Cycles on the torusDecompose a permutation into cyclesMoore IterationGoogle Code Jam - New Lottery...
Is there a math expression equivalent to the conditional ternary operator?
How can I portion out frozen cookie dough?
How to install "rounded" brake pads
Use Mercury as quenching liquid for swords?
A running toilet that stops itself
Should I file my taxes? No income, unemployed, but paid 2k in student loan interest
Cycles on the torus
How do you make a gun that shoots melee weapons and/or swords?
Having the player face themselves after the mid-game
How does learning spells work when leveling a multiclass character?
After Brexit, will the EU recognize British passports that are valid for more than ten years?
Sort array by month and year
Is "cogitate" used appropriately in "I cogitate that success relies on hard work"?
A vote on the Brexit backstop
An Undercover Army
Help! My Character is too much for her story!
Are small insurances worth it?
What is the orbit and expected lifetime of Crew Dragon trunk?
Precision notation for voltmeters
PTIJ: Sport in the Torah
I've given my players a lot of magic items. Is it reasonable for me to give them harder encounters?
Issue with units for a rocket nozzle throat area problem
Exempt portion of equation line from aligning?
Will the concrete slab in a partially heated shed conduct a lot of heat to the unconditioned area?
Cycles on the torus
Decompose a permutation into cyclesMoore IterationGoogle Code Jam - New Lottery GameCo-primality and the number piRotate every row and column in a matrixNumber of cycles of a permutationFire propagation simulator2D Array Middle PointPrint a Quinella TablePartitioning the grid into triangles
$begingroup$
Challenge
This challenge will have you write a program that takes in two integers n and m and outputs the number non-intersecting loops on the n by m torus made by only taking steps up and to the right. You can think of torus as the grid with wraparound both at the top and the bottom.
This is code-golf so fewest bytes wins.
Example
For example, if the input is n=m=5, one valid walk is
(0,0) -> (0,1) -> (0,2) -> (1,2) -> (2,2) -> (2,3) -> (2,4) ->
(2,0) -> (3,0) -> (4,0) -> (4,1) -> (4,2) -> (4,3) ->
(0,3) -> (1,3) -> (1,4) ->
(1,0) -> (1,1) -> (2,1) -> (3,1) -> (3,2) -> (3,3) -> (3,4) -> (4,4) -> (0,4) -> (0,0)
as shown in the graphic.
Some example input/outputs
f(1,1) = 2 (up or right)
f(1,2) = 2 (up or right-right)
f(2,2) = 4 (up-up, up-right-up-right, right-right, right-up-right-up)
f(2,3) = 7
f(3,3) = 22
f(2,4) = 13
f(3,4) = 66
f(4,4) = 258
code-golf combinatorics grid
asked 4 hours ago
Peter KageyPeter Kagey
878518
$endgroup$
add a comment |
$begingroup$
Challenge
This challenge will have you write a program that takes in two integers n and m and outputs the number non-intersecting loops on the n by m torus made by only taking steps up and to the right. You can think of torus as the grid with wraparound both at the top and the bottom.
This is code-golf so fewest bytes wins.
Example
For example, if the input is n=m=5, one valid walk is
(0,0) -> (0,1) -> (0,2) -> (1,2) -> (2,2) -> (2,3) -> (2,4) ->
(2,0) -> (3,0) -> (4,0) -> (4,1) -> (4,2) -> (4,3) ->
(0,3) -> (1,3) -> (1,4) ->
(1,0) -> (1,1) -> (2,1) -> (3,1) -> (3,2) -> (3,3) -> (3,4) -> (4,4) -> (0,4) -> (0,0)
as shown in the graphic.
Some example input/outputs
f(1,1) = 2 (up or right)
f(1,2) = 2 (up or right-right)
f(2,2) = 4 (up-up, up-right-up-right, right-right, right-up-right-up)
f(2,3) = 7
f(3,3) = 22
f(2,4) = 13
f(3,4) = 66
f(4,4) = 258
code-golf combinatorics grid
asked 4 hours ago
Peter KageyPeter Kagey
878518
$endgroup$
add a comment |
$begingroup$
Challenge
This challenge will have you write a program that takes in two integers n and m and outputs the number non-intersecting loops on the n by m torus made by only taking steps up and to the right. You can think of torus as the grid with wraparound both at the top and the bottom.
This is code-golf so fewest bytes wins.
Example
For example, if the input is n=m=5, one valid walk is
(0,0) -> (0,1) -> (0,2) -> (1,2) -> (2,2) -> (2,3) -> (2,4) ->
(2,0) -> (3,0) -> (4,0) -> (4,1) -> (4,2) -> (4,3) ->
(0,3) -> (1,3) -> (1,4) ->
(1,0) -> (1,1) -> (2,1) -> (3,1) -> (3,2) -> (3,3) -> (3,4) -> (4,4) -> (0,4) -> (0,0)
as shown in the graphic.
Some example input/outputs
f(1,1) = 2 (up or right)
f(1,2) = 2 (up or right-right)
f(2,2) = 4 (up-up, up-right-up-right, right-right, right-up-right-up)
f(2,3) = 7
f(3,3) = 22
f(2,4) = 13
f(3,4) = 66
f(4,4) = 258
code-golf combinatorics grid
asked 4 hours ago
Peter KageyPeter Kagey
878518
$endgroup$
Challenge
This challenge will have you write a program that takes in two integers n and m and outputs the number non-intersecting loops on the n by m torus made by only taking steps up and to the right. You can think of torus as the grid with wraparound both at the top and the bottom.
This is code-golf so fewest bytes wins.
Example
For example, if the input is n=m=5, one valid walk is
(0,0) -> (0,1) -> (0,2) -> (1,2) -> (2,2) -> (2,3) -> (2,4) ->
(2,0) -> (3,0) -> (4,0) -> (4,1) -> (4,2) -> (4,3) ->
(0,3) -> (1,3) -> (1,4) ->
(1,0) -> (1,1) -> (2,1) -> (3,1) -> (3,2) -> (3,3) -> (3,4) -> (4,4) -> (0,4) -> (0,0)
as shown in the graphic.
Some example input/outputs
f(1,1) = 2 (up or right)
f(1,2) = 2 (up or right-right)
f(2,2) = 4 (up-up, up-right-up-right, right-right, right-up-right-up)
f(2,3) = 7
f(3,3) = 22
f(2,4) = 13
f(3,4) = 66
f(4,4) = 258
code-golf combinatorics grid
code-golf combinatorics grid
asked 4 hours ago
Peter KageyPeter Kagey
878518
asked 4 hours ago
Peter KageyPeter Kagey
878518
asked 4 hours ago
Peter KageyPeter Kagey
878518
asked 4 hours ago
Peter KageyPeter Kagey
878518
asked 4 hours ago
Peter KageyPeter Kagey
878518
878518
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Python 2, 87 bytes
f=lambda m,n,z=0,l=[]:z==0if z in l else sum(f(m,n,(z+d)%m%(n*1j),l+[z])for d in(1,1j))
Try it online!
The interesting thing here is using a complex number z to store the coordinate of the current position. We can move up by adding 1 and move right by adding 1j. To my surprise, modulo works on complex numbers in a way that lets us handle the wrapping for each dimension separately: doing %m acts on the real part, and %(n*1j) acts on the imaginary part.
answered 2 hours ago
xnorxnor
91.8k18187444
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["\$", "\$"]]);
});
});
}, "mathjax-editing");
StackExchange.ifUsing("editor", function () {
StackExchange.using("externalEditor", function () {
StackExchange.using("snippets", function () {
StackExchange.snippets.init();
});
});
}, "code-snippets");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "200"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fcodegolf.stackexchange.com%2fquestions%2f181203%2fcycles-on-the-torus%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Python 2, 87 bytes
f=lambda m,n,z=0,l=[]:z==0if z in l else sum(f(m,n,(z+d)%m%(n*1j),l+[z])for d in(1,1j))
Try it online!
The interesting thing here is using a complex number z to store the coordinate of the current position. We can move up by adding 1 and move right by adding 1j. To my surprise, modulo works on complex numbers in a way that lets us handle the wrapping for each dimension separately: doing %m acts on the real part, and %(n*1j) acts on the imaginary part.
answered 2 hours ago
xnorxnor
91.8k18187444
$endgroup$
add a comment |
$begingroup$
Python 2, 87 bytes
f=lambda m,n,z=0,l=[]:z==0if z in l else sum(f(m,n,(z+d)%m%(n*1j),l+[z])for d in(1,1j))
Try it online!
The interesting thing here is using a complex number z to store the coordinate of the current position. We can move up by adding 1 and move right by adding 1j. To my surprise, modulo works on complex numbers in a way that lets us handle the wrapping for each dimension separately: doing %m acts on the real part, and %(n*1j) acts on the imaginary part.
answered 2 hours ago
xnorxnor
91.8k18187444
$endgroup$
add a comment |
$begingroup$
Python 2, 87 bytes
f=lambda m,n,z=0,l=[]:z==0if z in l else sum(f(m,n,(z+d)%m%(n*1j),l+[z])for d in(1,1j))
Try it online!
The interesting thing here is using a complex number z to store the coordinate of the current position. We can move up by adding 1 and move right by adding 1j. To my surprise, modulo works on complex numbers in a way that lets us handle the wrapping for each dimension separately: doing %m acts on the real part, and %(n*1j) acts on the imaginary part.
answered 2 hours ago
xnorxnor
91.8k18187444
$endgroup$
Python 2, 87 bytes
f=lambda m,n,z=0,l=[]:z==0if z in l else sum(f(m,n,(z+d)%m%(n*1j),l+[z])for d in(1,1j))
Try it online!
The interesting thing here is using a complex number z to store the coordinate of the current position. We can move up by adding 1 and move right by adding 1j. To my surprise, modulo works on complex numbers in a way that lets us handle the wrapping for each dimension separately: doing %m acts on the real part, and %(n*1j) acts on the imaginary part.
answered 2 hours ago
xnorxnor
91.8k18187444
answered 2 hours ago
xnorxnor
91.8k18187444
answered 2 hours ago
xnorxnor
91.8k18187444
answered 2 hours ago
xnorxnor
91.8k18187444
91.8k18187444
add a comment |
add a comment |
If this is an answer to a challenge…
…Be sure to follow the challenge specification. However, please refrain from exploiting obvious loopholes. Answers abusing any of the standard loopholes are considered invalid. If you think a specification is unclear or underspecified, comment on the question instead.
…Try to optimize your score. For instance, answers to code-golf challenges should attempt to be as short as possible. You can always include a readable version of the code in addition to the competitive one.
Explanations of your answer make it more interesting to read and are very much encouraged.…Include a short header which indicates the language(s) of your code and its score, as defined by the challenge.
More generally…
…Please make sure to answer the question and provide sufficient detail.
…Avoid asking for help, clarification or responding to other answers (use comments instead).
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fcodegolf.stackexchange.com%2fquestions%2f181203%2fcycles-on-the-torus%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
