Problem 44387. Birthday cake

Created by Matthew Eicholtz

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>It's Cody's 5th birthday, and you've been tasked with putting the candles on the cake. Your goal is to maximize the distance between the 5 required candles.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Given a rectangular cake with specified length and width, return the highest possible minimum distance between any two candles.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Important notes</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>You may assume that a candle can be placed directly on the edge of the cake (even though that would be physically challenging!).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>Required tolerance: &lt;0.01</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

1236 Solutions
90 Solvers

Last Solution submitted on Mar 21, 2023

Last 200 Solutions

Problem Comments

16 Comments

16 Comments

Show 13 older comments

David Verrelli on 17 Oct 2017

The Test Suite has the highest minDist as 16 for a cake of size 16×32, but I am getting 16.564. Likewise for a couple of other sizes.

Matthew Eicholtz on 17 Oct 2017

Thanks for the feedback, David. You are absolutely correct. I will fix the test suite.

Matthew Eicholtz on 17 Oct 2017

Ok, I have updated the result for tests 3 and 7. Also, I changed the requirement from 3 decimal places to 2 so that minor discrepancies aren't as big an issue. Please let me know if you catch any other errors.

David Verrelli on 17 Oct 2017

Thanks. I think it's all good now :-)

Alfonso Nieto-Castanon on 18 Oct 2017

well, this was harder than I was anticipating :)

David Verrelli on 19 Oct 2017

It might be advisable to include additional test cases to avoid hard-coded & non-general 'solutions'. Some additional cases are reported in Solution 1299656.

Alfonso Nieto-Castanon on 19 Oct 2017

I second David's suggestion

Matthew Eicholtz on 19 Oct 2017

I agree, David. I'll expand the test suite today.

Alfonso Nieto-Castanon on 20 Oct 2017

great! one suggestion would be to add some cases with cake sides ratios between .45 and .55 but different than .5 to avoid solutions that hard-code the .5 case? (e.g. birthdaycandles(5,11) = 5.5204 ; birthdaycandles(12,23) = 12.2028). The behavior in that range seems most interesting, as the solution space seems to transition smoothly between the two "stable" configurations

Matthew Eicholtz on 20 Oct 2017

Done. Thanks for helping me refine things further, Alfonso.

Daniel Turizo on 20 Oct 2017

The last two cases have a solution of 258.83 and 517.65, I am getting 258.82 and 517.64 respectively. Is this intended and I am wrong? or is it just numerical roundoff?

Are Mjaavatten on 21 Oct 2017

I agree with Daniel Turizo that the round-off is wrong for the two last cases. I had to introduce a fudge factor of 1.00003 to get the value in the test suite, even though I use an analytical solution.

Daniel Turizo on 21 Oct 2017

That right. I am also using an analytical solution and I had to introduce that ugly 1.0003 factor too.

Matthew Eicholtz on 23 Oct 2017

Daniel and Are, thanks for the input. I modified the requirements so that the player should not need to round to 2 decimal places anymore. The "correct" answers now have higher precision, and a solution's answer must be within a tolerance of 0.01. With this format, you should not need the fudge factor you were using (either way, at least one of your submissions should work!).

Alfonso Nieto-Castanon on 24 Oct 2017

I am getting 517.6381 for test #23 (same value using algebraic formula or 1d optimization) compared to the testsuite 517.6500 value, could you please double-check?

Matthew Eicholtz on 24 Oct 2017

Good catch. Test suite updated.

Solution Comments

Solution 1308439

1 Comment

1 Comment

Matthew Eicholtz on 23 Oct 2017

New tests will be added to make this hard-coded solution obsolete.

Solution 1300066

1 Comment

1 Comment

Ivan on 19 Oct 2017

почему b = 2 * wid - sqrt(3) * len / 2;?

Solution 1299305

2 Comments

2 Comments

David Verrelli on 19 Oct 2017

Not a general solution.

Ivan on 19 Oct 2017

yeah! I've done the same... ))

Solution 1297083

3 Comments

3 Comments

David Verrelli on 19 Oct 2017

Not a general solution.

Thomas Steffen on 21 Dec 2017

Seems like a general approach to me, but the boundaries are not correct. I found it easier to calculate the three options, and then pick the worst.

David Verrelli on 27 Jun 2019

Fair point.

Solution 1293226

1 Comment

1 Comment

David Verrelli on 19 Oct 2017

Good insight in your formula for the first case of your if statement.

Problem Recent Solvers90

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 44387. Birthday cake

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers90

Suggested Problems

More from this Author44

Problem Tags

Community Treasure Hunt

Problem 44387. Birthday cake

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers90

Suggested Problems

More from this Author44

Problem Tags

Community Treasure Hunt

Players