E D R , A S I H C RSS

Erdos Numbers

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

About ErdosNumbers

—๊ฐ€๋ฆฌ ถœ‹ ˜ ˆ˜•™ž ด —๋ฅด๋˜‹œ(Paul Erdos, 1913-1996)๋Š” 20„ธ๊ธฐ˜ ๊ฐ€žฅ œ ๋ช…•œ ˆ˜•™ž ๊ฐ€šด๋ฐ •˜๋‚˜๋กœ ๊ผฝžŒ๋‹ค. —๋ฅด๋˜‹œ™€ •จ๊ป˜ ๋…ผ๋ฌธ„ “ด ๊ฒฝ—˜ด žˆ๋Š” ˆ˜•™ž๋“ค๋„ กด๊ฒฝ„ ๋ฐ›„  •๋„๋‹ˆ ๊ทธ˜ ๋ช…„„ งž‘•  ˆ˜ žˆ„ ๊ฒƒด๋‹ค.
•˜ง€๋งŒ ๋ถˆ–‰•˜๊ฒŒ๋„ ๋ชจ๋“  ‚ฌ๋žŒ๋“คด ๊ทธ™€ •จ๊ป˜ ๋…ผ๋ฌธ„ “ธ ๊ธฐšŒ๋ฅผ –ป„ ˆ˜ žˆ๋Š” ๊ฒƒ€ •„๋‹ˆ—ˆ๊ธฐ ๋•Œ๋ฌธ— —๋ฅด๋˜‹œ™€ •จ๊ป˜ ๋…ผ๋ฌธ„ ผ๋˜ ‚ฌ๋žŒ๊ณผ ๋…ผ๋ฌธ„ ๊ฐ™ด “ฐ๋Š”  •๋„๋กœ ๋งŒ•ด•ผ –ˆ๋‹ค. ด๋Ÿฐ ดœ ๋กœ ธ•ด —๋ฅด๋˜‹œ ˆ˜๋ผ๋Š” ๊ฒƒด ƒ๊ฒผ๋‹ค. —๋ฅด๋˜‹œ™€ •จ๊ป˜ ๋…ผ๋ฌธ„ “ด ‚ฌ๋žŒ˜ —๋ฅด๋˜‹œ ˆ˜๋Š” 1ด๋‹ค. —๋ฅด๋˜‹œ™€ ง ‘ •จ๊ป˜ ๋ˆˆ๋ฌธ„ “ฐ„ •Š•˜ง€๋งŒ —๋ฅด๋˜‹œ ˆ˜๊ฐ€ 1ธ ‚ฌ๋žŒ๊ณผ •จ๊ป˜ ๋…ผ๋ฌธ„ “ด  ด žˆ๋Š” ‚ฌ๋žŒ˜ —๋ฅด๋˜‹œ ˆ˜๋Š” 2๋‹ค.
ฃผ–ด„ ๋…ผ๋ฌธ๊ณผ ๋…ผ๋ฌธ  €ž๋ฅผ ๋ฐ”ƒ•œผ๋กœ —๋ฅด๋˜‹œ ˆ˜๋ฅผ ๊ณ„‚ฐ•˜๋Š” ”„๋กœ๊ทธ๋žจ„ ๋งŒ๋“ค–ด•ผ •œ๋‹ค.

Input

ž…๋ ฅ˜ ฒซ๋ฒˆงธ –‰—๋Š” ‹œ๋‚˜๋ฆฌ˜ค ๊ฐœˆ˜๊ฐ€ ๋“ค–ดžˆ๋‹ค. ๊ฐ ‹œ๋‚˜๋ฆฌ˜ค๋Š” ๋…ผ๋ฌธ ๋ฐด„ฐ๋ฒ ดŠค˜ ด๋ฆ„˜ ๋ชฉ๋กœผ๋กœ ๊ตฌ„๋œ๋‹ค. ๊ฐ ‹œ๋‚˜๋ฆฌ˜ค˜ ฒซ๋ฒˆงธ „—๋Š” P™€ Nด๋ผ๋Š” ž—ฐˆ˜ ๋‘ ๊ฐœ๊ฐ€ ž…๋ ฅ๋œ๋‹ค. ๊ทธ ๋‹คŒ „—๋Š” ๋…ผ๋ฌธ ๋ฐด„ฐ๋ฒ ดŠค๊ฐ€ ž…๋ ฅ๋˜๋ฉฐ ๊ฐ ๋…ผ๋ฌธ๋งˆ๋‹ค •œ „”ฉ  €ž— ๋Œ€•œ  •๋ณด๊ฐ€ ž…๋ ฅ๋œ๋‹ค. ๊ฐ ๋…ผ๋ฌธ— ๋Œ€•œ  •๋ณด๋Š” ๋‹คŒ๊ณผ ๊ฐ™€ ‹œผ๋กœ ๊ธฐˆ ๋œ๋‹ค.

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

P๊ฐœ˜ ๋…ผ๋ฌธ  •๋ณด ๋ฐ‘—๋Š” ๊ฐ๊ฐ •˜๋‚˜”ฉ˜ ด๋ฆ„ด ๋“ค–ดžˆ๋Š” N๊ฐœ˜ –‰ด ž…๋ ฅ๋œ๋‹ค. ด๋ฆ„€ ๋‹คŒ๊ณผ ๊ฐ™€ ˜•‹œผ๋กœ ž…๋ ฅ๋œ๋‹ค.

Martin, G.

Output

๊ฐ ‹œ๋‚˜๋ฆฌ˜ค— ๋Œ€•ด "Scenario i"(i๋Š” ‹œ๋‚˜๋ฆฌ˜ค ๋ฒˆ˜ธ)๋ผ๋Š” ๋‚ดšฉด ๋“ค–ดžˆ๋Š” –‰„ šฐ„  ถœ๋ ฅ•œ๋‹ค. ๊ทธ ๋‹คŒ „๋ถ€„ฐ๋Š” ž…๋ ฅ๋œ ๋ชจ๋“  ด๋ฆ„— ๋Œ€•ด ด๋ฆ„๊ณผ —๋ฅด๋˜‹œ ˆ˜๋ฅผ ถœ๋ ฅ•œ๋‹ค.  €ž˜ ด๋ฆ„€ ž…๋ ฅ๋œ ˆœ„œ๋Œ€๋กœ ถœ๋ ฅ๋œ๋‹ค. —๋ฅด๋˜‹œ ˆ˜๋Š” ‹œ๋‚˜๋ฆฌ˜ค— ๋“ค–ดžˆ๋Š” ๋…ผ๋ฌธ ๋ฐด„ฐ๋ฒ ดŠค๋ฅผ ๊ธฐ๋ฐ˜œผ๋กœ ๊ณ„‚ฐ•œ๋‹ค. ๋ฐด„ฐ๋ฒ ดŠค— žˆ๋Š” ๋…ผ๋ฌธœผ๋กœ ๋ณผ ๋•Œ —๋ฅด๋˜‹œ™€  „˜€ ๊ด€๊ณ„๊ฐ€ —†๋Š”  €ž๋“ค˜ —๋ฅด๋˜‹œ ˆ˜๋Š” "infinity"๋กœ ถœ๋ ฅ•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‘„ž ‚ฌšฉ–ธ–ด ๊ฐœ๋ฐœ‹œ๊ฐ„ ฝ”๋“œ
ฐจ˜๊ถŒ C++ 6‹œ๊ฐ„ ErdosNumbers/ฐจ˜๊ถŒ
™ฉžฌ„  Java 4‹œ๊ฐ„ ErdosNumbers/™ฉžฌ„ 
ž„ธƒ Python 1‹œ๊ฐ„ 20๋ถ„ ErdosNumbers/ž„ธƒ
๋ฌธ๋ณดฐฝ C++ . ErdosNumbers/๋ฌธ๋ณดฐฝ
กฐ˜„ƒœ C++ . ErdosNumbers/กฐ˜„ƒœ

“ฐ๋ ˆ๋“œ

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