Problem 44074. GJam 2017 Kickstart: Parentheses (Small)

Created by Richard Zapor

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This Challenge is derived from <a href = "http://code.google.com/codejam/contest/6304486/dashboard#s=p2">GJam 2017 Kickstart Parentheses</a>. This is the first 100 small cases with max L+R&lt;=20.<a href = "http://code.google.com/codejam">Google Code Jam 2017 Qualifier</a> is March 7, 2017. Typically four challenges with small and large aspects with 27 hours to complete.The GJam story is given L left and R right parentheses determine the maximum number of parentheses pairings.Input: [L,R], the quantity of parentheses typesOutput: [V], the maximum number of parentheses pairingsExamples: [L,R] [V]; [3,2] [3]For the case ()()(, for example, the three balanced groups are () from indexes 1 to 2, () from indexes 3 to 4, and ()() from indexes 1 to 4.Theory: Brute force permutations and counting will not succeed in a timely manner for L+R=20. Determining the inherent mathematical pattern is usually the best way to succeed in GJam. <a href = "http://code.google.com/codejam/contest/6304486/scoreboard#vf=1">GJam Kickstart solutions(C++,Python)</a>.

This Challenge is derived from <http://code.google.com/codejam/contest/6304486/dashboard#s=p2 GJam 2017 Kickstart Parentheses>. This is the first 100 small cases with max L+R<=20.

<http://code.google.com/codejam Google Code Jam 2017 Qualifier> is March 7, 2017. Typically four challenges with small and large aspects with 27 hours to complete.

The GJam story is given L left and R right parentheses determine the maximum number of parentheses pairings.

*Input:* [L,R], the quantity of parentheses types

*Output:* [V], the maximum number of parentheses pairings

*Examples:* [L,R] [V]; [3,2] [3]

For the case ()()(, for example, the three balanced groups are () from indexes 1 to 2, () from indexes 3 to 4, and ()() from indexes 1 to 4.

*Theory:* Brute force permutations and counting will not succeed in a timely manner for L+R=20. Determining the inherent mathematical pattern is usually the best way to succeed in GJam. <http://code.google.com/codejam/contest/6304486/scoreboard#vf=1 GJam Kickstart solutions(C++,Python)>.

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Last Solution submitted on Apr 04, 2023

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Jean-Marie Sainthillier on 27 Feb 2017

It's a pleasure to see you again Richard.

James on 27 Feb 2017

Welcome back, Richard. I have a question on the scoring - Would (()) count as one (Left 2 and Right 3) or two (L1 and R4, and L2 and R3)? I guess the more general question is can you have a balanced string inside of another balanced string?

Tim on 1 Mar 2017

Something seems to be amiss--this page says "5 solutions," but the graph is empty, and clicking "5 solutions" produces "No results." The main page says "0 solutions" but also " Solved."

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Problem 44074. GJam 2017 Kickstart: Parentheses (Small)

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Problem 44074. GJam 2017 Kickstart: Parentheses (Small)

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