Problem 44075. GJam 2017 Kickstart: Parentheses (Large)

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 large cases with 1&lt;=L+R&lt;=10^5.<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=10^5. 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 large cases with 1<=L+R<=10^5.

<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=10^5. 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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