Problem 44077. GJam 2017 Kickstart: Vote (Large)

This Challenge is derived from GJam 2017 Kickstart Vote. This is the first 100 large cases with 0<=M<N<=2000.

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 N and M votes, where N>M, determine the number of voting sequences for which N is always in the lead divided by the total number of sequences(N+M)!.

Input: [N,M], the quantity of votes to N and M

Output: [V], the ratio of N always leading sequences to total sequences

Examples: [N,M] [V]; [2,1] [0.33333333]

For the case [2,1] there are 6 sequences [N1N2M1,N2N1M1,N1M1N2,N2M1N1,M1N1N2,M1N2N1] with only the first two always having N in the lead.

Theory: Brute force permutations and counting will not succeed in a timely manner for 0<=M<N<=2000 as 2000! may be a bit large. Determining the inherent mathematical pattern is usually the best way to succeed in GJam. GJam Kickstart solutions(C++,Python).

Solution Stats

84.62% Correct | 15.38% Incorrect
Last Solution submitted on Feb 08, 2023

Problem Comments

Solution Comments

Show comments

Problem Recent Solvers10

Suggested Problems

More from this Author308

Problem Tags

Community Treasure Hunt

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

Start Hunting!