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Erdos Numbers

์›๋ฌธ๋ณด๊ธฐ
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์ธ๊ธฐ๋„:B(A,B,C), ์„ฑ๊ณต๋ฅ :๋‚ฎ์Œ(๋‚ฎ์Œ,๋ณดํ†ต,๋†’์Œ), ๋ ˆ๋ฒจ:2(1~4)

About ErdosNumbers

ํ—๊ฐ€๋ฆฌ ์ถœ์‹ ์˜ ์ˆ˜ํ•™์ž ํด ์—๋ฅด๋˜์‹œ(Paul Erdos, 1913-1996)๋Š” 20์„ธ๊ธฐ์˜ ๊ฐ€์žฅ ์œ ๋ช…ํ•œ ์ˆ˜ํ•™์ž ๊ฐ€์šด๋ฐ ํ•˜๋‚˜๋กœ ๊ผฝํžŒ๋‹ค. ์—๋ฅด๋˜์‹œ์™€ ํ•จ๊ป˜ ๋…ผ๋ฌธ์„ ์“ด ๊ฒฝํ—˜์ด ์žˆ๋Š” ์ˆ˜ํ•™์ž๋“ค๋„ ์กด๊ฒฝ์„ ๋ฐ›์„ ์ •๋„๋‹ˆ ๊ทธ์˜ ๋ช…์„ฑ์„ ์ง์ž‘ํ•  ์ˆ˜ ์žˆ์„ ๊ฒƒ์ด๋‹ค.
ํ•˜์ง€๋งŒ ๋ถˆํ–‰ํ•˜๊ฒŒ๋„ ๋ชจ๋“  ์‚ฌ๋žŒ๋“ค์ด ๊ทธ์™€ ํ•จ๊ป˜ ๋…ผ๋ฌธ์„ ์“ธ ๊ธฐํšŒ๋ฅผ ์–ป์„ ์ˆ˜ ์žˆ๋Š” ๊ฒƒ์€ ์•„๋‹ˆ์—ˆ๊ธฐ ๋•Œ๋ฌธ์— ์—๋ฅด๋˜์‹œ์™€ ํ•จ๊ป˜ ๋…ผ๋ฌธ์„ ์ผ๋˜ ์‚ฌ๋žŒ๊ณผ ๋…ผ๋ฌธ์„ ๊ฐ™์ด ์“ฐ๋Š” ์ •๋„๋กœ ๋งŒ์กฑํ•ด์•ผ ํ–ˆ๋‹ค. ์ด๋Ÿฐ ์ด์œ ๋กœ ์ธํ•ด ์—๋ฅด๋˜์‹œ ์ˆ˜๋ผ๋Š” ๊ฒƒ์ด ์ƒ๊ฒผ๋‹ค. ์—๋ฅด๋˜์‹œ์™€ ํ•จ๊ป˜ ๋…ผ๋ฌธ์„ ์“ด ์‚ฌ๋žŒ์˜ ์—๋ฅด๋˜์‹œ ์ˆ˜๋Š” 1์ด๋‹ค. ์—๋ฅด๋˜์‹œ์™€ ์ง์ ‘ ํ•จ๊ป˜ ๋ˆˆ๋ฌธ์„ ์“ฐ์ง„ ์•Š์•˜์ง€๋งŒ ์—๋ฅด๋˜์‹œ ์ˆ˜๊ฐ€ 1์ธ ์‚ฌ๋žŒ๊ณผ ํ•จ๊ป˜ ๋…ผ๋ฌธ์„ ์“ด ์ ์ด ์žˆ๋Š” ์‚ฌ๋žŒ์˜ ์—๋ฅด๋˜์‹œ ์ˆ˜๋Š” 2๋‹ค.
์ฃผ์–ด์ง„ ๋…ผ๋ฌธ๊ณผ ๋…ผ๋ฌธ ์ €์ž๋ฅผ ๋ฐ”ํƒ•์œผ๋กœ ์—๋ฅด๋˜์‹œ ์ˆ˜๋ฅผ ๊ณ„์‚ฐํ•˜๋Š” ํ”„๋กœ๊ทธ๋žจ์„ ๋งŒ๋“ค์–ด์•ผ ํ•œ๋‹ค.

Input

์ž…๋ ฅ์˜ ์ฒซ๋ฒˆ์งธ ํ–‰์—๋Š” ์‹œ๋‚˜๋ฆฌ์˜ค ๊ฐœ์ˆ˜๊ฐ€ ๋“ค์–ด์žˆ๋‹ค. ๊ฐ ์‹œ๋‚˜๋ฆฌ์˜ค๋Š” ๋…ผ๋ฌธ ๋ฐ์ดํ„ฐ๋ฒ ์ด์Šค์˜ ์ด๋ฆ„์˜ ๋ชฉ๋ก์œผ๋กœ ๊ตฌ์„ฑ๋œ๋‹ค. ๊ฐ ์‹œ๋‚˜๋ฆฌ์˜ค์˜ ์ฒซ๋ฒˆ์งธ ์ค„์—๋Š” P์™€ N์ด๋ผ๋Š” ์ž์—ฐ์ˆ˜ ๋‘ ๊ฐœ๊ฐ€ ์ž…๋ ฅ๋œ๋‹ค. ๊ทธ ๋‹ค์Œ ์ค„์—๋Š” ๋…ผ๋ฌธ ๋ฐ์ดํ„ฐ๋ฒ ์ด์Šค๊ฐ€ ์ž…๋ ฅ๋˜๋ฉฐ ๊ฐ ๋…ผ๋ฌธ๋งˆ๋‹ค ํ•œ ์ค„์”ฉ ์ €์ž์— ๋Œ€ํ•œ ์ •๋ณด๊ฐ€ ์ž…๋ ฅ๋œ๋‹ค. ๊ฐ ๋…ผ๋ฌธ์— ๋Œ€ํ•œ ์ •๋ณด๋Š” ๋‹ค์Œ๊ณผ ๊ฐ™์€ ์‹์œผ๋กœ ๊ธฐ์ˆ ๋œ๋‹ค.

Smith, M.N., Martin, G., Erdos, P.: Newtonian forms of prime factors matrices

P๊ฐœ์˜ ๋…ผ๋ฌธ ์ •๋ณด ๋ฐ‘์—๋Š” ๊ฐ๊ฐ ํ•˜๋‚˜์”ฉ์˜ ์ด๋ฆ„์ด ๋“ค์–ด์žˆ๋Š” N๊ฐœ์˜ ํ–‰์ด ์ž…๋ ฅ๋œ๋‹ค. ์ด๋ฆ„์€ ๋‹ค์Œ๊ณผ ๊ฐ™์€ ํ˜•์‹์œผ๋กœ ์ž…๋ ฅ๋œ๋‹ค.

Martin, G.

Output

๊ฐ ์‹œ๋‚˜๋ฆฌ์˜ค์— ๋Œ€ํ•ด "Scenario i"(i๋Š” ์‹œ๋‚˜๋ฆฌ์˜ค ๋ฒˆํ˜ธ)๋ผ๋Š” ๋‚ด์šฉ์ด ๋“ค์–ด์žˆ๋Š” ํ–‰์„ ์šฐ์„  ์ถœ๋ ฅํ•œ๋‹ค. ๊ทธ ๋‹ค์Œ ์ค„๋ถ€ํ„ฐ๋Š” ์ž…๋ ฅ๋œ ๋ชจ๋“  ์ด๋ฆ„์— ๋Œ€ํ•ด ์ด๋ฆ„๊ณผ ์—๋ฅด๋˜์‹œ ์ˆ˜๋ฅผ ์ถœ๋ ฅํ•œ๋‹ค. ์ €์ž์˜ ์ด๋ฆ„์€ ์ž…๋ ฅ๋œ ์ˆœ์„œ๋Œ€๋กœ ์ถœ๋ ฅ๋œ๋‹ค. ์—๋ฅด๋˜์‹œ ์ˆ˜๋Š” ์‹œ๋‚˜๋ฆฌ์˜ค์— ๋“ค์–ด์žˆ๋Š” ๋…ผ๋ฌธ ๋ฐ์ดํ„ฐ๋ฒ ์ด์Šค๋ฅผ ๊ธฐ๋ฐ˜์œผ๋กœ ๊ณ„์‚ฐํ•œ๋‹ค. ๋ฐ์ดํ„ฐ๋ฒ ์ด์Šค์— ์žˆ๋Š” ๋…ผ๋ฌธ์œผ๋กœ ๋ณผ ๋•Œ ์—๋ฅด๋˜์‹œ์™€ ์ „ํ˜€ ๊ด€๊ณ„๊ฐ€ ์—†๋Š” ์ €์ž๋“ค์˜ ์—๋ฅด๋˜์‹œ ์ˆ˜๋Š” "infinity"๋กœ ์ถœ๋ ฅํ•œ๋‹ค.

Sample Input 

~cpp 
1
4 3
Smith, M.N., Martin, G., Erdos, P.: Newtonian forms of prime factor matrices 
Erdos, P., Reisig, W.: Stuttering in petri nets
Smith, M.N., Chen, X.: First oder derivates in structured programming
Jablonski, T., Hsueh, Z.: Selfstabilizing data structures
Smith, M.N.
Hsueh, Z.
Chen, X.

Sample Output 

~cpp 
Scenario 1
Smith, M.N. 1
Hsueh, Z. infinity
Chen, X. 2

ํ’€์ด

์ž‘์„ฑ์ž ์‚ฌ์šฉ์–ธ์–ด ๊ฐœ๋ฐœ์‹œ๊ฐ„ ์ฝ”๋“œ
์ฐจ์˜๊ถŒ C++ 6์‹œ๊ฐ„ ErdosNumbers/์ฐจ์˜๊ถŒ
ํ™ฉ์žฌ์„  Java 4์‹œ๊ฐ„ ErdosNumbers/ํ™ฉ์žฌ์„ 
์ž„์ธํƒ Python 1์‹œ๊ฐ„ 20๋ถ„ ErdosNumbers/์ž„์ธํƒ
๋ฌธ๋ณด์ฐฝ C++ . ErdosNumbers/๋ฌธ๋ณด์ฐฝ
์กฐํ˜„ํƒœ C++ . ErdosNumbers/์กฐํ˜„ํƒœ

์“ฐ๋ ˆ๋“œ

Link..๋ผ๋Š” ์ฑ…์ด ์ƒ๊ฐ๋‚˜๋Š”๊ตฐ์š”. ์—๋ฅด๋„์Šค ๋„˜๋ฒ„... - ์ž„์ธํƒ
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