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Answer 1

Evil Overlord, Part 1: Moon Base Scouting

code-challenge restricted-time

I'm starting these "Evil Overlord" challenges as a way to experiment with non-golf scoring. Though I may have one or two code golf challenges.

---

If you're going to be an evil overlord, there are 2 things that you need: an inner sanctum, and mad-science tech.

To fill these requirements, your science minions have developed a fusion reactor, and Elon Musk has agreed to help you establish a Moon base. Now you just need to pick a spot.

These are the criteria that will be used:

• You'll need some Helium-3 to power your reactor, so scoring will be based on proximity to deposits. More on this under Scoring.
• It cannot be on the far side of the Moon, because then you won't have comms to deliver ultimatums with.
• Elon Musk has given you a tight deadline (that absolutely MUST be followed), so you have a runtime limit. Details under Restrictions.

Input

Your input will be a list of ³He deposits, with information on size and location. Some will be on the far hemisphere.

Output

You should output a single coordinate for where the Moon base should be. It can't be on the far side, but you can still collect ³He from there.

Coordinates and Distances

The coordinates in the test cases are radial coordinates from a pole at the center of the visible hemisphere. You can use a different coordinate system (e.g. use a map projection) but please specify it if you do.

Since this is a sphere, calculating distances is done with the following equation that I shamelessly stole from this Wikipedia article:

cos(c) = cos(a)cos(b)+sin(a)sin(b)cos(C)

For our purposes:

• a and b are the latitudes from the pole.
• c is the angular distance between the points.
• C is the difference in longitude between the points.

Restrictions

To do. I don't remember the specs of the computer I have in mind, and I don't know what a reasonable time limit would be.

Scoring

You will be scored by the amount of Helium-3 that you can mine. The formula for how much you get from a single deposit is as follows:

^{(There's no real reason for this specific formula; I liked the curve it produced is all.)}

d is the angular distance calculated between the two points, in radians; s is the size of the deposit. Deposits more than 1 radian away don't give you anything.

Test Cases and Winning

Beta generator for test cases, for which I'd appreciate debugging in the Sandbox:

function makeTestCase(deposits) {
    var depositList = Array(deposits);
    for (var i = 0; i < deposits; i++) {
        var point = getSphericalPoint();
        depositList[i] = [point[0], point[1], getDistNum()];
    }
    return depositList;
}

function getSphericalPoint() {
    const pointgen = () => Math.random() * 2 - 1;
    do {
        var [x, y, z] = [pointgen(), pointgen(), pointgen()];
    } while (x*x + y*y + z*z >= 1);
    return [Math.atan(y / Math.sqrt(x*x + z*z)), Math.atan2(x, z)];
}

function getDistNum() {
    return Math.sqrt(-1 / Math.log(Math.random()));
}
try {
console.log(makeTestCase(10));
} catch (e) {
    console.log(e.message);
}

The test cases will be arranged as follows:

• A test case with only a few deposits, with a heatmap showing score for each point.
• A few test cases with a few dozen deposits each, for debugging.
• Test cases and a generator for them with 100+ deposits each.
• 10 or so ranked test cases (made with the above generator) that determine the winner. Until I evaluate the submissions, I will only post hashes of them.

---

Definitely has a long ways to go before it's ready to post, but I'd like to know if this has merit as a challenge.

To-do:

• Establish some test cases.
• Figure out the specs of the machine in question.
  • Once that's done, figure out a good time limit.
• Solidify the scoring formula—something better I can use?
• Figure out some tags.

Answer 2

Ordering the integer arrays code-golf integer array-manipulation

So, we have managed to print all integers. Yay! The next step is to extend this to the set of integer arrays. An integer array is an ordered array that only consists of integers. As in the linked challenge, integers can be negative too, but that should be out of the way now that we have found a way to order them. However, in this challenge, arrays of all lengths ([0, ∞)) must be accounted for.

Note that you don't necessarily have to print the arrays. You can do one of these things:

• Take an index (0- or 1-based) and return an integer array. In this case, your solution must be bijective from the natural numbers starting with the index base to the set of integer arrays.
• Take an integer array and return an index (0- or 1-based). This is essentially the inverse of the previous case, so your solution must be bijective from the set of integer arrays to the natural numbers starting with the index base you have chosen. If your language supports variadic functions, you can take the array as multiple integer arguments instead.
• Print all possible integer arrays. Note that every possible integer array must be eventually printed. If an array will be printed after infinite time, then it will not be eventually printed.

The arrays can be in any native format that represents an ordered collection.

In case you choose to print to an output stream, the output format is as following:

• Integers must be in decimal (digits 0123456789) or your language's native format.
• The minus sign's representation must be consistent and one of - or your language's native minus sign. It must be prefixed to its corresponding number, unless your language's native integer format happens to have it at other positions too. However, the minus sign must be adjacent to at least one of its corresponding integer's digits.
• The separators between integers and between arrays must be consistent.
• You can output any prefix as long as it's consistent, but you don't have to.
• The output should not have any ambiguities. For that reason, you must specify the separator between integers and the separator between arrays. Also, if you don't specify any of those, the number format's default is decimal with digits 0123456789, the minus sign's default is - and its default position is being prefixed, and no output prefix is assumed.
• You are allowed to output negative zero.
• If you want, you can output floating-point numbers with the fractional part be 0. This can be inconsistent, however it should be specified in the post.

This is code-golf, so the shortest solution wins! However, don't let that bring you down; if your solution is way longer than others' but in a unique language, then that's an achievement!

Sandbox questions

• Is the output stream text format too lenient? Doesn't seem like it.
• Should I add a link to the standard loopholes? I feel like that won't do much.
• Are the tags good enough?

Answer 3

Dollar Bill Auction

Answer 4

Operate on a subset of a register

code-golf matrix quantum-computing

Note: You do NOT need to know anything about quantum mechanics or quantum computing to understand this challenge. I've tried to include sufficient background for any old code golfer to realize what's going on.

Motivation (much of this can probably be skipped)

In quantum computing, the equivalent of a bit is a qubit. Like a bit, a qubit will have a state of OFF or ON (0 or 1) when observed, but unlike a bit, a qubit can exist in both states simultaneously while unobserved. Trippy.

What's even trippier is that they don't exist in simple superpositions (40% chance to observe 0, 60% for 1)—you can have two qubits that will behave the same when observed, but not when interacting with other qubits. Taking this into account, a convenient representation of a qubit's state is a complex vector, with bases |0> and |1>. A qubit with state (1+0i)|0> + (0+0i)|1> will always show 0 when observed, as will (0+1i)|0> + (0+0i)|1> or (0.6+0.8i)|0> + (0+0i)|1>. What matters here is the squared magnitude of each component—that's the probability of observing the corresponding basis vector. Noting this, (-0.5+0.5i)|0> + (-0.5-0.5i)|1> will "choose" randomly between the two possible states. This ability to have multiple states at once allows qubits to store much, much more information than an equal number of bits.

Now, since a qubit is a two-dimensional vector (as far as we're concerned), an operation on a qubit can be represented as a 2x2 matrix. For example, the identity:

[[1+0i  0+0i]
 [0+0i  1+0i]]

will take any qubit to an equivalent one, while the Hadamard transform, represented by the matrix:

[[1+0i  1+0i]
 [1+0i -1+0i]]

will turn any pure state (P(0) == 0 or 1) into an equal superposition of the two. Check out this challenge for generation of this matrix, generalized to n qubits! These matrices multiply a qubit's vector state to yield a new state.

A qubit on its own is little more useful than a bit. However, they can be put into registers with others, so a "qubyte" can store 0, 255, or any arbitrary superposition of the numbers between.

I won't go into depth on entanglement here, but I'll say that it is a property of these qubits that makes storing quantum registers as lists of qubits not work at all (and makes quantum computers outperform classical ones). It works much better to treat a register much like a qubit and give it a vector representation, this time with a basis vector for each observable state. For example, two (1+0i)|0> + (0+0i)|1> qubits together form a (1+0i)|00> + (0+0i)|01> + (0+0i)|10> + (0+0i)|11> register. Note that the probability distributions of outcomes are identical for the two representations—in this case, both qubits will and up as 0 in both representations.

Important stuff again

These registers are nice and all, but it's difficult (and often impossible—try it yourself on (-0.5+0.5i)|00> + (0+0i)|01> + (0+0i)|10> + (-0.5-0.5i)|11>!) to extract the state of a single qubit in a register from the register's vector—that is, you can have a register in a state unformable by individual qubits. Fortunately, to apply, say, the Hadamard transform to qubit 2 of a register, we can construct a matrix by which we can multiply the entire register but change only the one qubit. Neat!

Let's say we have an operation m on one qubit defined as:

[[x y]
 [z w]]

and a three-qubit register of qubits a|0> + b|1>, c|0> + d|1>, and e|0> + f|1>. This register has a vector form (treating the first of these qubits as the least significant) of:

eca|000> + ecb|001> + eda|010> + edb|011> + fca|100> + fcb|101> + fda|110> + fdb|111>

Defining g := ax + by and h := az + bw, we see that the result of applying m to a|0> + b|1> is g|0> + h|1>. What we want is a matrix that, when multiplied by the register state above, yields the same but with a and b replaced by g and h, respectively:

ecg|000> + ech|001> + edg|010> + edh|011> + fcg|100> + fch|101> + fdg|110> + fdh|111>

Let's look at a matrix that does just this:

[[x y 0 0 0 0 0 0]     [[eca]     [[ecax + ecby]     [[ecg]
 [z w 0 0 0 0 0 0]      [ecb]      [ecaz + ecbw]      [ech]
 [0 0 x y 0 0 0 0]      [eda]      [edax + edby]      [edg]
 [0 0 z w 0 0 0 0]  \/  [edb]  ——  [edaz + edbw]  ——  [edh]
 [0 0 0 0 x y 0 0]  /\  [fca]  ——  [fcax + fcby]  ——  [fcg]
 [0 0 0 0 z w 0 0]      [fcb]      [fcaz + fcbw]      [fch]
 [0 0 0 0 0 0 x y]      [fda]      [fdax + fdby]      [fdg]
 [0 0 0 0 0 0 z w]]     [fdb]]     [fdaz + fdbw]]     [fdh]]

How nice. Of course, we can operate of qubit 1 or 2 (0-indexed) with a modified version of the very same matrix:

[[x 0 y 0 0 0 0 0]
 [0 x 0 y 0 0 0 0]
 [z 0 w 0 0 0 0 0]
 [0 z 0 w 0 0 0 0]
 [0 0 0 0 x 0 y 0]
 [0 0 0 0 0 x 0 y]
 [0 0 0 0 z 0 w 0]
 [0 0 0 0 0 z 0 w]]

[[x 0 0 0 y 0 0 0]
 [0 x 0 0 0 y 0 0]
 [0 0 x 0 0 0 y 0]
 [0 0 0 x 0 0 0 y]
 [z 0 0 0 w 0 0 0]
 [0 z 0 0 0 w 0 0]
 [0 0 z 0 0 0 w 0]
 [0 0 0 z 0 0 0 w]]

These are the same as before, but with the 2x2 squares spread out a bit and overlapping. Verification of these matrices is left as an exercise for the reader.

You can also perform multi-qubit operations (like the controlled-NOT gate) on just part of a register in much the same fashion. Performing on qubits 0 and 2 of a 3-qubit register the following operation:

[[a b c d]
 [e f g h]
 [i j k l]
 [m n o p]]

can be accomplished with yet another 8x8 matrix:

[[a b 0 0 c d 0 0]
 [e f 0 0 g h 0 0]
 [0 0 a b 0 0 c d]
 [0 0 e f 0 0 g h]
 [i j 0 0 k l 0 0]
 [m n 0 0 o p 0 0]
 [0 0 i j 0 0 k l]
 [0 0 m n 0 0 o p]]

This can be generalized to an operation on m qubits of a register of n qubits, where 0 ≤ m ≤ n; in fact, that's what this challenge'll do!

Your task (at long last!)

Write a program or function. It must:

• Take as input a nonnegative integer n.

• Take as input a list of m distinct integers from 0 to n (inclusive).

• Take as input a 2^mx2^m matrix of integers that represents the operation to be performed on the qubits of an n-qubit register indicated (in order) by the aforementioned list.

• Return as output a 2ⁿx2ⁿ matrix of integers that represents an operation on the entire register equivalent to applying the given matrix to the indicated qubits.

Test cases

n = 4
qubits = {2}
Operation: [[1  2]
            [3  4]]
Return: [[1 0 0 0 2 0 0 0 1 0 0 0 2 0 0 0]
         [0 1 0 0 0 2 0 0 0 1 0 0 0 2 0 0]
         [0 0 1 0 0 0 2 0 0 0 1 0 0 0 2 0]
         [0 0 0 1 0 0 0 2 0 0 0 1 0 0 0 2]
         [3 0 0 0 4 0 0 0 3 0 0 0 4 0 0 0]
         [0 3 0 0 0 4 0 0 0 3 0 0 0 4 0 0]
         [0 0 3 0 0 0 4 0 0 0 3 0 0 0 4 0]
         [0 0 0 3 0 0 0 4 0 0 0 3 0 0 0 4]
         [1 0 0 0 2 0 0 0 1 0 0 0 2 0 0 0]
         [0 1 0 0 0 2 0 0 0 1 0 0 0 2 0 0]
         [0 0 1 0 0 0 2 0 0 0 1 0 0 0 2 0]
         [0 0 0 1 0 0 0 2 0 0 0 1 0 0 0 2]
         [3 0 0 0 4 0 0 0 3 0 0 0 4 0 0 0]
         [0 3 0 0 0 4 0 0 0 3 0 0 0 4 0 0]
         [0 0 3 0 0 0 4 0 0 0 3 0 0 0 4 0]
         [0 0 0 3 0 0 0 4 0 0 0 3 0 0 0 4]]

n = 3
qubits = {0, 2}
Operation: [[1  2  3  4 ]
            [5  6  7  8 ]
            [9  10 11 12]
            [13 14 15 16]]
Return: [[1  2  0  0  3  4  0  0 ]
         [5  6  0  0  7  8  0  0 ]
         [0  0  1  2  0  0  3  4 ]
         [0  0  5  6  0  0  7  8 ]
         [9  10 0  0  11 12 0  0 ]
         [13 14 0  0  15 16 0  0 ]
         [0  0  9  10 0  0  11 12]
         [0  0  13 14 0  0  15 16]]

n = 3
qubits = {2, 0}
Operation: [[1  2  3  4 ]
            [5  6  7  8 ]
            [9  10 11 12]
            [13 14 15 16]]
Return: [[1  3  0  0  2  4  0  0 ]
         [9  11 0  0  10 12 0  0 ]
         [0  0  1  3  0  0  2  4 ]
         [0  0  9  11 0  0  10 12]
         [5  7  0  0  6  8  0  0 ]
         [13 15 0  0  14 16 0  0 ]
         [0  0  5  7  0  0  6  8 ]
         [0  0  13 15 0  0  14 16]]
Wow, things get weird.

Operation: 2^m x 2^m identity matrix
Return: 2^n x 2^n identity matrix

n = 5

qubits = {3, 0, 4, 2, 7}

Operation: Pastebin

Return: [Pastebin] (TODO)

Rules

As usual, standard loopholes apply. Builtins are allowed, but try to include a solution sans builtin as well.

You can 1-index or reverse the list if desired.

I/O is flexible.

This is code-golf, so the shortest solution (in bytes) in each language wins!

---

Sandboxy stuff

Anything worth mentioning that I missed?

Is there another application of this that might be easier to explain and scare fewer people off?

Thanks!

Answer 5

Bot Wars at the Auction

king-of-the-hilljavascript

I have seen KOTH challenges where the bots fight each other, and I have seen KOTH challenges where the bots are in an auction. So I came up with this:

The Challenge:

You must build a javascript bot that will fight other bots using weapons purchased in an auction. These items are: swords, bows, and shields. You can also purchase healing and quivers. Your function is called once per "Turn", and only 1 weapon action and 1 move action can be called in each turn. You start with 200 health, and 2000 coins. Fight in arena with each bot in its own 5 by 5 square. For example, 16 bots would be a 20 by 20 arena.

Auctions:

During an auction, 2 items will be sold per surviving bot. In the initial auction, 3 items will be sold for each bot. It is up to the bots how they will bid: some bots may spend lots on a cool sword, while others could choose to buy healing in large amounts. There is an auction every few hundred turns. Items start at cost 1.

Fighting:

After the auction, your bots will be pitted against each other. With swords to strike nearby enemies, bows to attack distant bots, and shields to defend yourself, what could go wrong? If you find yourself low on health, you can heal (Which takes between 6 and 8 turns).

Input:

As input, your function receives an object filled with functions that can be used to control your bot. This object is also at window.bots["yourbot"].auction or window.bots["yourbot"].fight.

Object:

//within window.bots["yourbot"]
mode: integer, //0=Dead, 1=Auction, 2=Fight
items: object, //All items owned
coins: integer,
health: integer,
auction: {
    itemlist: array, //Array of item objects
    placeBid(coins), //Bid on item
    incrementBid(amount), //Bids (current + amount)
    item: {
        current: integer, //Current highest bid
        bidder: string, //Current highest bidder
        type: integer, //1=Sword, 2=Bow, 3=Quiver, 4=Shield, 5=Healing
        power: integer, //Item power (Attack amount, healing amount, or block percentage)
        units: integer //Only for healing and quivers; amount of turns taken to heal, or amount of arrows in quiver
    }
},
fight: {
    botList: array, //List of bots
    surrenderTo(bot), //Surrenders to a specific bot
    move: {
        north(), //Y+
        east(), //X+
        south(), //Y-
        west(), //X-
    }
    use: {
        swordAttack(bot OR [x,y]), //Attacks a bot, but only if it is adjacent to attacker
        bow(bot OR [x,y]), //Shoots bow at bot, bot must be within 5 spaces
        shield(), //Raises shield for 5 turns
        heal(sor) //Uses least powerful healing or takes input sort function
    }
    util: {
        getNearest(), //Returns nearest bot
        getBot(name), //Returns a specific bot by name
        atLocation([x,y]), //Returns bot at a certain location
        gridSize(), //Returns the side length of the square arena
        getPosition(), //Returns array [x,y] of caller bot
        see([x,y]), //Returns true or false, depending on if there is a bot in a certain location
    }
}

//within other bot nearestBot(), getBot(), botList, or atLocation(x, y)
location: array, //[x,y]
name: string, //Bot's name
items: object //All objects owned by bot

//within items
type: integer, //1=Sword, 2=Bow, 3=Quiver, 4=Shield, 5=Healing
power: integer, //Item power (Attack amount, healing amount, or block percentage)
units: integer //Only for healing and quivers; amount of turns taken to heal, or amount of arrows in quiver

How it Works:

You will start in an auction. With your 2000 coins, you can bid on items using the functions placeBid(price) or incrementBid(amount). If nobody bids for 5 turns, the item is sold. Once the items are all gone, the fight begins. The initial auction focuses mainly on swords, bows, and shields. During the fight, you can attack players using simple methods like bow(nearestPlayer()), or more complex methods involving mapping the area with see([x,y]) and atLocation([x,y]). When the fight round is over, another auction starts, which mainly focuses on healing and quivers. When the fight begins again, you will be able to heal (Make sure you shield right before doing so!). After that fight, another auction will commence. This will repeat until one person remains, or all other bots use surrenderTo(bot). Inflicting damage on another bot gets you 1 coin per point, and you get a 500 coin bonus for killing a bot. If a bot surrenders to you, you earn 100 coins. Store information that you bot may use in window.bots[yourBotName]. Note that a copy of this object is passed to your bot, but storing a varibale in this object will only affect it locally. Coordinates range from [0,0] in the corner to [max,max] in the opposite corner, max being round(22.36 * sqrt(botCount)).

Function Specifications:

placeBid(coins)
    Inputs amount of coins to set the bidding at
    If lower than current highest bid or another bid in that turn, returns 1
    If input is invalid, returns 2
    Will set auction.item.current to coins and auction.item.bidder to your bot name
incrementBid(amount)
    Inputs amount of coins to increase bidding by
    Adds to highest bid in last turn
    If lower than current highest bid or another bid in that turn, returns 1
    If input is invalid, returns 2
    Will add amount to auction.item.current and auction.item.bidder to your bot name
moveNorth()
    Will move bot 1 space Y+
    Returns 1 if bot is at far North edge of arena
moveEast()
    Will move bot 1 space X+
    Returns 1 if bot is at far East edge of arena
moveSouth()
    Will move bot 1 space Y-
    Returns 1 if bot is at far South edge of arena
moveWest()
    Will move bot 1 space X-
    Returns 1 if bot is at far West edge of arena
getNearest()
    Returns the nearest bot as of the last turn
    Read information: location, name, items
getBot(name)
    Inputs a string, containing the name of a bot
    If bot does not exist, returns 1
    If bot is dead, returns 2
    If input is invalid, returns 3
    Returns bot as of last turn
atLocation([x,y]) or atLocation(x,y)
    Inputs an array containing coordinates, or two integer coordinates
    Returns bot as of last turn
    If no bot exists in that spot, returns 0
    Invalid input returns 1
gridSize()
    Returns an integer containing the side length of the arena
getPosition()
    Returns an array [x,y] containing the position of the bot
surrenderTo(bot)
    Takes bot as input
    Will set mode to 0 on your bot
    Gives bot surrendered to 100 coins
    Returns 1 if input is invalid
    Returns 2 if bot is dead or inexistant
see([x,y])
    Returns true if bot is in location
    Returns false if input is invalid or no bot exists in location
swordAttack(bot OR [x,y])
    Takes either a bot or [x,y] coordinates as input
    Does as much damage as your best sword
    Will return 1 if input is invalid
    Will return 2 if bot is dead/nonexistant, or if coordinates are out of bounds
    Will return 3 if you don't have a sword
    Will return 4 if bot/coordinates are not within 1 space of your bot
bow(bot OR [x,y])
    Takes either a bot or [x,y] coordinates as input
    Doesas much damage as your best bow
    Will return 1 if input is invalid
    Will return 2 if bot is dead/nonexistant, or if coordinates are out of bounds
    Will return 3 if you don't have a bow, and 5 if you have no arrows
    Will return 4 if bot/coordinates are not within 20 spaces of your bot
shield()
    Blocks as much damage as your best shield as a percentage
    Lasts for 5 turns (Includes turn activated)
    Will return 1 if you don't have a shield
heal()
    Uses your weakest heal, or you can specify a sort function to define the order they are used
    Cannot move for 6-8 turns (Selected randomly)
    Will return 1 if you don't have heal

Item Specifications:

Sword
    The sword is used to attack bots within 1 space
    Has set damage amount (Geometric distribution 10-100)
    Is found in:
        Auction 1 = 35%
        Auction 2 = 30%
        Auction 3 = 15%
        Auction 4 = 5%
Bow
    The bow is used to remotely attack bots within 20 spaces
    Has set damage amount (Geometric distribution 4-40)
    Is found in:
        Auction 1 = 30%
        Auction 2 = 20%
        Auction 3 = 10%
        Auction 4 = 5%
Quiver
    Quivers are purchased with arrows in them, used for shooting bows
    Starts with specific amount of arrows (Geometric distribution 5-20)
    Is found in:
        Auction 1 = 7.5%
        Auction 2 = 10%
        Auction 3 = 25%
        Auction 4 = 40%
        Other auctions = 45%
Shield
    Shields are used to defend against attack
    Starts with a specific block percentage (Geometric distribution 5%-75%)
    Can be used while healing
    Is found in:
        Auction 1 = 20%
        Auction 2 = 30%
        Auction 3 = 20%
        Auction 4 = 10%
Heal
    Heal is used to regenerate during battle
    Heal level is geometric distribution 20-80
    Is found in:
        Auction 1 = 7.5%
        Auction 2 = 10%
        Auction 3 = 30%
        Auction 4 = 40%
        Other auctions = 55%

Example bot:

function readyToFight(obj) {
    var items = obj.items;
    var types = [];
    var coins = obj.coins;
    for (var i = 0, n; i < items.length; i++) {
        n = items[i];
        types.push(n.type);
    }
    if (obj.mode == 1) {
        obj = obj.auction;
        if (obj.item.type == 1) {
            if (types.indexOf(1) != -1) {
                for (var i = 0, n; i < items.length; i++) {
                    n = items[i];
                    if (n.type == 1 && n.power < obj.item.power) {
                        var bid = true;
                    }
                }
                if (n.item.price < coins) {
                    obj.incrementBid(1);
                }
            } else {
                if (n.item.price < coins) {
                    obj.incrementBid(1);
                }
            }
        } else if (obj.item.type == 2) {
            if (types.indexOf(2) != -1) {
                for (var i = 0, n; i < items.length; i++) {
                    n = items[i];
                    if (n.type == 2 && n.power < obj.item.power) {
                        var bid = true;
                    }
                }
                if (n.item.price < coins) {
                    obj.incrementBid(1);
                }
            } else {
                if (n.item.price < coins) {
                    obj.incrementBid(1);
                }
            }
        } else if (obj.item.type == 3) {
            if (n.item.price < n.item.units * 2) {
                obj.incrementBid(1);
            }
        } else if (obj.item.type == 4) {
            if (types.indexOf(4) != -1) {
                for (var i = 0, n; i < items.length; i++) {
                    n = items[i];
                    if (n.type == 4 && n.power < obj.item.power) {
                        var bid = true;
                    }
                }
                if (n.item.price < coins) {
                    obj.incrementBid(1);
                }
            } else {
                if (n.item.price < coins) {
                    obj.incrementBid(1);
                }
            }
        } else if (obj.item.type == 5) {
            if (n.item.price < n.item.power * 5) {
                obj.incrementBid(1);
            }
        }
    } else if (obj.mode == 2) {
        hp = obj.health;
        obj = obj.fight;
        if (types.indexOf(2) != -1) {
            obj.use.bow(obj.nearestPlayer());
        } else if (obj.health < 50 && types.indexOf(5) != -1) {
            obj.use.heal();
        } else {
            //Be scared, or implement better fighting techniques!
        }
    } else {
        //Bot can still see the arena and auction when dead, but cannot fight or bid
    }
}

Notes:

Standard Loopholes prohibited, javascript only

Answer 6

Single-Digit Representations of Natural Numbers

Tags: code-golf, test-battery, expression-building, arithmetic, math

Introduction

Dr. Inder Taneja is a Mathematics Professor at the Federal University of Santa Catarina who wrote and published "Single Digit Representations of Natural Numbers". In this paper, he describes each natural number from 0 to 1000 in terms of each of the digits 1 through 9 in as few digits as possible and using only the five basic arithmetic operations.

For example, the entry for "282" written only using the digit "3" looks like this:

3 + 3 * (3 * (3 ^ 3 + 3) + 3)

Similarly, "466" written using the digit "7" looks like this:

7 * 77 + 77 / 7 - 77 - 7

This is also described in the first half of this video on the Numberphile youtube channel.

This code-golf challenge will ask you to write a program (or function, class, etc.) which takes two inputs and outputs a valid mathematical expression according to the rules used by Dr. Taneja. Your score will be calculated based on the size of your code and the quality of your outputs.

Details

Write a program (or function, class, etc.) which takes two integers as input. The first of these will be an integer from 0 to 1000, inclusive. The second number will be a digit from 1 to 9, inclusive.

The program shall output an expression of the first input as a series of arithmetic operations on numbers whose digits are exclusively the digit specified as the second input.

In addition to parentheses ( and ), the following arithmetic operators are allowed in your output:

• addition (represented by the +)
• subtraction (represented by the -)
• multiplication (represented by the *)
• division (represented by the /)
• power (represented by the ^)

Numbers, as stated before, must be composed entirely of the digit specified by the second input, but they can be any number of digits. Numbers can be positive or negative. Number tokens cannot contain any characters besides the digit specified and, if negative, a - at the beginning.

Any form and amount of whitespace, including no whitespace at all, is allowed around each token in your output, where "token" refers to a number, operator, or parentheses. Your program's output may not contain any other characters.

The order of operations are evaluated in the usual manner.

Scoring

Dr. Taneja claims that his answers use "as few digits as possible"; unfortunately, his paper does not show how to prove that a solution is truly minimal. In the spirit of preserving that goal, however, the quality of your solutions will contribute to your score.

The quality of an output is measured, as Dr. Taneja says, by the number of digits used. For example, consider the output for "466" and "7":

7 * 77 + 77 / 7 - 77 - 7

This has a score of 1 + 2 + 2 + 1 + 2 + 1 = 9. Smaller is better.

Your code's score is:

score = 2 * <worst_scoring_output> + <solution_bytecount>

The lowest scoring valid solution wins.

You may determine your worst output either by test battery (trying every input) or logical proof. The following shell script can be used to compute your worst-scoring output, assuming your program is an executable which takes input as command-line arguments and provides output to stdout on a single line. When executing this script, provide the path to your program executable as a command-line argument.

// TODO: write a shell script which could compute your bonus score

Rules

Input and output may use any convenient method. This includes writing a function which takes the inputs as arguments to the function and returns or prints a string as described.

This is code-golf, so the size of your code in bytes forms a significant part of your score. The standard loopholes are forbidden, this includes parsing the original paper to "look up" Dr. Taneja's solution for a combination of inputs.

Reasonable adjustments to the output format are allowed; for instance: if your language has a native Expression object for mathematical expressions but its toString() (or equivalent) method represents the power operator as two asterisks rather than a caret, you may use the native representation.

Similarly, if it is easier for you to format your output as an equation rather than a one-sided expression, you may do so. For example, you may output <number> = <expression> or <expression> = <number> rather than simply <expression> (where the number is the first input to the program and the expression is the output as defined in the challenge section). Note that in this case, only the digit count of your expressions contribute to your score.

Example Input and Output

Your outputs may vary, but are still valid provided all explicitly-stated rules are respected.

Input:

282 3

Output:

3 + 3 * (3 * (3 ^ 3 + 3) + 3)

Input:

0 7

Output:

7 - 7

Input:

1000 9

Output:

999 + 9 / 9

Input:

466 7

Output:

7 * 77 + 77 / 7 - 77 - 7

Answer 7

ASCII-betical order

code-challenge printable-ascii

---

The full printable ASCII set (chars 32-126) in ascending order looks like this:

 !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~

Your task is to create a program or function which takes in an integer n and outputs the n^th item of an OEIS sequence. The catch: your score is the length of your code, plus thrice the number of ASCII chars in your code not included in the longest strictly increasing substring.

Rules

A valid strictly increasing substring of your code is defined as so:

• Each character within the substring, except the first, must have a higher ASCII value than the previous.

Other rules:

• The sequence may be 0- or 1-indexed.
• The sequence you choose may not be a constant sequence, such as A000012.
• Entries may only include printable ASCII and newlines. Newlines are ignored when calculating the longest increasing substring.

Examples

This JavaScript function outputs A000027 (the natural numbers):

n=>[]^n

The longest increasing substring of characters is =>[]^n. Therefore, the score is 7 + 3 × (7 - 6) = 10.

This function does exactly the same thing:

_abcdefghijklmnopqrstuvwxyz=>[]^_abcdefghijklmnopqrstuvwxyz

The longest increasing substring is =>[]^_abcdefghijklmnopqrstuvwxyz. The score is 59 + 3 × (59 - 32) = 140.

This function also does the same thing:

n/*!"#$%&'()*/=>[]^n

The longest increasing substring is !"#$%&'()*/=>[]^n. Therefore, the score is 20 + 3 × (20 - 17) = 29.

The lowest score wins.

---

Sandbox questions

• Is the scoring system sufficient?
• Is there a better option for the challenge?
  • Output n'th item in some OEIS sequence
  • Output first n items of some OEIS sequence
  • Output the score of the input
  • etc.
• What about languages with extended code pages? Should only the ASCII chars be counted, or should the bytes of the program be considered instead?
• Any other concerns?

Answer 8

The Derby Stakes

The Derby is a horse race run (near) annually since 1780 near the town of Epsom and is the middle leg of the Triple Crown. The race covers one mile, four furlongs, and six yards. Over the years it has had as few as 4 and as many as 34 entries. The fastest winning time was in 2010 at 2m31.33, but I'm old-fashioned and like horse race results only to the nearest fifth of a second. So let's call it 2:31 2/5.

The task

We will ID horses by number from 0 or 1 (your choice) up to the number of horses in the race (could be anything from 4 to 34).

The task is to take a list of the average horse speeds in miles per hour and produce a report of the race. The report has:

1. the winning horse ID and its winning time;
2. the other horse IDs in their order of finish and the difference between each time and the time of the horse that finished ahead of it.

However:

3. the times are to the nearest fifth of a second. There can be ties, which must be listed in random order;
4. some horses might not finish the race, in which case their average speed is 0.

I/O

The input will have between 4 and 34 non-negative numbers (average speeds) rounded to one decimal place, in any convenient format for your language. The horse ID is just the index (starting at 0 or 1) of their average speed.

The output can be any convenient format, as long as the winner is "first" (in the sense of top-most or left-most) and the other horses are listed in a way that makes their finishing order clear.

The times have to be rounded to the nearest fifth of a second, but otherwise can be represented however you like, such as the number of seconds, or some format like 2:31.4 or whatever. If the time is in "seconds flat", as they say, either 2:32.0 or 2:32 (for example) is fine.

For horses that don't finish the race, no time difference really makes sense, so anything that just indicates they didn't finish is fine. But the do have to appear in the report, and if more than one horse does not finish they have to be listed randomly.

The point with the output is that it needs to be clear, but the format itself is not so important.

You also need to state in your answer how you have ensured that ties are output in a random order.

Test case

31.8, 0, 32.9, 32.1, 30.8, 31.8, 31.1, 33.1  

8 2:43.6
3 0:01.0
4 0:04.0
1 0:01.6
6 0:00.0
7 0:03.8
5 0.01.8
2 DNF

"I made the ranking of ties random by using `rank(x, ties.method = "random")` in R."

I chose a particular time format and used "DNF" for the horse that didn't finish, but you don't need to adhere to these.

I will make more test cases if this challenge seems interesting to anyone.

This is codegolf. Standard loopholes forbidden.

Answer 9

How far can I throw a ball up the hill?

code-golfmathnumbergeometry

Given an initial velocity, an angle to throw the ball, and the angle of a hill, determine how far the ball will go before it hits the ground due to gravity.

Refer to the image below. V=initial velocity vector, a1=angle of hill, a2=angle ball is thrown at, d=distance ball will travel

Inputs

• The velocity the ball is thrown at (m/s)
• The angle from level ground that the ball is thrown at (radians or degrees)
• The angle from level ground the hill is at

Output

• The number of meters the ball travels before hitting the ground

---

Specifics

• Gravity will pull the ball downwards at 9.81 m/s^2
• Due to floating point rounding, the answer only need be correct within 0.1 of my test case examples
• The input angle can be between 0 and pi/2 radians (or 90 degrees)
• An angle of 0 means the ball is thrown horizontally across the ground, which hits the ground at 0 meters
• An angle of pi/2 radians (or 90 degrees) means the ball is thrown vertically and hits the ground at 0 meters
• The angle of the hill will always be less or equal than the angle the ball is thrown at
• This is code golf, fewest bytes wins

Related to task 3

---

Test cases

pi/4  (20, 0.7853981633974483, 0) = 40.8
pi/5  (20, 0.6283185307179586, 0) = 38.8
pi/6  (10, 0.5235987755982988, 0) = 8.8
pi/3  (10, 1.0471975511965976, 0) = 8.8
pi/2  (5,  1.5707963267948966, 0) = 0.0
0     (5,  0,                  0) = 0.0

---

Sandbox

I'm not sure what standard rules are used when accounting for floating point errors, is allowing a .1 margin of error fine?

Test cases for angles > 0 to come.

Answer 10

Queuez

A typical stack-based lanaguage uses nilads, monads, dyads, and occasionally operations with larger numbers of arguments. As each operation is processed, the values are stored on a stack, so that if you want to apply an operation to the result of other operation(s), you simply invoke those operations (and predecessor operations if necessary), at which point their results will end up on the stack ready for the operation you provide next.

Queuez is a fictional language which works differently: instead of the results being stored on a stack, they are stored in a queue, so you have to be careful how you manage your order of operations. For example, let's imagine that digits are nilads and - and / are dyads and you want to calculate ((a / c) - f) / ((b / d) - e). In a stack-based language you would write this as ac/f-bd/e-/, however in Queuez you need to write this as acbd/f/e--/. Explanation:

Command Stack
a       a
c       a c
/       a/c
f       a/c f
-       a/c-f
b       a/c-f b
d       a/c-f b d
/       a/c-f b/d
e       a/c-f b/d e
-       a/c-+f b/d-e
/       (a/c-f)/(b/d-e)
Command Queue
a       a
c       a c
b       a c b
d       a c b d
/       b d a/c
f       b d a/c f
/       a/c f b/d
e       a/c f b/d e
-       b/d e a/c-f
-       a/c-f b/d-e
/       (a/c-f)/(b/d-e)

Please write a program or function that converts a program written in a fictional stack-based language into the equivalent Queuez. The actual nilads, monads and dyads of the two lanaguages will be arbitrarily mapped to three sets of at least 10 printable ASCII characters of your choice (you are not required to use letters or mathematical symbols); your answer only has to output the correct rearrangement based on which characters you have chosen to represent nilads, monads and dyads. You can assume that there will be one value left on the stack/queue at the end of the program. Normal code-golf rules apply.

If you prefer, you can reverse the dyad argument order, but this must apply both to the original stack-based language and the output. For instance, for the input edb/-fca/-/ you would need to output dbcae/f/--/:

Command Stack
e       e
d       d e
b       b d e
/       b/d e
-       b/d-e
f       f b/d-e
c       c f b/d-e
a       a c f b/d-e
/       a/c f b/d-e
-       a/c-f b/d-e
/       (a/c-f)/(b/d-e)
Command Queue
d       d
b       b d
c       c b d
a       a c b d
e       e a c b d
/       b/d e a c
f       f b/d e a c
/       a/c f b/d e
-       b/d-e a/c f
-       a/c-f b/d-e
/       (a/c-f)/(b/d-e)

Answer 11

Multidimensional orthodiagonal steps

Step further in step generation.
Navigation in 2d matrix is common, but something uncommon is even more insteresting.
Now I'll ask you to develope shortest solutions to generate all possible steps in N-dimensional matrix.

Challenge

Your code takes positive integer number N > 0 as input.
Your code must output all possible steps in matrix of N dimensions. In other words, you need to output coordinates of all cells that touch (0;...;0) cell in any way.

Examples:

Input: 1
Output:

(-1)
(1)

Input: 2
Output:

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

Input 3: Output:

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

Rules

1. Standart loopholes are disalowed
2. Input number is always integer and always greater than zero
3. Output order is not relevant
4. Output is flexible. Coordinates just need to be distinguishable
5. This is code-golf, so shortest answer in bytes wins

Answer 12

Fridge magnet substitution (posted)

Answer 13

Treasure Map Drawing Bot

You're organizing a treasure hunt for your friends. To conduct things more easily, you want to draw a map of all locations where you hid the precious objects.

Input

A string consisting of the locations of the objects separated by newlines. Each location is represented by two non-negative integer coordinates describing the position in the field by an x- and y-coordinate, 0 0 being the upper left corner. Example:

1 2
3 0
0 1

Challenge

Your function or program should be able to construct a map denoting every given location with an x where the mark is found in row y + 1 and column x + 1 in the output. Unmarked locations are represented with a . The map also consists of a frame where the corners are +s, the vertical lines are |s and the horizontal lines are -s. Map for the input example given above:

+----+
|   x|
|x   |
| x  |
+----+

Possible Test Cases

---

"0 0"
=>
+-+
|x|
+-+

---

"0 10
 5 5
 10 0"
=>
+-----------+
|          x|
|           |
|           |
|           |
|           |
|     x     |
|           |
|           |
|           |
|           |
|x          |
+-----------+

---

""
=>
++
++

---

"0 0
 0 2
 2 0"
=>
+---+
|x x|
|   |
|x  |
+---+

---

Of course, this is code-golf, meaning that the solution with the lowest byte count wins!

Answer 14

Is it a table?

Challenge

Take an bitmap (in .bmp, 2D array, string containing line break, etc.), check whether it's a table, i.e. the outer border is a rectangle, and each separated (edge-connected) empty part in it is a rectangle.

Equivalently, each space area, including the outside one, has exactly 4 edges.

You can't assume there is or is no space outside of the table.

Test cases

True samples:

############# 
#           #
#           #
#############
#     #     #
#     #     #
#############

###########
#         #
#         #
#         #
###########
#   #     #
#####     #
# # #######
# # #     #
###########

###########
###########
##   #   ##
##   #   ##
##### #####
######   ##
######   ##
###########

Note that in this test case the smallest space area (with 1 space) is a rectangle, although it doesn't have a rectangular border with #.

False Samples:

###########
#     #   #
#     #   #
#     #####
#         #
###########

In this test case the lower-left empty region is a concave hexagon.

###########
#    #     #
#    #     #
############

The outer border is not a rectangle.

############
#          #
#          #
#   ####   #
#   #  #   #
#   ####   #
#          #
############

The outer empty region has a "hole" inside.

Winning criteria

Shortest code win.

Answer 15

king-of-the-hill game hexagonal-grid random javascript

Formic Functions 2: Hierarchies

---

     Watch live | Active answers | Add new answer | Chat room | Source code | Leaderboard

               This is an open-ended challenge. New answers and updates are always welcome.

We've seen the territorial highland ants wander the lands in search of food. There have also been talks of aggressive forest ants lurking down below whilst feasting on fungi. These ants, however, are unlike any you've seen before. Collecting food is their goal, as always, but colonies don't need a queen - all ants of this subfamily are capable of creating offspring. There's a catch, though. New ants have less strength than their parent, unless the parent ant spends a large amount of food on them. Ants are capable of killing others weaker than them, and weaker ants are worth less, so your ants need to make careful choices.

---

Watching the game

Because this competition is made in JavaScript, you can see what other players have made already directly in your browser. Just click on one of the links above - you'll figure out the rest.

Chat

To keep the comment section clean, I highly encourage you to use the dedicated chat room for questions and discussion.

Leaderboard

No official tournaments available yet.

Screenshots

Here are a couple of images taken at the end of a game that should entice you:

No screenshots available yet.

You can look at more simply by running games in your browser. The controller also allows you to zoom in so you can track the ants' decisions that result in the large-scale patterns you ultimately see.

---

Definitions

A value range is indicated by a number followed by two dots and another number. "0..7" means "between 0 and 7, inclusive". A different type of range is indicated by a number followed by a plus sign. "1024+" means "greater than or equal to 1024".

---

Programming

Your task is to provide a JavaScript class that implements a getAction(view) function and optionally a constructor. All code provided by you will be run under strict mode.

The constructor is called with no arguments. It must take no more than one second to run. It must be side-effect free and must consistently result in an identical object after every run.

The getAction(view) function (henceforth known as the ant function) is called like this: yourConstructedObject.getAction(someViewArray);. It must also be side-effect free and must consistently return an object, and provide the same output every time if provided the same input.

At the start of every game, your ant function is granted 1 second of reserve time. It is also granted an additional 10 milliseconds of time every time it is called. Time measurement starts right before the function call and ends upon return. That time is then taken away from the reserve time. Your function must not run out of the reserve time.

The constructed object and any temporary data combined must not consume more than 64 MB of memory at any time.

Here's a template for you to fill in:

class Entry { // TODO: Change the "Entry" to whatever you want, preferably your entry name. Remember that this is a JavaScript class name, so you can't use some characters.
  constructor() {
    // TODO: Optionally fill this in.
  }

  getAction(view) {
    // TODO: Fill this in.
  }
}

---

Arena

The arena is a toroidal (edge wrapping) grid of hexagonal cells arranged in a rhombus of side length 1500. Initially, all cells have the color 0 and 0.1% have food placed on them, for a total of 2250 pieces of food. Up to 12 entries are randomly chosen every game and have their corresponding ants (one per entry) spawned in random locations, with no more than one ant occupying any cell. The initial turn order of ants is also randomized.

Game

The game lasts 32768 turns, which are processed sequentially. Every turn, in an unchanging order, each ant has its corresponding function called with the local state of the arena passed as an argument. In other words, your ant function is called separately for every ant you control. The action chosen by the ant function is then taken immediately - other ants see the arena changes even during the same turn.

---

Ants

State

Each ant carries the following properties with them:

• Position: Implementation-defined.
  • Ants do not have access to their global position.
• Tier: An integer representing the tier of an ant.
  • Equal to 0 for all ants not spawned by other ants.
  • Doesn't change over an ant's lifespan.
  • The lower its tier, the less valuable an ant is.
  • There is no theoretical limit on how high or low tier can be.
• Age: An integer representing how old an ant is.
  • Initially 0 for all ants.
  • After every action an ant takes its age goes up by one.
• Food: An integer representing the amount of food an ant is carrying.
  • Initially 0 for all ants.
  • An ant may carry an unlimited amount of food.
• Memory: An integer in the range 0..15 representing the memory of an ant.
  • Initially equal to 0 for all ants not spawned by other ants.
  • An ant may change it as part of any action.
  • Holds no meaning for the controller.
• Owner: Implementation-defined.
  • Allows ants to see whether another one is a friend or not.

Sight

Each ant sees 6 cells in its neighborhood, as well as the cell it is currently occupying. Each cell contains the following properties:

• color: An integer in the range 0..7 representing the current color of a cell.
• food: A boolean representing whether or not a piece of food is present on a cell.
• ant: An object if an ant is present on a cell, undefined otherwise. If present, the object has the following properties:
  • tier: Maps to Tier.
  • age: An integer in the range 0..3 representing an ant's age on a logarithmic scale. 0 actual age maps to 0, 1..31 actual age maps to 1, 32..1023 actual age maps to 2 and 1024+ maps to 4. [Sandbox note: I'm torn about whether or not the ants should have access to this information.]
  • [Sandbox] Alternative for or complement to age: older: A boolean representing whether or not an ant's age is higher that of the currently active ant.
  • food: An integer in the range 0..3 representing the amount of stored food by an ant on a logarithmic scale. 0 actual food maps to 0, 1..3 actual food maps to 1, 4..15 actual food maps to 2 and 16+ actual food maps to 3.
  • memory: Maps to Memory.
  • friend: A boolean representing whether or not an ant is under control of the same entry as the currently active ant.

Every turn sight is passed to your ant function as an array of 7 objects, arranged in this order:

 0 1
5 6 2
 4 3

The view is randomly rotated by a multiple of 60 degrees every time your ant function is called. This means that it's impossible to extract a consistent sense of direction without clever use of the environment.

Accessing one's own state is done by retrieving the ant object of the 7^th element of the array, like this: const me = view[6].ant;

Actions

Each ant must perform an action every turn. The possible actions are as follows:

• Move: Move to the desired cell.
  • Format: {cell: 0..6, action: 0}
  • When moving onto a cell with food on it, an ant automatically picks up the piece of food present.
  • When moving onto a cell with an ant on it, of the two ants only one remains. If the still ant's tier value is lower than that of the moving ant, then the still ant dies and is permanently removed from the game. Otherwise, the unfortunate fate awaits the moving ant instead. In either case, the remaining ant gains all the food of the ant that died and one more.
  • Staying still is a valid action and may hold merit in certain situations.
• Paint: Change the color of the desired cell to the desired color.
  • Format: {cell: 0..6, action: 1, color: 0..7}
  • Changing the color of a cell to the same one is a valid action.
• Place food: Put a piece of food onto the desired cell.
  • Format: {cell: 0..6, action: 2}
  • Placing a piece of food onto a cell with an ant on it results in that ant immediately picking it up.
  • Placing food costs food. An ant may only place a piece of food if it has at least one food stored, and one food is taken away from it.
  • Placing food onto own cell is a valid action, but placing food onto a cell with a piece of food already on it is not.
• Spawn: Create a new ant under control of the same entry on the desired cell.
  • Format: {cell: 0..6, action: 3, tier: -1..+1, state: 0..15}
  • A parent ant must choose to spend 1, 4 or 16 food on the new ant by specifying a tier equal to -1, 0 or +1 respectively.
  • A parent ant may only spawn an ant of the desired tier if it has the necessary amount of food to do so, and that amount is taken away from it.
  • Spawning results in an ant of a tier equal to that of its parent plus the tier value specified.
  • A parent ant must choose the initial memory of the new ant by specifying a state. [Sandbox note: I'm considering not letting parents set the initial memory of offspring.]
  • The new ant is inserted into the turn order right before its parent.
  • Spawning an ant counts as movement for the new ant, and is resolved as such.
  • Spawning an ant onto own cell is a valid action and may hold merit in certain situations.
• Memorize: Replace the currently active ant's memory with the desired number.
  • Format: {memory: 0..15}
  • Memorization is not an action itself. It must be appended to one of the four previously mentioned actions.
  • An ant may choose to leave this field undefined. No memory change occurs then. [Sandbox note: Torn about this as well.]

Format refers to the JavaScript object that must be returned by your ant function to perform a specific action.

Example outputs:

• {cell: 0, action: 0} // Move to cell 0.
• {cell: 6, action: 0} // Do nothing.
• {cell: 6, action: 1, color: 0} // Set own cell color to 0.
• {cell: 3, action: 2} // Put a piece of food onto cell 3. Invalid if there is a piece of food on cell 3.
• {cell: 2, action: 3, tier: -1, state: 3} // Spawn an ant 1 tier lower than that of your own with initial memory equal to 3 on cell 2 at the cost of 1 food. Invalid if you have no food.
• {cell: 5, action: 3, tier: +1, state: 11, memory: 14} // Spawn an ant 1 tier higher than that of your own with initial memory equal to 11 on cell 5 at the cost of 16 food whilst committing 14 to memory. Invalid if you have less than 16 food.
• {cell: 6, action: 3, tier: 0, state: 0} // Spawn an ant with tier equal to that of your own with initial memory equal to 0 on your own cell at the cost of 4 food. A conflict occurs and the newly spawned ant dies, giving you a piece of food. Effectively, ou lost 3 pieces of food. Invalid if you have less than 4 food.
• {cell: 6, action: 3, tier: +1, state: 0} // Spawn an ant 1 tier higher than that of your own with initial memory equal to 0 on your own cell at the cost of 16 food. A conflict occurs and you die, giving the newly spawned ant a piece of food (and any additional food you might've had). Effectively, you upgraded yourself at the cost of 15 food. Invalid if you have less than 16 food.
• {cell: 3, action: 0, color: 5, test: true, memory: 1} // Move to cell 3 whilst committing 1 to memory. Values ofcolorandtestare irrelevant. You may choose to include unrelated properties - they are simply ignored. [Sandbox note: Maybe the controller shouldn't allow color in this case? This looks like it might be a good breeding ground for hard-to-detect bugs.]

Example invalid outputs (not exhaustive):

• {cell: 7, action: 0} // Error: Value of "cell" outside required range 0..6.
• {cell: 3} // Error: "action" left undefined.
• {action: 1, color: 4} // Error: "cell" left undefined.
• {cell: 4, action: 3, tier: -1} // Error: "state" left undefined.

---

Scoring

At the end of each game, every entry participating in that game is evaluated according to this formula:

n is the number of ants belonging to the entry currently being evaluated
T_i is the tier of the i^th ant belonging to the entry currently being evaluated
F_i is the amount of food the i^th ant belonging to the entry currently being evaluated is holding

Or as pseudocode:

var evaluation = 0;
for (int i = 0; i < entry.ants.count; i++) {
  var ant = entry.ants[i];
  evaluation += Math.Pow(2, ant.tier) + Math.Pow(2, ant.tier - 1) * ant.food;
}

[Sandbox note: Should I count food as score or not?]

The final score of each entry is equal to the amount of entries whose evaluation was lower than that of the currently considered entry. This means that the highest score an entry can get is 11.

Tournaments

A tournament is nothing more than a series of individual games. At any point of a tournament the score of each entry is equal to the average of all of its scores.

Official tournaments

Official tournaments will be run by me on the latest version of Chrome on my personal computer, which at the time of writing is an AMD FX-8350, every time a new entry is posted or an existing one receives a meaningful edit. The leaderboard will be updated once the 1^st place becomes consistent between 6 subsets of played games (which gives a probability of 96.875% that the first place won't change).

As stated before, there is no permanent winner. This means that no checkmark will be awarded to any answer, ever. I will continue to run new tournaments for as long as is practical.

---

Submissions

Each submission must follow this general format:

---

Entry Title

[Optional text and pictures]

Code block with your JavaScript class

[Optional text, pictures and code blocks]

---

Not adhering to the above format may result in the submission not being properly picked up by the controller.

Explanations and pictures are highly encouraged, though not necessary. Making your entry pretty and well-documented will entice me (and probably a lot of people) to upvote it.

Disqualification

Your entry will be disqualified if it is found to not adhere to the specification correctly. Most of the time problems will be caught by the controller and reported, but some rules can't be checked programmatically, so they'll be enforced by hand. I reserve the right to disqualify an entry manually if it breaks the rules or if I subjectively believe it has not been made with fair competition in mind. I hope I haven't left any loopholes (and therefore won't have to exercise this power), but if I did then this rule prevents them from potentially ruining the entire challenge.

Disqualification during a game results in all of your ants being immediately and permanently removed from the turn order. Disqualification during a tournament invalidates all games in which your entry has participated and terminates the active game (as it would've been invalid anyway). Disqualification during an official tournament, aside from having the effects of a regular tournament disqualification, prohibits your entry from taking part in any future official tournament until meaningfully edited.

This is not supposed to be an additional challenge - helpful error messages along with your ant function's output and the input that disqualified it will be attached to the disqualification notice. I will also paste these messages into a comment informing you of a disqualification should your entry be disqualified during an official tournament.

Multiple entries and editing

You may provide multiple entries, provided that they do not team up against the others. As long as each entry is working solely towards its own victory, you are permitted to tailor your strategy to take advantage of others' weaknesses. You may also edit your answers whenever you choose. It is up to you whether you post a new entry or edit an existing one; just don't flood the game with nearly identical variations. If you make a variation of another person's entry, remember to give them credit by linking to their entry from your own.

Example entries

---

Randant

This entry demonstrates the minimal amount of code needed for something to be considered valid. It returns the same output regardless of input.

class Randant {
  getAction() {
    return {cell: 0, action: 0};
  }
}

Because the orientation is random every time, Randant will perform a random walk instead of going straight.

Despite being very simple, this is a perfectly valid submission. It won't ever get disqualified either, because moving is guaranteed to be a valid action.

See Smart Randant on how one could go about improving this entry.

---

Smart Randant

This entry demonstrates basic mechanics that ought to be commonly used between more advanced entries. It is an improvement of Randant's general design. It depends on input this time around.

class SmartRandant {
  getAction(view) {
    const me = view[6].ant; // Get data about myself

    function wrap(number, cycleLength = 6, negativeSafety = 1) { // Defining functions inside the getAction(view) function is fine
      return (number + cycleLength * negativeSafety) % cycleLength; // Wraps numbers (allows for cyclic array access)
    }

    function stronger(a, b) { // Checks if ant a is stronger than ant b
      return a && (!b || a.tier > b.tier);
    }

    view.forEach((cell, i) => { // Modifying the view is perfectly acceptable (here we do it to store the index alongside each cell)
      cell.index = i;
    });

    const dirs = view.slice(0, 6);
    const safe = dirs.filter((cell, i) => !stronger(dirs[cycle(i - 1)].ant, me) && !stronger(dirs[cycle(i + 1)].ant, me) && stronger(me, cell.ant)); // Create an array of cells that are safe to move to
    // TODO: Also consider attacking other ants that are at the same strength level as us by spawning a stronger ant on their face

    if (safe.length) { // If we've got some safe spaces to move to...
      const victims = safe.filter((cell) => cell.ant && stronger(me, cell.ant)); // Prioritize killing other ants

      if (victims.length) { // If we've got someone to kill...
        const target = victims.reduce((prev, next) => stronger(next.ant, prev.ant) ? next : prev); // Find the strongest victim and target it

        return {cell: target.index, action: 0};
      }

      const food = safe.filter((cell) => cell.food); // Otherwise prioritize grabbing food

      if (food.length) { // If we've got some food to grab...
        return {cell: food[0].index, action: 0} // Just grab any piece
        // TODO: Grab the piece that has the most pieces of food next to it
      }

      return {cell: safe[0].index, action: 0} // Otherwise move to any safe cell
    }

    return {cell: 6, action: 0}; // If we don't have a safe cell to move to, just stay still and hope for the best
    // TODO: Handle this situation better
  }
}

As you can see, Smart Randant is a lot smarter than his counterpart. Smart Randant dropped his suicidal tendencies by finding safe cells before moving. Note that despite not being suicidal, he may still be killed by particularly cunning entries. He's also more aggressive - he'll gladly attack opponents weaker than him and will grab nearby food. Finally, if he's got anywhere to go, he will go there. Otherwise, he'll just stay still, hoping for the best.

You may have also noticed that Smart Randant still has a lot to learn. You can edit your entries to your heart's content, so W.I.P. submissions are allowed, or even encouraged.

---

Straighter

This entry demonstrates smart usage of the environment for the purpose of fighting randomness. It travels in a straight line, leaving behind a path. It also utilizes and expands Smart Randant's basic framework.

[Placeholder]

---

Meta

The chat room is active already and is a better place for extended discussion than the comment section. I'd also love to dicuss some preliminary ideas for potential strategies to be used in future entries (though let's try to restrict this dicussion to nothing more than interesting isolated systems rather than full submissions - I'm not particularly interested in posting a nearly-solved challenge).

Most links are broken for now. The controller, for example, doesn't exist yet.

I'm aware that I'll have to make (or find) a custom number library that can handle nearly arbitrarily small and large powers of 2 for scoring (I've managed to design a system which spawns progressively less valuable ants every 2 turns at no cost, leading to a score equal to about 1 + 2e-16384).

Answer 16

Hexarun! king-of-the-hill javascript work-in-progress

Hexarun (stylized as Hexarun!) is a simultaneous game with complete information. Hexarun is intended for a minimum of three (3) players.

Overview

Up to twelve (12) players start on a regular hexagonal toroidal board with a number placed on each hexagon. The objective of the game is to collect the numbers by navigating the board. Players have complete knowledge of the board and the participating players. The number on a hexagon is reduced by the amount being collected. The game ends when all hexagons become zero or if the game becomes stale. The player whose collection has the highest sum wins the game.

Each game consists of multiple turns. Before the first turn, players choose their own starting location. During each turn, players move within their vicinity at the same time. If a player is alone in a numbered hexagon, this player collects the entire number. If multiple players move into a single hexagon simultaneously, they split the number. Numbers are not exchanged between players during each game.

Game specifications

1. Regular hexagonal toroidal board: Each edge of the board measures N=2*P hexagons where P is the number of players on the board. The numbers on the board are placed in concentric rings. The numbers on the edge of the board are 1, and each successive inner ring follows off the OEIS sequence A002024 which starts with 1, 2, 2, 3, 3, 3, 4, 4, 4, 4. As a final touch, increase the number in the center by 1 if it is not unique on the board. [Example Board (N=6)]

2. A game ends when...

   a. Hexagons become zero: Numbers on all hexagons are zero.

   b. Game becomes stale: Scores do not change during 6*P consecutive turns.

3. Legal moves...

   a. Run!: Moves into one of the six (6) neighboring hexagons.

   b. Nothing: Does literally nothing.

4. Number collection:

   a. Collect: At the end of a turn, a player alone on a hexagon scores s=h points, where h is the number on the hexagon at the beginning of the turn.

   b. Split: At the end of a turn, n>1 players standing on a hexagon scores s=h/n points, where h is the number on the hexagon at the beginning of the turn, and / is integer division. The number on the hexagon at the end of the turn becomes h-s*n, a.k.a. the remainder.

   Example: At the end of a turn, a total of 3 players are on a hexagon with number 10, then each gets 3 points and the hexagon becomes 1.

How to play

TODO

Tournament rules

TODO

Leaderboard

Answer 17

Base 18 & Decimal traffic light

Given a number n<180, output the n/10 part and the n%10 part in 7-seg.

7-seg shapes:

 000         222   333         555   666   777   888   999   AAA         CCC         EEE   FFF   GGG
0   0     1     2     3 4   4 5     6         7 8   8 9   9 A   A B     C         D E     F     G     H   H
0   0     1     2     3 4   4 5     6         7 8   8 9   9 A   A B     C         D E     F     G     H   H
0   0     1     2     3 4   4 5     6         7 8   8 9   9 A   A B     C         D E     F     G     H   H
             222   333   444   555   666         888   999   AAA   BBB         DDD   EEE   FFF         HHH
0   0     1 2         3     4     5 6   6     7 8   8     9 A   A B   B C     D   D E     F     G   G H   H
0   0     1 2         3     4     5 6   6     7 8   8     9 A   A B   B C     D   D E     F     G   G H   H
0   0     1 2         3     4     5 6   6     7 8   8     9 A   A B   B C     D   D E     F     G   G H   H
 000         222   333         555   666         888   999         BBB   CCC   DDD   EEE         GGG

• Either led on or (led off&background) should be constant, and the left characters mean the other state, or
• At least two of your background, led on and led off should be constant, and the left characters mean the left state.

code-golf ascii-art

Answer 18

Convincingly Fake Compression of Random Data cops-and-robbers

As you may know, it is impossible to write an compression method that takes strings of length \$n\$ and returns strings of length \$n - 1\$. This can be proven by a simple argument: Each compression function must be a bijection, because otherwise the compressed strings can not unambiguously be uncompressed. However, just considering bit strings, there are \$2^n\$ strings of length \$n\$, but only \$2^{n-1}\$ strings of length \$n-1\$, thus no such bijection can exist.

In other words, for each attempt to write such a compression function, there exist strings which cannot be compressed.

The task for the cops in this challenge is to write a function which looks like it can compress arbitrary fixed-length strings, and the task of the robbers is to find a string for which the compression function fails.

---

Sandbox

I'm not yet convinced if this will actually work as a challenge, mainly if it is feasible for the cops to write a submission which is not easily crackable. It might be easier for large \$n\$ so robbers can not brute force, so I could make the cops winning criterion about getting the safe submission with the lowest \$n\$. Any ideas for a better winning criterion?

Also do you think this will work as a challenge?

Answer 19

Progrqmming Puzzle andf Co9de Golf |

codegolf

Intro

We all make mistakes. You, me, everyone. But not computers. They aren't making any mistake. Not even a single typo.
Time to change this injustice.

Task

Your task will be to take a string as input, and display the string character by character, and with a cursor, as if someone was typing it. But there is a twist : sometimes, the "entered" character will be wrong. In that case there is a little pause, then the last entered character (which is supposed to be wrong) is deleted.

Rules

• Input and output will contain only printable ASCII characters.
• The cursor should be displayed as |, preceded by a space. This will always be displayed, from the empty string to the exact input displayed.
• Each "iteration" (new character) is separated by a 0.25s pause (It takes time to write right). You can have a marge error of 0.05s, meaning the pause have to be lower than 0.2s, and lower than 0.3
• Each character has exactly 1/10 chance to be wrong (that means it will be anything but the right character). In that case you should add a 1s pause ("Wait, did l really made a mistake?"), then delete this character, add a 0.25s pause (with a marge error of 0.05s), then continue.

Example

input

Hello!

Possible output

Note : I am planning to add a gif to show what the code should do. For now, consider every line as a gif frame

H |          // 0.25s pause
He |         // 0.25s   "
Hel |        // 0.25s   "
HelG |       // 1s      "
Hel |        // 0.25s   "
Hell |       // 0.25s   "
Hello |      // 0.25s   "
Hello! |     // done

Note for sandbox

• Is this challenge good enough ?
• Is this challenge already exist ?
• Is this challenge clear enough ?

Answer 20

Role reversal

This is related to an old question, but is different enough that answers should be quite different to the older one.

You are given a sentence referring to two different people. Return the sentence with the roles reversed.

For example, for the input I will give you a kiss., you should return You will give me a kiss.

There will always be exactly two people referred to in the sentence, and they will be referred to with different pronouns. Here's a table of the pronouns that might be used (pronouns in a row refer to the same person. Pronouns in a column can be switched with one another to reverse a role).

 I         me       my           mine         myself
 you       you      your         yours        yourself     
 she       her      her          hers         herself
 he        him      his          his          himself      
 they      them     their        theirs       themselves 

Capitalisation matters (the first letter of the sentence should be capitalised, the pronoun "I" should always be capitalised, and no other pronoun is capitalised when not starting a sentence).

Words/punctuation not appearing in the pronoun table above shouldn't be changed. A pronoun word shouldn't be replaced if it appears as a substring of another word (e.g. 'history' shouldn't he changed). None of the inputs will be contractions using pronouns (so there won't be any inputs with "I'm" or "you're" etc).

Input/output examples:

in: She gave them hers!
out: They gave her theirs!

in: He will eat me if I don't eat him.
out: I will eat him if he don't eat me.

in: Get it for them yourself!
out: Get it for you themselves!

in: I think I am going to see him tomorrow.
out: He think he am going to see me tomorrow.

in: I am not interested in history, is he?
out: He am not interested in history, is I?

Rules:

• This is code golf so the shortest answer wins.
• Standard loopholes are banned.

Answer 21

Use Japt Shortcuts

code-golfjapt

Japt is the PPCG Language of the Month for July, and I'm excited to try it out! In accordance with the Tips post I should use the Unicode Shortcuts. However, my keyboard seems to be lacking those important characters like "upside-down exclamation point" needed for optimum golfiness. Please write me a program to change horrible, verbose monstrosities like â m@VgUb==X into pristine, optimal code like â £VgUb¥X!

Challenge

Given Japt code as input, output the same code making maximal use of the Unicode Shortcuts Japt supports.

Rules

• Answers must support inputs containing any combination of valid Japt characters [Sandbox: is there a list of these? In particular, many languages need to use the NULL byte to indicate end of input, does Japt support NULL bytes in the middle of code?].
• Input may be in any reasonable format (string, list of chars, etc.)
• Output may be in any reasonable format, and does not need to be the same as the one used as input (e.g. "input as string => output as list of chars" is fine)
• If multiple shortcuts are possible, use the one that replaces the most characters. For example, === should be replaced by ¶ not ¥=.
• Your code does not need to handle ambiguous situations. For example, ==== could be shortened to ¶= or =¶, so behavior is undefined if such a string shows up in the input.
• Only shortcuts available in Japt 1.4.5 (most recent version at time of posting) need to be handled
• Non-unicode shortcuts like _ and @ don't need to be handled
• I've replaced easy-to-miss trailing spaces with ␠ where I found them. Those should be the literal space character ' ' when running tests or replacements. [Sandbox: Seriously, is there some better way to do this?]

Test Cases

?OvUf\l m_c %H} qV):0 => "?OvUf\l ®c %HÃqV):0"
Ov"y m_î íZ c p0} "p2␠ => Ov"y ®î íZ c p0Ã"²
=== => ¶
ñgJ òXYZ{XgJ <YgJ } mg mg␠ => ñÌòÈÌ<YÌÃmÎmÎ
w å+ m@Vå+ m+S+Xw} c => w å+ £Vå+ m+S+XwÃc

[Sandbox: The first two test cases are grabbed from some real Code Golf answers here and here. Should I replace them with something else?]

For reference, here is the full list of Unicode Shortcuts to be supported. It can also be found on the Japt Interpreter. Note that some shortcuts end in a space. [Sandbox: should I format this differently?]

¡   Um@
¢   Us2␠
£   m@
¤   s2␠
¥   ==
¦   !=
§   <=
¨   >=
©   &&
ª   ||
«   &&!
¬   q␠
®   m_
¯   s0,
°   ++
±   +=
²   p2␠
³   p3␠
´   --
µ   -=
¶   ===
·   qR␠
¸   qS␠
¹   )␠
º   ((
»   (((
¼   .25
½   .5
¾   .75
À   !==
Á   >>>
   ~~
à   }␠
Ä   +1
Å   s1␠
Æ   o@
Ç   o_
È   XYZ{X
É   -1
Ê   l␠
Ë   mDEF{D
Ì   gJ␠
Í   n2␠
Î   g␠
Ï   XYZ{Y
Ð   $new Date($
Ñ   *2
×   r*1␠

Answer 22

A note about this meta post:

I just have one example right now, but I will have three in the final.

I thought it would be interesting to have a problem about something I know a bit about. Right now it seems a bit mathy, but I wanted to ground the problem on something real. It feels more 'real-life' if you need to understand the spec in addition to golfing. The problem is I don't want it to seem like homework. Another problem is the actual computation that needs to take place isn't actually that hard once you understand the simplifications of the problem.

Let me know what you think.

---

\$\def\tensor#1{\smash{\underline{\underline{\smash{#1}}}}}\$

Challenge

Calculate the strain tensor and volume percent change of a cube given its material properties and stress tensor.

Background

Common Terms

• Strain: ε, The amount of elongation per unit length, Units: \$\frac{in}{in}\$

• Normal Stress: σ, The amount of force per unit area perpendicular to the cross section, Units: \$\frac{lbs}{in^2} = psi\$

• Shear Stress: τ, The amount of force per unit area parallel to the cross section, Units: \$\frac{lbs}{in^2} = psi\$

• Young's Modulus: E, The relationship between stress and strain: \$σ = Eε\$, Units: psi

• Poisson's Ratio: ν, The relationship between strain in different directions. For a uniaxial bar: \$ε_{22} = -ν ε_{11}\$, Units: unitless

• Index Notation: A short form for tensors written with subscripts \$i,j,k,l\$ to denote which element within the tensor. The number of subscripts the tensor has indicates what order it is. \$σ_{ij} \equiv \tensor{σ}\$ (Second Order)

• Kroniker Delta: \$δ_{ij}\$, has the value of 1 if i=j, otherwise its value is 0. Index Notation for the Identity Tensor.

$$ δ_{ij} = \left[\begin{array}{ccc} δ_{11} & δ_{12} & δ_{13}\\ δ_{21} & δ_{22} & δ_{23}\\ δ_{31} & δ_{32} & δ_{33}\\ \end{array}\right] = \left[\begin{array}{ccc} 1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1\\ \end{array}\right] = I $$

Tensors

A tensor in this context can be thought of as three directional components for each of the three positive faces of the cube.

Although a Stress Tensor is not a matrix, it can be represented in matrix form by a 3x3 or other matrices:

$${\tensor{σ}} = \left[\begin{array}{ccc} σ_{xx} & σ_{xy} & σ_{xz}\\ σ_{yx} & σ_{yy} & σ_{yz}\\ σ_{zx} & σ_{zy} & σ_{zz}\\ \end{array}\right] = \left[\begin{array}{ccc} σ_{11} & σ_{12} & σ_{13}\\ σ_{21} & σ_{22} & σ_{23}\\ σ_{31} & σ_{32} & σ_{33}\\ \end{array}\right] = \left[\begin{array}{c} σ_{11}\\ σ_{12}\\ \vdots \\ σ_{33}\\ \end{array}\right] = \left[\begin{array}{cccc} σ_{11} & σ_{12} & \dots & σ_{33}\\ \end{array}\right] $$

If a Tensor and a Kroniker Delta share the same indices, they are combined.

$$ σ_{ij} δ_{kj} = σ_{ik} $$

If a Tensor has repeating indices, then it is taken as a zero order tensor and the indices are summed.

$$ σ_{ij} δ_{ij} = σ_{ii} = \sum_{i=1}^{3} σ_{ii} \equiv tr(\tensor{σ}) = σ_{11} + σ_{22} + σ_{33} $$

Stress Strain Relationship

The relationship in one dimension is \$σ=Eε\$. For three dimensions we can use Hook's law to find the relationship between the strain tensor and the stress tensor as follows:

$$ σ_{ij} = C_{ijkl} ε_{kl} $$

This general case would need \$3^4 = 81\$ independent material properties to calculate the strain tensor. If we assume the cube has a symetric \$\tensor{σ}\$, symetric \$\tensor{ε}\$, is Elastic, Isotropic, Linear, and Homogeneous, then we only need two independent material properties: (Young's modulus: E, Poisson's Ratio: ν) or (Lamé modulus: λ, Shear modulus: μ). We can use either pair of values, but for this example it is much easier to calculate the strain tensor from the stress tensor using Young's Modulus and Poisson's Ratio.

And so we can simplify the stress tensor by what we know.

$${\tensor{σ}} = \left[\begin{array}{ccc} σ_x & σ_{xy} & σ_{xz}\\ & σ_y & σ_{yz}\\ Sym & & σ_z\\ \end{array}\right] $$

And our new relationship is:

$$ ε_{ij} = \frac{1+ν}{E} σ_{ij} - \frac{ν}{E} σ_{kk} δ_{ij} $$

Calculating the Dilation

The Volumetric Strain can be found by calculating the trace of the strain tensor for very small values of strain. This is because for small values \$ε^3 \ll ε^2 \ll ε\$.

$$ {\frac {ΔV}{V_0}} \approx tr(\tensor{ε}) $$

Putting it all together

Therefore, in summary we can calculate the strain tensor with the following:

Using Index Notation:

$$ ε_{ij} = \frac{1+ν}{E} σ_{ij} - \frac{ν}{E} σ_{kk} δ_{ij} $$

Using Matrix Notation:

$$ ε_{ij} = \frac{1+ν}{E} \left[\begin{array}{ccc} σ_{11} & σ_{12} & σ_{13}\\ σ_{12} & σ_{22} & σ_{23}\\ σ_{13} & σ_{23} & σ_{33}\\ \end{array}\right] - \frac{ν}{E} tr(\tensor{σ}) \left[\begin{array}{c} 1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1\\ \end{array}\right] $$

---

Then calculate the volumetric change:

Index Notation

$$ {\frac {ΔV}{V_0}} = ε_{ij} δ_{ij} = ε_{ii} $$

Matrix Notation

$$ {\frac {ΔV}{V_0}} = tr(\tensor{ε}) $$

Input

One positive long: Young's Modulus (Usually in the range 100 psi - 100,000,000 psi)

One positive decimal: Poissons's Ratio (Usually in the range 0.01 - 0.5)

Array of signed decimals for Stress Tensor (9 values)

Output

Array of Strain Tensor, to at least five significant figures (same format as input)

Percent volume change of cube, to at least five significant figures

Examples

(simple example for now)

Input:
Young's Modulus: 29,000,000 psi
Poisson's Ratio: 0.30
Stress Tensor: [[50000,      0,     0]
                [    0, -10000,     0]
                [    0,      0, 25000]] psi
Output:
Strain Tensor: [[0.00157,        0,       0]
                [      0, -0.00112,       0]
                [      0,        0, 0.00045]] in/in
Dilation: 0.08966%

Rules

IO is flexible

• Stress Tensor input can be any size array, or string

  • Input type and size must be the same as output

• No formatting or units required

This is code-golf, least number of bytes for each language wins

Answer 23

Haferman Carpet

Given nonnegative integer input \$n\$ output the \$n\$th iteration of the Haferman carpet.

Constructing the carpet

• The zeroth iteration is 1.
• When going from the \$n\$th to the \$(n+1)\$th iteration, replace each \$1\$ with the pattern [[0,1,0],[1,0,1],[0,1,0]] and each \$0\$ with the pattern [[1,1,1],[1,1,1],[1,1,1]].

Test cases

0 [[1]]

1 [[0,1,0],[1,0,1],[0,1,0]]

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

Standard I/O stuff

Sandbox

Is this a duplicate? I will make the rules more explicit later.

Answer 24

Syllabification and classification (Venpa)

Introduction

Venpa is a form of classical Tamil poetry, based upon certain rules of metric prosody. The complete rules form a context-free grammar, the task here is to test for a tiny subset of those rules.

Letters

• Vowels: a, A, i, I, u, U, e, E, y, Y, o, O, W
  • small case represents "short" vowels, CAPS represent "long" vowels
  • y represents the y sound in "my".
  • W represents the "ou" sound in "mouse", and always comes in capital (long) form.
• Consonant: everything else
  • the consonants can be in small case or capitals, whichever is convenient.

Word Segmenting

Words in the input are seen as composed of segments (which roughly correspond to the usual notion of a syllable). A segment divide occurs where:

• two or more consonants occur together, tr, rpp, etc.
• a long (capital) vowel occurs in the word, pO, W, mY etc.
• two vowels have occurred since the last segment's end (or the word's beginning).

sanjIvi has segments san, jI, vi.
Yvar has Y,var.
vigadakavi has viga,daka,vi.
vAnily has vA,nily.
padAgytAngiha has padA, gytAn, giha
radagajaturagapadAdi has rada, gaja, tura, gapa, dA, di

(Consonants at the end of segments make no difference after segmentation and can be ignored - gytAn=gytA, var=va.)

As you can see, the segments are of two types:

1. those with a single vowel, san, Y, vA, called a straight (S) segment
2. those with two vowels, viga, nily, padA called a sequence (Q) segment

So the segment patterns of the above words are:

  sanjIvi              =              san + jI + vi          = SSS
  Yvar                 =                 Y + var             = SS
  vigadakavi           =            viga + daka + vi         = QQS
  vAnily               =                vA + nily            = SQ
  padAgytAngiha        =           padA + gytAn + giha       = QQQ
  radagajaturagapadAdi = rada + gaja + tura + gapa + dA + di = QQQQSS

Permitted patterns

The rules for words allowed in a Venpa are:

1. a word should have one to three segments
2. a one or two segment word can have any pattern (S, Q, SQ, SS, QS, QQ)
3. a three segment word must end in a straight (S) segment

So out of the above, SSS, SS, QQS, and SQ are allowed, QQQ and QQQQSS are not.

Task

Given an input word in the above letters, output its segment pattern if it's an allowed word, or a false-y value if it's not an allowed word.

Input

• Will be a single word composed of the characters mentioned under the Letters heading above
  • (Small case w will not be present anywhere in the text (neither as a vowel nor as a consonant))

Output

• The segment pattern of the input word, if it's an allowed word
  • can use any two distinct unambiguous characters to represent S segments and Q segments
• A false-y value in your language if it's not an allowed word
• Output is undefined for invalid input (i.e. has characters other than those specified)

Test cases

vigadakavi 
=> QQS
Yvar 
=> SS
padAgytAngiha
=> falsey (QQQ not allowed)
vAnily
=> SQ
katradanA
=> SQS
radagajaturagapadAdi 
=> falsey (more than 3 segments)
TuppArkkuT
=> SSS
mazai
=> Q

Answer 25

DRAW me a picture: A QBasic metagolf challenge

metagolf test-battery graphical-output binary-matrix

The DRAW command in QBasic takes a string argument, consisting of instructions for moving the cursor and drawing line segments, and produces the appropriate line segments on the screen. The syntax of the instructions is very terse--perfect for a metagolf challenge!

The challenge

Write a program or function which:

• Given a 2-D array of on and off pixels, representing a black-and-white image,
• Generates a string that, when passed to QBasic's DRAW command, will draw that image on the screen,
• While keeping the generated string as short as possible.

More about DRAW

Your program may use the following DRAW instructions:

(more details pending)

• U - draw line upwards
• D - draw line downwards
• L - draw line to the left
• R - draw line to the right
• E - draw line diagonally up and to the right
• F - draw line diagonally down and to the right
• G - draw line diagonally down and to the left
• H - draw line diagonally up and to the left
• B - meta-instruction: prepend to any instruction to move the cursor accordingly but not draw the line
• N - meta-instruction: prepend to any instruction to draw the line but not move the cursor

(examples + pictures pending)

The following instructions are outside the scope of this challenge and may not be used (even if they would improve your score): C, P, S, M, X, A, and TA.

Output requirements

Conceptually, your program's output will be substituted for the ... in the following QBasic program:

SCREEN 9        ' Graphics mode, 640 x 350 pixels
DRAW "B M 0,0"  ' Set drawing cursor to top left corner
DRAW "..."

(If the length of your output exceeds any limits on line or string literal length, it may be split across multiple DRAW commands in such a way that the instructions are preserved.)

The program will then be run, and the output image compared to your program's input. Where the input array has a 1, the output image must have a white pixel; where the input array has a 0, the output image must have a black pixel. The portion of the screen outside the input array's dimensions must be entirely black pixels.

Practically speaking, I will probably write a verification script in some other language, just to make testing easier.

Details

Standard I/O methods apply. Output is case-insensitive. Input array dimensions will not exceed 640 x 350. (more rules pending)

Test cases

(test cases pending)

Scoring

Your submission's score is the sum of the lengths of its outputs on these test cases. In the case of a tie, the earlier submission wins.

Note: this challenge is probably a variation on the Traveling Salesman Problem, meaning that an optimal solution will take exponential time. In order to receive a score, your submission must complete all test cases, which means that you'll need to take a sub-optimal approach.

---

Sandbox questions:

• What's a good number of test cases?
• Should I instead score submissions on a second, hidden set of test cases to prevent overfitting? Or should the hidden test cases be the (first) tiebreaker?
• Is the implicit requirement "must complete all test cases before you can post it" enough of a bound on long execution times, or should I add a specific execution-time limit?

Answer 26

Note: this is my first time posting, so I need help fleshing out the details. I'm aware there are plenty of Roman Numeral problems, but this is somewhat different.

When in Rome, count as Romans do!

This problem is inspired by this website, which published the following diagram:

This diagram shows us that the longest Roman Numeral expression under 250 is that of 188, which requires 9 numerals to express.

The standard symbols used to express most Roman Numerals are the following: {I, V, X, L, C, D, M}. In this challenge, your goal is to, given an positive integer n, compute the number of valid Roman Numeral representations that can be composed through concatenating n of the standard symbols.

Then, your program must output the result of this computation modulo 3997 (to prevent answers from getting too long) in Roman Numerals!

Rules for Roman Numeral Expressions

Roman Numerals originally only had "additive" pairing, meaning that numerals were always written in descending order, and the sum of the values of all the numerals was the value of the number.

Later on, subtractive pairing, the use of placing a smaller numeral in front of a larger in order to subtract the smaller from the larger, became commonplace to shorten Roman Numeral expressions. Subtractive pairs cannot be chained, like the following: IXL. This is considered invalid.

The following are the modern day rules for additive and subtractive pairing.

1. Only one I, X, and C can be used as the leading numeral in part of a subtractive pair.
2. I can only be placed before V and X in a subtractive pair.
3. X can only be placed before L and C in a subtractive pair.
4. C can only be placed before D and M in a subtractive pair.
5. Other than subtractive pairs, numerals must be in descending order
6. M, C, and X cannot be equalled or exceeded by smaller denominations.
7. D, L, and V can each only appear once.
8. Only M can be repeated 4 or more times.

Test Cases

Input: 1
Output: VII

More to be added.

Sandbox Users

Thoughts on this problem? I know it is really badly formatted but I thought the concept was cool. Thanks for the help!

Answer 27

Most distinct Turing-complete character subsets

(Inspired by Fewest (distinct) characters for Turing Completeness)

code-challenge restricted-source

Challenge:

In any language you choose, find the greatest number of distinct and disjoint subsets of characters allowed in that language (i.e. no individual character is in more than one of the subsets), each of which separately makes the language Turing-complete.

Example:

JS (2): eval()"\u0123456789bcdf, []+=` (see answer to linked question).

Scoring:

Scoring is by total number of distinct Turing-complete subsets found. Higher scores are better. In case of a tie, the answer with the fewest total characters used across all subsets wins.

Notes:

Execution of arbitrary code is not required, only Turing completeness.

Explanations of why each of your subsets are Turing complete are highly encouraged.

In case this was unclear, whitespace characters are still counted as characters.

Sandbox notes:

Should I include some stipulation forbidding languages such as Unary which don't care about the particular characters used?
What is unclear about this specification? Where could I give a better/more complete explanation?

Answer 28

Chain Classification

answer-chaining

_related

Objective: Write a program (whose index in the chain of answers is \$n\$) which, when given any program with index \$i\$ (\$ 1 \le i \le n\$), outputs \$i\$.

(The program may do anything else given any other string input, including but not limited to: crashing, erorring, returning other numbers, sending an email to google support, and simulating the universe.)

Rules

• Your program may be in any language that has not appeared in the answer chain yet.
• You may output to STDOUT, STDERR, return as a function value, etc. Any reasonable method of output.
• You may take input from STDIN, command line arguments, function parameters, etc. Any reasonable method of input.
• You must output 1 for the first answer, 2 for the second, etc. Any other form of indexing is not allowed.
• You must use base 10 when outputting.
• You may not use the internet in any way, particularly to scrape the answers to this question.
• No person may answer twice in a row.
• No person may answer within 1 hour of their previous answer.
• Languages which differ by version are considered distinct. Thus, Python 2 and Python 3 can both be part of the chain.
• Languages which differ by compiler or interpreter are not considered distinct. So, Python 3 (Cython) and Python 3 are equivalent.

Answer format

# N. Language

    code

explanation

Try It Online links are appreciated, as well as links for the language itself.

You must include how your program performs input and output.

Meta

The first answer is:

1. Alumin

h

Try it online! Input and output through STDIN and STDOUT.

Answer 29

The Input String, But Every Time It Says The First Word, It's Recursion

You wanted to create the ultimate replacement remix, but didn't see a way to add more recursion that ends naturally. Then you saw The Entire Bee Movie But Every Bee Is Replaced With The Entire Bee Movie Without Bees. Unlike the other replacement remixes, all the inserted copies were from the same text. It was the answer - at each recursing, you could remove the word being replaced, making each copy shorter than the one before it and causing the recursion to eventually end. Your master plan was complete, all that was left was to write the program to fulfill it.

The Expansion Function

Let's define some function \$F\$ on a sequence of words. Words are sequences of characters not containing whitespace, which are separated by whitespace.

define \$F(S)\$:

if \$S\$ is empty, return nothing

let \$X\$ be the first word in \$S\$

let \$Y\$ be \$S\$ with all instances of the whole word \$X\$ removed

let \$Z=F(Y)\$

return \$S\$ with all instances of the whole word \$X\$ replaced by \$Z\$

Your task is to implement \$F\$.

Input

Input the sequence of words in some form. You may choose any input method.

Output

Output the sequence of words in some form. You may choose any output method.

Only the words in the output count for correctness. If you output as a string, the leading, trailing, and separator whitespace can be anything.

Scoring

This is code golf, so shortest code in bytes wins.

Examples

Small case

Input:

b o o k k e e p e r

Output:

r r p r r r r p r r e e p e r r r p r r r r p r r e e p e r k k e e p e r o o k k e e p e r

See the recursion:

Format:

value of S
result of F

r


p r
r

e e p e r
r r p r r

k         k         e e p e r
r r p r r r r p r r e e p e r

o                             o                             k k e e p e r
r r p r r r r p r r e e p e r r r p r r r r p r r e e p e r k k e e p e r

b                                                                         o o k k e e p e r
r r p r r r r p r r e e p e r r r p r r r r p r r e e p e r k k e e p e r o o k k e e p e r

Large case

Input:

peter piper picked a peck of pickled peppers a peck of pickled peppers peter piper picked if peter piper picked a peck of pickled peppers wheres the peck of pickled peppers peter piper picked

Output:

218854 words

Hello Sandbox

This section will not appear when the challenge is posted to the main site.

I can't seem to get the quote Markdown right, it might just be a parser bug where it thinks the quote continues even if there are no >s.

I originally put a description of \$F\$ as an implementation in pseudocode, but I'm considering finding a more mathematical description which tells you less about how to go about implementing it yourself. Still though, there is a challenge in optimizing this for tiny code.

Answer 30

Triangular snake

You're given a triangular field:

It has 4 ports.

You're also given five different pieces from A to E:

Each piece has a little piece of path inside it.

Your basic goal is to build paths between ports. There are some rules:

• Each cell of the field can be occupied by 0 or 1 pieces.
• A port can either point to an empty cell or be an endpoint of a path. That is, this is illegal:
• The path starts with a port and ends with a port.
• The path must not be broken up into pieces, i.e. every edge of a piece through which a path goes must not touch an empty cell or a border without a port.

This is an example of a legal path:

This path can be represented as "CBEDEAD" or "DAEDEBC".

Input

There is no input.

Output

Your ultimate task is to output all the possible paths. Your output must not contain illegal paths. You can output the paths in any readable way. Order, repetitions and letter case don't matter.

code-golf grid combinatorics