shortest distance of convex polygon with start and exit problem
I've been asked the following question:
You have N points, where two of them are the "start" and "exit"
You want to start at "start", go through every other node, and end up at "exit". What is the shortest path (using Euclidean distance) if the polygon formed by the N nodes is convex? Is there a better algorithm than brute force here?
edit1:
It was a problem asked in TAP in 2016 (Argentinian Programming Competition) and it was mentioned to me today. I suspect there must be a better than bruteforce algorithm here using the convexity property otherwise they woudn't ask it on a competition. Also the constraints for N were N < 400 so it wound't be solvable with a O(n!) solution
edit2:
One interesting case is this one:
Consider a very long and narrow rectangle, where the points are on the long sides of the rectangle, one in front of the other.
The start and exit points are on the opposite ends of this "tunnel"
doing a clockwise or counterclockwise turn you would end up travelling 2*L where L is the size of the long side of the rectangle.
Doing a zig-zag from start to end would be optimal here, since you only need to go through L once, and then some small steps from one side to the other.
algorithm data-structures graph-algorithm
asked Nov 13 '18 at 22:14
serianoxserianox
144
add a comment |
I've been asked the following question:
You have N points, where two of them are the "start" and "exit"
You want to start at "start", go through every other node, and end up at "exit". What is the shortest path (using Euclidean distance) if the polygon formed by the N nodes is convex? Is there a better algorithm than brute force here?
edit1:
It was a problem asked in TAP in 2016 (Argentinian Programming Competition) and it was mentioned to me today. I suspect there must be a better than bruteforce algorithm here using the convexity property otherwise they woudn't ask it on a competition. Also the constraints for N were N < 400 so it wound't be solvable with a O(n!) solution
edit2:
One interesting case is this one:
Consider a very long and narrow rectangle, where the points are on the long sides of the rectangle, one in front of the other.
The start and exit points are on the opposite ends of this "tunnel"
doing a clockwise or counterclockwise turn you would end up travelling 2*L where L is the size of the long side of the rectangle.
Doing a zig-zag from start to end would be optimal here, since you only need to go through L once, and then some small steps from one side to the other.
algorithm data-structures graph-algorithm
asked Nov 13 '18 at 22:14
serianoxserianox
144
If you want help with a homework question, you need to show some effort here. Do you suspect there is a better algorithm than brute force? What would it be like?
– Turnsole
Nov 13 '18 at 22:58
@Turnsole Not a homework question. It was a problem asked in TAP in 2016 (Argentinian Programming Competition) and it was mentioned to me today. I suspect there must be a better than bruteforce algorithm here using the convexity property otherwise they woudn't ask it on a competition. Also the constraints for N were N < 400 so it wound't be solvable with a O(n!) solution
– serianox
Nov 13 '18 at 23:32
Then you should edit your question description so that it does not seem that the question is a homework.
– Shudipta Sharma
Nov 14 '18 at 3:58
add a comment |
I've been asked the following question:
You have N points, where two of them are the "start" and "exit"
You want to start at "start", go through every other node, and end up at "exit". What is the shortest path (using Euclidean distance) if the polygon formed by the N nodes is convex? Is there a better algorithm than brute force here?
edit1:
It was a problem asked in TAP in 2016 (Argentinian Programming Competition) and it was mentioned to me today. I suspect there must be a better than bruteforce algorithm here using the convexity property otherwise they woudn't ask it on a competition. Also the constraints for N were N < 400 so it wound't be solvable with a O(n!) solution
edit2:
One interesting case is this one:
Consider a very long and narrow rectangle, where the points are on the long sides of the rectangle, one in front of the other.
The start and exit points are on the opposite ends of this "tunnel"
doing a clockwise or counterclockwise turn you would end up travelling 2*L where L is the size of the long side of the rectangle.
Doing a zig-zag from start to end would be optimal here, since you only need to go through L once, and then some small steps from one side to the other.
algorithm data-structures graph-algorithm
asked Nov 13 '18 at 22:14
serianoxserianox
144
I've been asked the following question:
You have N points, where two of them are the "start" and "exit"
You want to start at "start", go through every other node, and end up at "exit". What is the shortest path (using Euclidean distance) if the polygon formed by the N nodes is convex? Is there a better algorithm than brute force here?
edit1:
It was a problem asked in TAP in 2016 (Argentinian Programming Competition) and it was mentioned to me today. I suspect there must be a better than bruteforce algorithm here using the convexity property otherwise they woudn't ask it on a competition. Also the constraints for N were N < 400 so it wound't be solvable with a O(n!) solution
edit2:
One interesting case is this one:
Consider a very long and narrow rectangle, where the points are on the long sides of the rectangle, one in front of the other.
The start and exit points are on the opposite ends of this "tunnel"
doing a clockwise or counterclockwise turn you would end up travelling 2*L where L is the size of the long side of the rectangle.
Doing a zig-zag from start to end would be optimal here, since you only need to go through L once, and then some small steps from one side to the other.
algorithm data-structures graph-algorithm
algorithm data-structures graph-algorithm
asked Nov 13 '18 at 22:14
serianoxserianox
144
asked Nov 13 '18 at 22:14
serianoxserianox
144
edited Nov 14 '18 at 12:26
serianox
asked Nov 13 '18 at 22:14
serianoxserianox
144
asked Nov 13 '18 at 22:14
serianoxserianox
144
asked Nov 13 '18 at 22:14
serianoxserianox
144
144
If you want help with a homework question, you need to show some effort here. Do you suspect there is a better algorithm than brute force? What would it be like?
– Turnsole
Nov 13 '18 at 22:58
@Turnsole Not a homework question. It was a problem asked in TAP in 2016 (Argentinian Programming Competition) and it was mentioned to me today. I suspect there must be a better than bruteforce algorithm here using the convexity property otherwise they woudn't ask it on a competition. Also the constraints for N were N < 400 so it wound't be solvable with a O(n!) solution
– serianox
Nov 13 '18 at 23:32
Then you should edit your question description so that it does not seem that the question is a homework.
– Shudipta Sharma
Nov 14 '18 at 3:58
add a comment |
If you want help with a homework question, you need to show some effort here. Do you suspect there is a better algorithm than brute force? What would it be like?
– Turnsole
Nov 13 '18 at 22:58
@Turnsole Not a homework question. It was a problem asked in TAP in 2016 (Argentinian Programming Competition) and it was mentioned to me today. I suspect there must be a better than bruteforce algorithm here using the convexity property otherwise they woudn't ask it on a competition. Also the constraints for N were N < 400 so it wound't be solvable with a O(n!) solution
– serianox
Nov 13 '18 at 23:32
Then you should edit your question description so that it does not seem that the question is a homework.
– Shudipta Sharma
Nov 14 '18 at 3:58
If you want help with a homework question, you need to show some effort here. Do you suspect there is a better algorithm than brute force? What would it be like?
– Turnsole
Nov 13 '18 at 22:58
If you want help with a homework question, you need to show some effort here. Do you suspect there is a better algorithm than brute force? What would it be like?
– Turnsole
Nov 13 '18 at 22:58
@Turnsole Not a homework question. It was a problem asked in TAP in 2016 (Argentinian Programming Competition) and it was mentioned to me today. I suspect there must be a better than bruteforce algorithm here using the convexity property otherwise they woudn't ask it on a competition. Also the constraints for N were N < 400 so it wound't be solvable with a O(n!) solution
– serianox
Nov 13 '18 at 23:32
@Turnsole Not a homework question. It was a problem asked in TAP in 2016 (Argentinian Programming Competition) and it was mentioned to me today. I suspect there must be a better than bruteforce algorithm here using the convexity property otherwise they woudn't ask it on a competition. Also the constraints for N were N < 400 so it wound't be solvable with a O(n!) solution
– serianox
Nov 13 '18 at 23:32
Then you should edit your question description so that it does not seem that the question is a homework.
– Shudipta Sharma
Nov 14 '18 at 3:58
Then you should edit your question description so that it does not seem that the question is a homework.
– Shudipta Sharma
Nov 14 '18 at 3:58
add a comment |
1 Answer
1
active
oldest
votes
Is there a better algorithm than brute force here?
If you think this problem with dynamic programming you can get a solution O(n^2) that is possible to solve constraint for the constraint n < 400.
This link has a good explication, see problem B: https://caloventorendos.blogspot.com/2016/09/solucionario-tap-2016.html
answered Nov 18 '18 at 3:47
ivangalbanivangalban
5116
add a comment |
Your Answer
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: "1"
;
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: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
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%2fstackoverflow.com%2fquestions%2f53290319%2fshortest-distance-of-convex-polygon-with-start-and-exit-problem%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
Is there a better algorithm than brute force here?
If you think this problem with dynamic programming you can get a solution O(n^2) that is possible to solve constraint for the constraint n < 400.
This link has a good explication, see problem B: https://caloventorendos.blogspot.com/2016/09/solucionario-tap-2016.html
answered Nov 18 '18 at 3:47
ivangalbanivangalban
5116
add a comment |
Is there a better algorithm than brute force here?
If you think this problem with dynamic programming you can get a solution O(n^2) that is possible to solve constraint for the constraint n < 400.
This link has a good explication, see problem B: https://caloventorendos.blogspot.com/2016/09/solucionario-tap-2016.html
answered Nov 18 '18 at 3:47
ivangalbanivangalban
5116
add a comment |
Is there a better algorithm than brute force here?
If you think this problem with dynamic programming you can get a solution O(n^2) that is possible to solve constraint for the constraint n < 400.
This link has a good explication, see problem B: https://caloventorendos.blogspot.com/2016/09/solucionario-tap-2016.html
answered Nov 18 '18 at 3:47
ivangalbanivangalban
5116
Is there a better algorithm than brute force here?
If you think this problem with dynamic programming you can get a solution O(n^2) that is possible to solve constraint for the constraint n < 400.
This link has a good explication, see problem B: https://caloventorendos.blogspot.com/2016/09/solucionario-tap-2016.html
answered Nov 18 '18 at 3:47
ivangalbanivangalban
5116
answered Nov 18 '18 at 3:47
ivangalbanivangalban
5116
answered Nov 18 '18 at 3:47
ivangalbanivangalban
5116
answered Nov 18 '18 at 3:47
ivangalbanivangalban
5116
5116
add a comment |
add a comment |
Thanks for contributing an answer to Stack Overflow!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
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%2fstackoverflow.com%2fquestions%2f53290319%2fshortest-distance-of-convex-polygon-with-start-and-exit-problem%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
If you want help with a homework question, you need to show some effort here. Do you suspect there is a better algorithm than brute force? What would it be like?
– Turnsole
Nov 13 '18 at 22:58
@Turnsole Not a homework question. It was a problem asked in TAP in 2016 (Argentinian Programming Competition) and it was mentioned to me today. I suspect there must be a better than bruteforce algorithm here using the convexity property otherwise they woudn't ask it on a competition. Also the constraints for N were N < 400 so it wound't be solvable with a O(n!) solution
– serianox
Nov 13 '18 at 23:32
Then you should edit your question description so that it does not seem that the question is a homework.
– Shudipta Sharma
Nov 14 '18 at 3:58