide a script myself? Your suggestions are greatly appreciated.

edit:

after 3 days of being posted here in the sandbox, I still have no clear answer to the above question. I therefore propose to ask participants to include their own plot in the answer, which they can make with whatever plotting tool they wish. If people feel inclined to cheating, they only fool themselves, don't they?

Introduction

To create a circle you can stick a nail in a piece of board, put a loop of string around it and hold it taut with a pencil at the other end. Move the pencil and you get a circle. If you put the loop of string around two nails and move your pencil, you create an ellipse. But what happens if you use three nails, or four, or ten perhaps? It's gonna get ugly soon if you try this in real life, and that's where computers come in handy.

Challenge

Your task is to write a program or function that accepts two inputs:

• A list of (x,y) coordinates (viz. the nails), of arbitrary length>2.
• The length of the rope.

And produces the following output:

• A list of coordinates of the poly-oval, which could be fed to a plotting-tool. Plotting the output does not need to be part of your program!

References

• A graphical example can be found here: Robert Dickau
• Some handy math on ellipses: ambrsoft

Details:

• You may assume that the input coordinates form a convex shape (no inner points on which your program could crash).

• As coordinates, you can use tuples, pairs, complex numbers or even two separate scalars if you like.

• The output resolution (ie. the length of the list) is not so important, but is should give a fair representation of the real curve. In my experience, you'll need between 100 and 1000 points. For smaller rope lengths, you need an even higher resolution.

Rules and scoring:

• This is code-golf, so shortest answer in bytes for each language wins.
• Standard rules and default I/O rules apply.
• Loopholes forbidden (of course).

Example Input and Output

Provide at least one example input and output. Make sure they match your own description of what the input should look like.

Input can be any of the following:

P = [2+0j, -2+1j, -2-1j]

P = [(2,0),(-2,1),(-2,-1)]

X = [2,-2,-2] and Y = [0,1,-1]

Output should be in one of the following forms:

[0.862+1.591j, 0.703+1.668j, 0.527+1.729j, ...]

[(0.862,1.591), (0.703,1.668), (0.527,1.729), ...]

X = [0.862, 0.703, 0.527, ...], Y = [1.591, 1.668, 1.729, ...]

Answer 5

I mainly need help with scoring as I want to encourage use of esolangs.

I also would like to know how to improve the answer-ability of this question in languages that don't specifically have defined functions

---

Church booleans

A church boolean is a function that returns x for true and y for false where x is the first argument to the function and y is the second argument to the function. Further functions can be composed from these functions which represent the and not or and xor logical operations.

Challange

Construct the church booleans and and not or and xor church gates in a language of your choice.

Scoring

The total length of all of the code required to make church true and false in your language and the and not or and xor church gates excluding the functions name. (for example, false=lambda x,y:y in python would be 12 bytes). You can reuse these names later in your code.

Pseudo code Examples:

true(x, y) -> x
false(x, y) -> y
and(true, true)(x, y) -> x
and(true, false)(x, y) -> y
# ... etc

Answer 6

Distant Programs

Create a program that, when run, prints "Do you still love me?" with or without a newline at the end.

Your score is the Levenshtein distance to the closest non-erroring program (the non-erroring program doesn't have to do anything, although it might), and you want the largest score. Ties are broken by whichever code is shorter, in bytes.

Your program can read it's own source code, through the filesystem or otherwise. If your program must have a specific name, the length of that name should be included in your byte count.

Notes:

• Compiler warnings are not counted as errors for this challenge.
• An erroring program can output, frobricate, do anything as long as it eventually errors.

---

Notes for the sandbox:

• Is the specification clear?
• Is it possible to create a solution that can simply be repeated to get any arbitrary score? If so it would pretty much ruin the challenge as it is, and I think it should be possible but I can't get it to work.
• What tags would this use?

Answer 7

proof-golf rubiks-cube

Solve All the Rubik's Cubes!

I want to solve a Rubik's Cube. Unfortunately, I am blind, and my friend doesn't know how to solve a Rubik's Cube, so I just make one move at a time and ask my friend if it is solved. This generally doesn't work very well, so I would like to know a specific thing I could do to increase my chances of eventually fixing it. Also, I don't like memorizing things, so please keep your solution as short and simple as possible.

Rules

• I cannot see the cube or anything about it.
• The only thing my friend will tell me about the cube is whether or not it is solved.
• My friend and I are fully willing to wait until the heat death of the universe to solve this, if necessary.
• I don't have a great memory, so keep your instructions as short as possible.
• I can feel around the cube enough to turn whatever face you tell me to turn in whatever direction.
• I can turn the cube in my hands.
• I can memorize anything you give me, but I won't like it.

Solution Format

Give me a description of turns to do on my Rubik's Cube, to be repeated endlessly (or until I solve it).

F: Turn the front face clockwise
B: Turn the back face clockwise
R: Turn the right face clockwise
L: Turn the left face clockwise
U: Turn the top face clockwise
D: Turn the top face clockwise

x: Turn the cube so the top face becomes the front
y: Turn the cube so the left face becomes the front
z: Turn the cube so the left face becomes the top

' can be appended to any of these commands to make them go in the opposite direction.

Also, to make things easier, you can give me inner repetitions. Write these as

{...commands...}*4

where 4 is the number of times it is repeated. Inner repetitions can be nested.

Scoring

Non-memorability:

• Each turn gives one point.
• For nested repetitions, double the point value of everything inside the repetition and add the number of times I do it.

Effectiveness:

• Any sequence of moves on a Rubik's cube will eventually return to the initial state. The effectiveness is how many turns are required before this happens (roughly equivalent to how many states it passes through).

Total score = non-memorability / effectiveness

Solutions that are easier to remember are probably better than solutions that are hard to remember but will be solved.

Lowest total score wins.

Questions:

• Will people actually answer this question?
• Is the specification clear enough?
• This is my first question. Is there anything else I need to consider before posting?

Answer 8

Talk interpreter

"Talk" is a baroquified accumulator-based language that is created in order to make it difficult to put on Try It Online. The "Talk" language has 4 commands:

• 00 If the accumulator is 0, set the accumulator to 0.
• 01 If the accumulator is 0, set the accumulator to 1.
• 10 If the accumulator is 1, set the accumulator to 0.
• 11 If the accumulator is 1, set the accumulator to 1.

Input:

• The input can be taken via any acceptable input method by our standard I/O rules.

• The input will always be a sequence of the commands above.

• The program will take an input that is either 1 or 0 to set the accumulator to.

Output:

• On the end of a command execution, the accumulator is outputted implicitly.

Rules:

• The input has to be a single string or character list, and splitting it in parts of size 2 is part of the challenge.
• As this is code-golf, the shortest answer, in bytes, wins.

  ---

  code-golfinterpreter

Answer 9

Normalized Malbolge to Malbolge translator

In this task, you will write a program/function that takes a Normalized Malbolge program and outputs the resulting Malbolge program. (This is a secret tool that all Malbolge programmers are using!)

Input

A data structure that (somehow) represents a Normalized Malbolge program.

Output

A data structure that represents the resulting Malbolge program.

Examples

jpoo*pjoooop*ojoopoo*ojoooooppjoivvvo/i<ivivi<vvvvvvvvvvvvvoji:
(=BA#9"=<;:3y7x54-21q/p-,+*)"!h%B0/.~P<<:(8&66#"!~}|{zyxwvugJ%

jjjj*<jjjj*<v
('&%#^"!~}{XE

jjjjjjjjjjjjjjjjjjjjjjj*<jjjjjjjjjjjjjjjjjjjjjjjj*<v
('&%$#"!~}|{zyxwvutsrqpnKmlkjihgfedcba`_^]\[ZYXWVT1|

How to convert

This is a placeholder for the convertion process.

def normal_to_malbolge(prog):
    pos = 0
    malbolge = ""
    for i in prog:
        char = ord("' ( > D Q b c u".split()["*jpovi</".find(i)]) - pos
        while char < 33:
            char += ord("~")-32
        malbolge += chr(char)
        pos += 1
    return malbolge

Explanation

Iterate over the normalized Malbolge program, and then convert all "*jpovi</"'s to a character in "'", '(', '>', 'D', 'Q', 'b', 'c', 'u'. Then, minus the position.

While the temporary Malbolge representations' ASCII code is less than 33, increment the char by the ASCII code of "~" minus 32.

Append the resulting character to the output.

Rules

• This is a code-golf contest; the shortest answer wins.
• No standard loopholes please.

• The default I/O methods are allowed.

  Sandbox

• Is it a duplicate? This probably is.

• Is the challenge well-written?

Answer 10

I need help rewording the prompt.

I learned from last time about having convoluted scoring and having too broad of a focus from my last question. I hope this one is more clear.

Church Subtraction

Lambda calculus has always been a fascination of mine and the emergent behaviors of passing functions into each other is delightfully complex. Church numerals are representations of natural numbers contructed from the repeated application of a function (normally the unary addition of a constant). For example, the number zero returns and "ignores" the input function, one is f(x), two is f(f(x)) and so on:

ident = lambda x: x
zero = lambda f: ident
succ = lambda n: lambda f: lambda x: f(n(f)(x))
one = succ(zero)
add1 = lambda x: x + 1
to_int = lambda f: f(add1)(0)
print(to_int(one))
>>> 1

From this we can easily see that addition is accomplished by applying the first function to x then applying the second function to x:

add = lambda m: lambda n: lambda f: lambda x: n(f)(m(f)(x))
print(to_int(add(one)(two)))
>>> 3

Addition is relatively easy to understand. However, to a newcomer it might be inconceivable to think of what subtraction looks like in a Church encoded number system. What could it possibly mean to un-apply a function?

Challenge

Implement the subtraction function in a Church encoded numeral system. Where subtraction performs the monus operation and unapplies a function n times if the result will be greater than zero or zero otherwise. This is code-golf so shortest code wins.

Input

Two Church numerals that have been encoded in your choice of language. The input can be positional or curried. To prove these are true Church numerals they will have to take in any function and apply them repeatedly (add1 is given in the examples but it could be add25, mult7, or any other unary function.)

Output

A Church numeral. It should be noted that if m < n then m - n is always the same as the identity function.

Examples:

minus(two)(one) = one
minus(one)(two) = zero
...

also acceptable:

minus(two, one) = one
minus(one, two) = zero

Credit:

This github gist for giving me a python implementation of Church Numerals.

Answer 11

Determine the minimal indices needed to cover all queries

code-golf

This challenge is based on Mongo's handling of compound indices and index intersection, inspired by a problem that came up at work, but I'll restate the relevant details here.

Background

In any database, relational or not, the primary purpose of indices is to optimize data lookup.

For example, if the task of finding all code-golf questions on this site had to be accomplished by looping through all posts and looking for the code-golf tag, it would be unusably slow. An index, however, organizes this data in a way that enables fast and efficient lookup of the data we want, which drastically reduces the resource cost of queries in exchange for some more work and space in maintaining the index.

However, the cost of maintaining indices is not negligible, so it quickly becomes untenable to create 2^N indices for N fields. (Databases designed for this purpose do exist and are the better choice when this functionality is actually needed. I'm ignoring this fact because it's a more interesting challenge this way.) Thus, careful index construction and selection is important to get the most bang for your buck.

Details

A simple index only organizes data based on one field but Mongo provides two ways to efficiently query on more than one field: compound indices and index intersection.

Compound Indices

Compound indices organize data based on a sequence of fields, e.g. [A, B, C]. Here, order matters. If data is sorted by A then B then C, then doing a lookup based on C first cannot be done efficiently since there are no guarantees on where the desired data might be located within the index (whereas one could do e.g. a binary search based on A).

Note: compound indices enable efficient queries on prefixes of that index as well. That is, a compound index on [A, B, C] enables efficient queries that have [A], [A, B], or [A, B, C]. However, as previously mentioned, it does not support queries that have [B], [C], [A, C], or [B, C].

Index Intersection

Exactly two indices can be used to optimize a query if there does not already exist a compound index for the desired fields. That is, if there is an index on [A] and an index on [B], then a query on [A, B] can be executed fairly efficiently (though not as efficiently as if there was a compound index, but let's ignore that). This also applies to prefixes of indices, so an index on [A, B, C] and an index on [C] can be intersected to support a query with [A, C].

Problem

Given N fields, determine the minimal indices needed to make all possible queries on those fields efficient. That is, minimize the total number of fields indexed. There may be more than one minimal set.

Note: the order of fields in the query doesn't matter since the query analyzer can reorder these fields to be as optimal as possible before running the query.

Input/Output

Input is a single positive integer and the output should consist of clearly-delimited sequences.

Examples

A variety of output formats are shown here to demonstrate what I mean by "clearly-delimited sequences".

N: 1

[0]

N: 2

AB
B

N: 3

[['A', 'B', 'C'], ['B', 'C'], ['C']]

['AB', 'BC', 'CA']

To elaborate on the first example in this N=3 case, the first index covers a query with all three fields, index intersections cover all choices of two fields, and index prefixes cover all queries with one field.

Note: for N=5, the obvious pattern does not hold; the indices ABCDE BCDE CDE DE E do not enable an efficient query on A, C, E.

---

Meta

I am really hoping this doesn't boil down to [A, B, ..., X], [B, ..., X], [C, ..., X], ... [X]. I haven't taken a look at the N=4 case yet though so I don't know if this pattern holds.

Thankfully, the pattern breaks down for N=5.

Answer 12

N-bonacci from a Seed

Tags: code-golfmathfibonacci

An N-bonacci sequence is a Fibonacci-like sequence where the N previous terms are added to get the next term. The Fibonacci series is a 2-bonacci sequence.

Given a list of integers L of length l and an integer n, output the first n digits of the l-bonacci sequence starting with the sequence L.

Input

Input is a list, array, delimited string, stream, etc of integers, and an integer. Input is flexible, provided L and n are separable. It is guaranteed that n >= 0, and l >= 1.

Output

Output the first n digits of the l-bonacci sequence starting with L. Output is flexible here also: a list, array, string, stream, etc.

Samples:

[1,1], 5       --> 1, 1, 2, 3, 5
[0,1,2], 1     --> 0
[10,1,-1], 10  --> 10, 1, -1, 10, 10, 19, 39, 68, 126, 233
[-1,0,1], 0    --> //no output, or empty output
[-1], 3        --> -1, -1, -1
[-1,-2,1,0], 9 --> -1, -2, 1, 0, -2, -3, -4, -9, -15

This is code-golf, so smallest in bytes wins.

Related

Answer 13

Solve a cubic equation code-golf

(Is this really not a duplicate?)

Answer 14

Randomize \$SL_n(\mathbb R)\$

Given a positive integer \$n > 1\$, return a random element from \$SL_n(\mathbb R)\$.

Details

• \$SL_n(\mathbb R)\$ is the set of \$n \times n\$ matrices with determinant \$1\$.
• In theory the output must cover the whole \$SL_n(\mathbb R)\$ (that is, if the RNG you're using was perfect and we could actually represent real numbers).
• We don't require an uniform distribution.
• Instead of real numbers it is sufficient to work with floating point numbers.

Answer 15

king-of-the-hill

Battleships TDM

In this (not so simple) game of commanding a battleship, you are tasked to defeat the opposing team. Cooperation is essential in order to win the battle.

Each ship starts with $${500\cdot\bigg\lfloor\frac{10}{\log{\frac{n}{3}}}}\bigg\rfloor$$ health (rounded down), where n is a number of players. At 30 players, it is 5000.

Setup

The game starts with a square map of length 50+3n. On top and bottom there is 15% of the width, in which the players' ships will spawn. The rest of the map will be prodedurally generated with islands.

The sample map looks like this:

Phase 1: Issuing commands

On your turn, your program will be given a file input.txt located in the program's directory, with following format:

TURN=(turn number)
SIZE=(size of the map)
YOUR_SHIP=(first 6 chars from SHA1 hash of your ship's name; in case of conflicts a random one will be generated)
YOUR_TEAM=(your team's id)
HEALTH=(your ship's health)
POS=(position of your ship in 0,0 format)
SPEED=(your ship's speed)
DIR=(your ship's direction)
TERRAIN:
(21x21 square of characters, centered on the ship)
PROXIMITY:
(line-separated list of ships within 10 squares, with its properties separeated by semicolon)
CHAT:
(line-separated history of text sent by teammates from the last and current round)

For example:

TURN=21
SIZE=110
YOUR_SHIP=acf44a
YOUR_TEAM=1
HEALTH=3231
POS=64,121
SPEED=3
DIR=NW
TERRAIN:
.....................
###.............x....
##.................##
(etc.)
PROXIMITY:
bd439a=1;69,132;S;3 (ship's id, team, position, direction, speed)
43351f=2;78,112;NE;4
(etc.)
CHAT:
58ab38@21: ENEMY_SHIP 582af2 @ 142,62 NE 3
902dd1@20: 033b2c 4 92,62 SW 1
(etc.)

The map shows . for water, # for land, x for wrecks, 1 and 2 for ships belonging to particular team.

Your program is allowed 3 actions per turn. The actions are:

NONE - do nothing
TURN_LEFT - rotates ship counterclockwise by 45 degrees
TURN_RIGHT - rotates ship clockwise by 45 degrees
SPEED_UP - increases speed by 1. At speed 5 it is ignored.
SPEED_DOWN - decreases speed by 1. At speed -1 it is ignored. 
MESSAGE=message - sends a message to chat
FIRE=x,y - fire a projectile in specified location. Can be done only once per turn. 
           The cannon has range of 25. Issuing a command which exceeds it is ignored.

For example:

TURN_LEFT
SPEED_UP
FIRE=62,69

must be written to output.txt. After each round the file is cleared.

Phase 2: Movement phase

All ships in random order move forward defined by their speed.

• If ship hits the land or wreck during movement, the ship stops and takes damage worth 50x of ship's speed.

• If ship hits the map border, same situation applies.

• If ship hits other ship, it is considered ramming:

  • If rammed from the front, both ships receive damage worth 100x sum of ships' speeds. Both ships stop.

  • If rammed from the back, rammed ship receives damage worth 20x difference of ships' speeds. Rammed ship moves one step forward and ramming ship ends its movement.

  • If rammed from the side, rammed ship receives damage worth 100x speed of ramming ship, while the ramming one receives 50x. Ramming ship stops.

  • If rammed at the angle, rammed ship receives damage worth 50x speed of ramming ship, while the ramming one receives 20x. Ramming ship stops.

  • If the rammed ship is friendly, ramming ship receives 1 point of friendly fire.

Phase 3: Firing phase

In the same order ships fire from the cannons (if any). If the cannon hits a target:

• That is within range 10: Shots deal 500 + 0-99 damage

• That is beyond range 10: Shots deal 500 + 0-99 damage + 0-99 damage for each unit beyond 10th (up to 2084 total damage at range 25)

• If the target is friendly, the damage is 0 and shooting ship receives 1 point of friendly fire.

• There is 5% chance to make a hit critical: The total damage is tripled and shooter recieves 1 critical point.

• If it is a fatal blow, it is considered a destruction:

  • The fatal blow dealer receives a fatal point.

  • Attacker with most dealt damage receives a kill point (it may be the same ship as the dealer).

  • Everyone else with a hit receives an assist point.

  • If it is a solo kill, the dealer receives 2 of each points instead.

Phase 4: Checking conditions

Each ship is considered a wreck if:

• Health reaches below 0 HP,

• Ship gains 5 friendly fire points.

Wrecks remain on the map, but they are removed from the queue and program of such ships is being not executed.

Game ends whenever entire team gets destroyed or after 1000 turns, in which the points are being calculated as follows:

• 1 point for each 10 damage dealt

• 500 points for each kill

• 200 points for each fatal blow

• 100 points for each assist

• 150 points for each critical hit

• -250 points for each friendly fire hit

• 1000 points for each winning team member

• Points for achievements (names are just for decoration):

500 (awarded once) Beyond the horizon - Hit on enemy from 13 sq or more
500 (awarded once) Maximum range - Hit on enemy from 23 sq or more
500 (awarded once per participant) Coordinated attack - 3 or more ships attacking the same target
500 (awarded once) Hammer - Ram a ship on full speed
500 (awarded each time) - Survive a critical hit
1000 (awarded once per participant) Anihilation - Both ships getting destroyed in headfront ramming

The ship with most points after 10 games wins.

Code

The controller code is here.

Rules

Your program can:

• store data in files within its own directory

• communicate with teammates through the team's chat

Your program cannot:

• read files outside its scope

• disrupt the communications

• Attack friendly ships on purpose

• Copy other competitors' functionality (No duplicates)

• Use standard loopholes

Sandbox questions

• I'm not sure whether to allow the challenge in any usual language or require one specific (in this case Java 8)?
• Wouldn't be achievements unnecessary? If not, could be any added/modified/removed?
• Are there some rules that require clarification?

Answer 16

Black And White Shirts 3

This is the third in a series. The first can be found here, and the second here. The premise is similar to the first two, but with some changes and a new goal.

Assume I have some number of black shirts and some number of white shirts, both at least 1. Both colors of shirt have a non-zero Vividness. All shirts of a given color start with the same Vividness.

Every day, I pick out a clean shirt to wear, and it becomes dirty. Once I run out of all clean black shirts or all clean white shirts, I wash all my dirty shirts of both colors and start over. Clean shirts do not get washed. Whenever a shirt gets washed, its color changes based on its Vividness and the Vividness and colors of the other shirts being washed, then its Vividness goes down by one to a minimum of 0. All things being equal, over time, all shirts will generally tend towards a shade of gray.

If a shirt is ever closer to the opposite color (eg. a black shirt looks light gray), it becomes a shirt of that color.

When picking which shirt to wear, I choose the shirt which is either closest to black or closest to white. If there is a tie, I choose the one with the highest Vividness.

Challenge:

Take in an arbitrarily long sequence of two indicators (eg. b b w w b w b b w b...) representing my choice of shirt to wear on that day. Continue execution until either my last black shirt or my last white shirt loses its last vividness. Once this occurs, stop consuming input and print out the colors of all shirts.

Inputs:

Number of black shirts, number of white shirts, Vividness of black shirts, Vividness of white shirts, and a sequence of shirt selections of arbitrary length at least long enough for one color of shirt to run out of Vividness (can be considered infinitely long). The selection can be represented by any two characters (eg. b, w).

Output:

Color of all shirts, sorted from lightest to darkest, as a percent of how close it is to white, rounded to the nearest whole percent. A completely black shirt is 0, and a completely white shirt is 100.

Color changing:

The color of a shirt tends towards the average of all shirts' colors in the wash. How close it gets depends on its own Vividness.

TODO: Determine if this rule is necessary (I don't think it is): If all shirts in the wash have 0 Vividness, none of them change color.

When washed, shirts are changed based on the following pseudocode algorithm (some of which may not be necessary for your simulation):

struct shirt {
    int vividness
    float color
}

func washShirts(shirt[] allDirtyShirts) {
    totalVividness = allDirtyShirts.sum(shirt => shirt.vividness)
    if (totalVividness == 0)
        return

    averageDirtyColor = allDirtyShirts.sum(shirt => shirt.color * shirt.vividness) / totalVividness

    for each shirt in allDirtyShirts
    {
        shirt.color = (shirt.color * shirt.vividness + averageDirtyColor) / (shirt.vividness + 1)
        if shirt.vividness > 0
            shirt.vividness--
        if shirt.isBlack && shirt.color > .5
            shirt.isBlack = false
        else if !shirt.isBlack && shirt.color < .5
            shirt.isBlack = true
    }
}

Make sure that all shirts base their calculation on the Vividness and color values of all other shirts before the change. Perform no rounding beyond normal floating point restraints within your language of choice (within reason) during any calculation. Only round the value during output. When rounding for output, choose any convenient rounding method among:

• truncating (always round down)
• rounding to the nearest integer
  • .5 rounds up
  • .5 rounds down
  • .5 rounds to the nearest even integer

Test cases:

Note: These test cases use rounding to the nearest even integer. Your output may vary in some cases.

1 2 1 1 w b
100 75 25

3 3 2 1 w b w b w w w w w w w w
71 71 71 14 14 0
#note that processing would stop after w b w b w. The remaining input would be ignored.

#todo: more test cases

General rules:

• This is code-golf, so shortest answer in bytes wins.
• Default I/O rules apply

Answer 17

Title: Lossless Compression

Implement the following lossless compression pseudo-algorithm and its decompressor; scored by the number of bytes output by your compression algorithm, after you've put your source-code for both the compressor and decompressor through your own implementation of the compressor algorithm, described below:

Algorithm Description

Essentially, this is a simple dictionary compression algorithm (which isn't always guaranteed to compress the output, especially for short inputs). You want to scan for sequences of characters that appear multiple times, and then create a lookup; in order to shorten the input string.

The input string to generate your score must contain all characters in your submission; however the program must also be capable of compressing successfully the test-cases below.

The dictionary (which forms part of the output string) can use any other character as an indexer character, except a single separate character of your choice (| in my examples), which is reserved.

The output format should be a sequence of IndexcharValuestring| (i.e. index character, followed by the value string, followed by the separator - collectively "the dictionary"); followed by the compressed input string.

Some examples:

1. testRattesttestRattesttesttesttestRattest -> _test|+Rat|_+__+____+_ - because test is represented by _ and Rat is represented by +; then the compressed string is shown. each section is separated by the character |.

To decompress, simply replace _ with test and + with Rat in the output (after the last |).

The dictionary entry can also be nested - for example:

ininputinputininput -> &in|*&put|&**&* because in is represented by & and &put is represented by *

Exactly which characters end up being grouped will depend on your compression algorithm. For example, the previous string could also be output as &input|in&&in&, or &in|*put&|&&**&put

Note that the recursive compression could go even further, but at this point the output gets longer again:

ininputinputininput -> &in|*&put|^&*|^*^

It's up to you how much compression your algorithm performs, as long as it matches or beats the longest of the outputs for each example in this post.

2. AbcAbcDefDefDeggggggggggggggggggAbc

could output:

-Abc|£De|#£f|*ggg|--##£****-

3. Well I've heard there was a secret chord That David played and it pleased the Lord But you don't really care for music, do you? Well it goes like this, The fourth, the fifth, the minor fall and the major lift! The baffled king composing Hallelujah. Hallelujah Hallelujah Hallelujah Hallelujah

could output:

+ you|/ing |-ed |%pl|¬it|#or|^th|)ll|(he|"T( |$t( |*We) |_Ha)elujah|*I've (ard t(re was a secret ch#d That David %ay-and ¬ %eas-$L#d But+ don't rea)y care f# music, do+? *¬ goes like ^is, "four^, $fif^, $min# fa) and $maj# lift! "baffl-k/compos/_.____

4. %Testttttttttt%%%%%%%%

could output:

$%%%%|_ttttt|%Tes__$$

5. aAbBcCdDeEfFgGhHiIjJkKlLmMnNoOpPqQrRsStTuUvVwWxXyYzZ0123456789 ?!.,;

must output:

aAbBcCdDeEfFgGhHiIjJkKlLmMnNoOpPqQrRsStTuUvVwWxXyYzZ0123456789 ?!.,;

(because no compression is possible)

Acceptance Criteria

In order to class as valid, the algorithm you create should:

• Meet the algorithm description above
• Be able to match or beat the length of the test cases above (shorter = better)
• Output from the compressor (and therefore input for the decompressor) should be in the format shown (dictionary and separator characters may differ). Input for the compressor (and therefore output for the decompressor) should also be in the format shown.

Sandbox Notes and Questions

• Is the challenge clear?
• Is the scoring mechanism fair? I'm still not sure how to deal with characters vs bytes
• Is the spirit of the challenge clear? (i.e. to actually make an algorithm, rather than simply beat the examples and get the best score)
• Is there any interest in this challenge?

Answer 18

Posted. I prefer to retain the content for potential issues.

Duck, duck, gone!

Here is the (quite childish) Five little ducks song(it is not long):

Five little ducks went out one day,
over the hills and up away.
Mother Duck said, "Quack Quack Quack Quack",
but only four little ducks came back.

Four little ducks went out one day,
over the hills and up away.
Mother Duck said, "Quack Quack Quack Quack",
but only three little ducks came back.

Three little ducks went out one day,
over the hills and up away.
Mother Duck said, "Quack Quack Quack Quack",
but only two little ducks came back.

Two little ducks went out one day,
over the hills and up away.
Mother Duck said, "Quack Quack Quack Quack",
but only one little duck came back.

One little duck went out one day,
over the hills and up away.
Mother Duck said, "Quack Quack Quack Quack",
but none of the little ducks came back.

Mother duck herself went out one day,
over the hills and up away.
Mother Duck said, "Quack Quack Quack Quack",
and all of the little ducks came back.

Your task is not to output this song. You should take a verse and output the next verse (the next verse of the last verse is the first verse).

Rules

• No standard loopholes, please.
• Input/output will be taken via our standard input/output methods.
• The exact verse must be outputted, and there should be no differences when compared to the song lyrics. The input will not be different when it is compared to the song lyrics too.

Examples

Mother duck herself went out one day,
over the hills and up away.
Mother Duck said, "Quack Quack Quack Quack",
and all of the little ducks came back.

Expected:

Five little ducks went out one day,
over the hills and up away.
Mother Duck said, "Quack Quack Quack Quack",
but only four little ducks came back.

Three little ducks went out one day,
over the hills and up away.
Mother Duck said, "Quack Quack Quack Quack",
but only two little ducks came back.

Expected:

Two little ducks went out one day,
over the hills and up away.
Mother Duck said, "Quack Quack Quack Quack",
but only one little duck came back.

Sandbox

• Is it detailed enough?
• Is the input/output rules clear enough?
• Do I need any more information?

---

code-golfstring

Answer 19

Polynomials Through Points

You will get a set of n Cartesian coordinates. You must output a polynomial going through all of the points.

Input

• Points are 2-dimensional.
• You may assume that no two points share a x coordinate.
• You may take points as a tuple of pairs, or pair of equal length tuples.
• 1<n<1000

Output

• For polynomial y=x^3+3*x^2+1, you may output as:
  • y=x^3+3*x^2+1
  • x^3+3*x^2+1
  • y=x^3+3*x^2+0*x+1
  • x^3+3*x^2+0*x+1
  • y=x^3+3*x^2+x^0
  • x^3+3*x^2+x^0
  • y=x^3+3*x^2+0*x^1+x^0
  • x^3+3*x^2+0*x^1+x^0
  • y=1*x^3+3*x^2+1
  • 1*x^3+3*x^2+1
  • y=1*x^3+3*x^2+0*x+1
  • 1*x^3+3*x^2+0*x+1
  • y=1*x^3+3*x^2+1*x^0
  • 1*x^3+3*x^2+1*x^0
  • y=1*x^3+3*x^2+0*x^1+1*x^0
  • 1*x^3+3*x^2+0*x^1+1*x^0
  • [1,3,0,1]
• You may output any polynomial satisfying the condition.

Rules

• Stabdard loopholes are forbidden.
• Any method approved by Standard I/O is allowed.
• This is code-golf, so shortest code wins!

Answer 20

Shortest way to get an EOF Error

It's simple, simply write the shortest code to raise an EOF Error. An EOF Error happens when the language expects more code to be entered into the source code; however, the language encounters an EOF character. So here is a sample Python program to throw an EOF error.

id(

Python expects more code to be entered, but EOF is entered instead. Therefore it throws an "EOF Error" (technically a Syntax Error though, but the interpreter says unexpected EOF while parsing).

To simplify that, output text to STDERR containing the string EOF. Normally a language will exit after outputting to STDERR with an error, so if you are hard-coding the value out to STDERR, you should also exit the program with a 1 value.

Input/Output

Your input will be none; however, you should output a message to STDERR that proves that the program generates an EOFError.

Rules

• Since this is code-golf, the shortest answer wins.
• No standard loopholes please.
• Any method approved by Standard I/O is allowed.

---

code-golferror-message

Feedback

• Is this clear enough?
• I don't believe this is a duplicate (I found this, but it's restricted to a single language), but does anyone recognise this?
• The tags as code-golf, error-message. Anything else?
• Any further feedback?
• Is it possible to have trivial answers on most languages for this challenge?

Answer 21

A Musical Tuner

code-golfnumbermusic

Oh no! My tuner's batteries ran out, I need to play in a concert in a few minutes, and I need to know if my instrument's in tune! I need this tuner quick, so it needs to be short.

Background

In music, all notes are given a letter from A-G/H, an optional sharp/flat ♯/♭, and a number specifying what octave it is in, starting from 0. This is called scientific pitch notation.

In equal temperament, \$\sqrt 2 \approx 1.05946 \$ is an important ratio, as used in the formula $$ P_n = P_a (\sqrt2)^{n-a} $$ where

• \$ P_n \$ is the desired frequency, in hertz.
• \$ n \$ is the number of keys from the left on a piano the desired note is.
• \$ P_a \$ is the reference frequency, in hertz.
• \$ a \$ is the number of keys from the left on a piano the reference note is.

A piano begins at \$ A_0 \$ as the 1st key, and with reference frequency of \$ A_4 = P_a = 440 \$ Hz, at the 49th key.

The whole step, the tonal distance between two notes separated by one key, is divided into 100 cents. A half step is exactly 50 cents.

The Challenge

Write a full program that, when given a decimal number in hertz, outputs the closest note in scientific pitch notation, and how far it is from that note in cents.

Input

A positive number in hertz. This can be a string, number, list of whole number and decimal, etc. You can always assume this to be positive, and a number with maximum 3 decimal places.

The input is in the range \$ 27.5 \le P_n \le 4186 \$.

Output

A note in scientific pitch notation, and how many cents it is from, in the form

[Note letter][Sharp/Flat][Octave number][+/-][Cents]

• If a note is determined to be close to a natural note, no sharps or flats should be output.
• Output either sharps or flats.
• Sharps can be either ♯/# , and flats either ♭/b.
• Octave number ranges from 0 to 8.

Other Rules

• Standard loopholes apply.
• Shortest code wins.

Test Cases

Input --> Output
440 --> A4
261.626 --> C4
24.995 --> G♯0-8 (OR G#0-8)
1320.068‬ --> E6+1
3674.882‬ --> B♭7-13 (OR Bb7-13 OR A7+13)

Answer 22

Fewest number of button presses to set the cook time

A GolfCo™ microwave oven has a 12-button keypad like this:

[1]  [2]  [3]
[4]  [5]  [6]
[7]  [8]  [9]
     [0]  [+30]
   [START]

How the microwave operates

The microwave reads and processes button presses as follows:

1. Buttons [0]-[9] add the corresponding digit to the right end of the cook time, up to 4 digits total. Once started, these buttons do not function.
2. The [+30] button adds 30 seconds to the cook time, and starts the cooking process (if not already started).
3. The [START] button starts the cooking process.

The microwave can be programmed with a cooking time ranging from 1 second to 99 minutes and 59 seconds.

Any one or two-digit cook time is interpreted as seconds only, ranging from 1 to 99 seconds.

Any three or four-digit cook time is interpreted as two digits of minutes and two digits of seconds. In this mode, the minutes portion of the cook time can range from 0 to 99 minutes, while the seconds can range from 0 to 59 seconds.

The challenge

Given a time in minutes:seconds (eg. "4:45" for four minutes and 45 seconds), print the button sequence with the least number of button presses required to set the cook time and start the cooking process.

As this is code golf, the smallest program in bytes wins.

Input

Input will be given in the common MM:SS format, where "MM" specifies minutes and "SS" specifies seconds, separated by a colon.

Minutes can be zero padded to 2 digits or the leading zero omitted, at the golfer's discretion. Minutes can range from 00 to 99.

Seconds will always be 2 digits, ranging from 00 to 59.

The cook time will range from 00:01 to 99:59.

Output

The program will output the sequence of button presses needed to program the cook time and start the microwave.

Buttons [0] to [9] will be output as the corresponding digit "0"-"9".

The [+30] button will be output as "+".

The [START] button will be output as "S".

Test cases

Input                  Output
=======================================
04:45 (or 4:45)        4 4 5 S
00:08                  8 S
00:30                  +
00:35                  5 +
00:20 (or 0:20)        2 0 S
01:20 (or 1:20)        8 0 S
01:25 (or 1:25)        8 5 S     ("2 5 + +" and "1 2 5 S" are both too long)
01:30 (or 1:30)        + + +     ("9 0 S" is also correct)
01:35 (or 1:35)        5 + + +   ("1 3 5 S" is also correct)
01:39 (or 1:39)        9 + + +   ("1 3 9 S" is also correct)
01:40 (or 1:40)        1 4 0 S   ("1 0 + + +" is incorrect)
01:50 (or 1:50)        1 5 0 S   
02:00 (or 2:00)        2 0 0 S   ("+ + + +" is also correct)
02:30 (or 2:30)        2 3 0 S   ("+ + + + +" is incorrect)
03:00 (or 3:00)        3 0 0 S   
10:00                  1 0 0 0 S
99:59                  9 9 5 9 S

Answer 23

Measure the Discrepancy

code-golfmathsequence

Given a finite sequence of real numbers \$ s_1, s_2, \ldots, s_n\$ and an interval \$I=[a,b]\$ that contains the whole sequence, find its discrepancy \$D_n\$.

Definition*

Let \$I = [a,b]\$ be an interval that covers the whole sequence \$(s_i)_i\$, that means for all \$i\$ we have \$s_i \in I\$. The discrepancy \$D_n\$ is defined as

$$D_n = \sup_{[u,v] \subseteq I} \left| \frac1n N(u,v) - \frac{v-u}{b-a} \right|$$

Here \$N(u,v) = \#\{i \mid 1 \leqslant i \leqslant n, s_i \in [u,v]\}\$ denotes the number of values of the sequence \$(s_i)_i\$ that are in the interval \$[u,v]\$.

^{* Technically the discrepancy \$D\$ is defined for infinite sequences as \$D = \lim_{n\to \infty} D_n\$. Intuitively speaking, the *discrepancy measures how uniformly distributed the sequence is in the given interval \$I\$. Sampling an uniform distribution on \$i\$ infinitely many times results in an discrepancy of \$D=0\$.}

Examples

to be added...

Answer 24

Subtract two numbers with Rule 110

Background :

It is known that Rule 110 is Turing complete, but in general, I have seen a lack of actual programs that utilize this property of Rule 110, so I propose that we do something about it ;)

Some explanation

Rule 110 is a one dimensional cellular automaton, consisting of cells on/off, and the neighbors of those cells change the cell in the next iteration. Here is a page detailing how rule 110 works, but here is also a basic table that summarizes the rule (the center number is the current cell's state, the two on the outside are its neighbors, the number to the right of the equals is the state for the next generation)

111 = 0
110 = 1
101 = 1
100 = 0
011 = 1
010 = 1
001 = 1
000 = 0

The Challenge

I want you to subtract two numbers, unsigned, eight bits long (No handling of negatives, input one will always be greater than or equal to input two)

Note : Index 0 is where the first 1 starts, which denotes your program, simply because the "tape" is infinite, and leading zeroes cannot be distinguished, so it must start at the first one

Input have to be inputted in unary, and must be inputted at a set interval from a specific point from the beginning of your program, and the inputs must not overlap. That may sound confusing, but here are some examples.

First, clarification on input. Input needs to be 8 bits long, and must be formatted to be so, if you had zero, it would be inputted as follows : 00000000, 2 would be 00000011, 7 would be 01111111 etc..., up to eight.

The first input is at intervals of 2 starting at index 1, the second input has an interval of 3 and starts at 25

1 _ 01 _ 01 _ 10 _ 10 _ 10 _ 10 _ 10 _ 101 = 011 = 111 = 000 = 110 = 110 = 110 = 001 = 1010100101

The "_" is the first input, the "=" is the second input, they cannot overlap, and the interval represents the set distance that they must be seperated by. The bits themselves are inputed as ones, so if my first input was 00000111 and my second input 00111111 then my program would look like this

1 0 01 0 01 0 10 0 10 0 10 1 10 1 10 1 101 0 011 0 111 1 000 1 110 1 110 1 110 1 001 1 1010100101

The output is also defined in a similar fashion, from the start of the program (denoted by a 1) at specific intervals the bits represent the unary output

Example:

input one = 00011111, input two = 00000011

output = 00000111

Score

The number of bytes from the first one to the last one in the initial program. Lowest score wins! Good luck!!!

I thought this was ready for the main, but it wasn't, so if ya'll have any problems, please let me know and I'll address them, as I will for the problems already proposed

Answer 25

code-golf math combinatorics algorithm

Disconnect a social network

^{A version of this question was used in the 2019 International Mathematical Olympiad, which is now public. Modifications italicised.}

A social network has n users, some pairs of whom are friends. Whenever user A is friends with user B, user B is also friends with user A. Events of the following kind may happen repeatedly, one at a time:

Three users A, B, and C such that A is friends with both B and C, but B and C are not friends, change their friendship statuses such that B and C are now friends, but A is no longer friends with B, and no longer friends with C. All other friendship statuses are unchanged.

Given the initial graph of users, find whether sequence of such events so that at the end of the sequence each user is friends with at most one other user exists, and if so output that sequence.

Test cases

These cases have n followed by a list of friendships in the graph, and output as a list of triples of people in order A-B-C (and 0 if no sequence of triples exists - note that this is different from [] in this particular output scheme, here [] means that the graph already satisfies the condition that each user is friends with at most one other user).

3, [[1,2], [2,3]]
[[1,2,3]]

3, [[1,3], [2,3]]
[[2,3,1]]

3, []
[]

3, [[1,2]]
[]

3, [[1,2], [1,3], [2,3]]
0

6, [[1,2], [2,3], [3,4], [4,5], [5,6]]
[[1,2,3], [1,3,4], [1,4,5], [1,5,6]]

6, [[1,2], [1,6], [2,3], [3,4], [4,5], [5,6]]
0

7, [[1,2], [1,3], [1,4], [2,3], [5,6]]
[[2,1,4], [1,3,2], [1,2,4]]

4, [[1,2], [1,3], [1,4], [2,3], [2,4], [3,4]]
0

6, [[1,2], [1,3], [1,4], [1,5], [1,6], [4,5], [4,6], [5,6]]
[[2,1,4], [3,1,5], [5,1,6], [2,4,6], [4,5,3]]

5, [[1,2], [1,3], [2,3], [2,4], [2,5], [3,4], [3,5]]
0

Input and output format are flexible as long as they conform to standard I/O requirements, and standard loopholes are forbidden. (In particular, for the impossible case, the output can be anything which is not an output from a possible graph, such as [[0,0,0]] or an additional 'success' boolean.)

This is code-golf, so the shortest code wins!

Answer 26

code-golfmathsparsing

Shorthand Combined Functions

I was doing some investigation into trig functions using compound angles recently, and noticed that the results are really long and tedious to write: $$ cos(A+B) = cosAcosB - sinAsinB\\ cos(A-B) = cosAcosB + sinAsinB\\ sin(A+B) = sinAcosB + sinBcosA\\ sin(A-B) = sinAcosB - sinBcosA\\ $$ $$ tan(A+B) = \frac{tanA+tanB}{1 - tan A tan B} $$ $$ tan(A-B) = \frac{tanA-tanB}{1 + tan A tan B} $$

Realising this, I devised a shorter, golfier way, of writing such expressions:

<direction><operator>[functions](variables)

Where direction is either « or » and operator is in the string +-*/

---

When the direction is «, functions in functions are applied to variables in the following method (assuming functions is f, g, h and variables is x, y, z and the operator is +)

$$ f(x)f(y)f(z) + g(x)g(y)g(z) + h(x)h(y)h(z) $$

When there isn't a given operator, it is assumed that it is * (multiplication)

When the direction is », however, functions in functions are applied to variables in the following method (assuming functions is f, g and variables is x, y and the operator is +):

$$ f(x)g(y) + f(y)g(x) $$ Once again, when there isn't a given operator, it is assumed that it is * (multiplication)

The Challenge

Given a shorthanded string as described above, output the expanded expression

Test Cases

Input -> Output
«+[cos,sin](a,b) -> cos(a)cos(b) + sin(a)sin(b)
»+[cos,sin](a,b) -> cos(a)sin(b) + sin(a)cos(b)
«[f](x,y,z,n) -> f(x)f(y)f(z)f(n)
«+[f](x,y,z,n) -> f(x) + f(y) + f(z) + f(n)
«+[f,g]() -> 
»*[f,g]() ->
»-[f,g](a,b) -> f(a)g(b) - f(b)g(a)
»[g,f](a,b) -> g(a)f(b)g(b)f(a)
«+[tan](a,b) -> tan(a) + tan(b)
»+[](a,b) -> 
»-[f,g](x,y,z) -> f(x)g(y)z - f(y)g(z)x - f(z)g(x)y
«/[f,g](x,y,z) -> f(x)f(y)f(z) / g(x)g(y)g(z)
«[]() ->
»[]() -> 

Let it be known that:

• The direction will always be given
• The operator is optional
• The [] denoting the functions will always be present, but will not always contain functions
• The () denoting the variables will always be present, but will not always contain variables

Therefore, if no functions/variables are present, then an empty output is required. Whitespacing within the answer doesn't matter (i.e. newlines/extra spaces don't invalidate outputs).

Input can also be taken as:

[direction, operator, [functions], [variables]]

In which case, direction will be a string, operator will be either an empty string or an operator, functions will be a (sometimes empty) list of strings, as will variables.

As per usual, standard loopholes are forbidden, and, as this is code-golf, the shortest code (in bytes) wins.

Feedback

So what do you guys think? Do I need to add a more detailed explanation for how everything would work? Also, would it be requested to have input taken as [direction, operator, [functions], [variables]]?

Answer 27

This message is open for anyone to adopt and post to main. The full post can be found in the revision history. For more details, see the chat room or meta post.

Answer 28

It was found that this challenge is a duplicate. if you would like to see the challenge, please look in the revision history.

Answer 29

Follow the Path

Posted here.

Answer 30

Fermat's Last Theorem, mod n

It is a well known fact that for all integers \$p>2\$, there exist no integers \$x, y, z>0\$ such that \$x^p+y^p=z^p\$. However, this statement is not true in general if we consider the integers modulo \$n\$.

You will be given \$n\$ and \$p\$, which are two positive integers with \$n>1\$. Your task will be to write a function or program to compute all positive integers \$x, y, z<n\$ such that \$(x^p+y^p)\$ and \$z^p\$ give the same remainder when divided by \$n\$.

Input

Any reasonable method of input is allowed. E.g. two separate user inputs, ordered pair, two function parameters, etc.

Output

Any reasonable method of output is valid, it may be produced by a function or output to the screen. The order the triples are listed does not matter. Triples such as (1, 2, 3) and (2, 1, 3) are considered distinct, and all distinct triples should be listed exactly once. No invalid/trivial triples such as (0, 0, 0) should be output.

Examples

n p -> Possible Output
----------------------------------------------------------------
2 3 -> []
3 3 -> [(1,1,2),(2,2,1)]
3 4 -> []
4 3 -> [(1,2,1),(1,3,2),(2,1,1),(2,2,2),(2,3,3),(3,1,2),(3,2,3)]

Scoring

Shortest code in bytes with no standard loopholes wins.

code-golf number-theory