Problem 2260. GJam 2011 Africa Qual A: Maximum Loop Size

Created by Richard Zapor

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This Challenge is derived from <a href = "http://code.google.com/codejam/contest/837485/dashboard">GJam 2011 Africa: Closing the Loop</a>. Small Case
Google Code Jam 2014 Kicks Off its Qualifier round April 11. <a href = "http://code.google.com/codejam">GJam Registration</a>. The Test Suite, at the bottom, contains a full GJam file input read, process, and Output example.Create the maximum length Loop of alternating Segment types (0 or 1). Return Maximum Length. Segment connection Knots reduce the Length by 1, including the end to the start knot. 
If no valid loop can be created then return 0.Input: M, 2xN matrix of [Lengths(1:N);Types(1:N)], Types are 0 or 1Output: L, maximum Loop Length of valid alternating segment typesExample:
M=[6 1 7 3;1 0 1 0], L=13Additional GJam solutions can be found at <a href = "http://go-hero.net/jam">Example GJam Matlab solutions</a>. Select Find Solutions, change Language to Matlab. There were only 50 Qualifier Matlab entrants in 2013 and a mere 2 Matlab users achieved round 2.

This Challenge is derived from <http://code.google.com/codejam/contest/837485/dashboard GJam 2011 Africa: Closing the Loop>. Small Case
Google Code Jam 2014 Kicks Off its Qualifier round April 11. <http://code.google.com/codejam GJam Registration>. The Test Suite, at the bottom, contains a full GJam file input read, process, and Output example.

Create the maximum length Loop of alternating Segment types (0 or 1). Return Maximum Length. Segment connection Knots reduce the Length by 1, including the end to the start knot. 
If no valid loop can be created then return 0.

*Input:* M, 2xN matrix of [Lengths(1:N);Types(1:N)], Types are 0 or 1

*Output:* L, maximum Loop Length of valid alternating segment types

*Example:*
M=[6 1 7 3;1 0 1 0], L=13

Additional GJam solutions can be found at <http://go-hero.net/jam Example GJam Matlab solutions>. Select Find Solutions, change Language to Matlab. There were only 50 Qualifier Matlab entrants in 2013 and a mere 2 Matlab users achieved round 2.

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Last Solution submitted on Oct 01, 2020

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Rafael S.T. Vieira on 20 Sep 2020

You need to explain these problems better. It's not always clear what we are supposed to do. I guess that at Google Jam they've explained it better, but the link is currently broken. For instance if you give me two types and ask me to alternate between them I can create an infinite sequence...so why should we stop at some point?

Rafael S.T. Vieira on 20 Sep 2020

I guess that this is the official description https://open.kattis.com/problems/closingtheloop (found it at a blog.) Please copy from there if that's the case. Basically, Each number represents a length of rope that we are tying in a loop, and each knot consumes 1 unit (1/2 unit from each different type). We must answer what the maximum length of rope is possible for this loop. For instance, if we have 1 unit of red rope (type 0) and tie it with one piece of blue rope (type 1), we end up with a loop of zero units (due to the two knots that should not be taken into account for the length).

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Problem 2260. GJam 2011 Africa Qual A: Maximum Loop Size

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Problem 2260. GJam 2011 Africa Qual A: Maximum Loop Size

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