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3N+1 Problem

•™๊ต—„œ ฃŒ•„ ‹ฌž˜๊ธฐ œ„• acm programming contest ๊ธฐถœฌธ œฅผ ’€–Š”ฐ, ToyProblems —„œ„ ‹คฃฐงŒ•œ ‰ฌš ฌธ œ๊ฐ€ žˆ๊ธฐ—  ‡๊ฒŒ †Œ๊ฐœ•‹ˆ‹ค. ›ฌธ๊ธฐ

 ฌธ œŠ”

ธ๊ธฐ„:A(A,B,C), „ฑ๊ณตฅ :‚ฎŒ(‚ฎŒ,†ต,†’Œ),  ˆฒจ:1(1~4)

CS—„œ “ฑžฅ•˜Š” ฌธ œ˜ ข…ฅ˜Š” —ฌŸฌ๊ฐ€€๊ฐ€ žˆŠ”ฐ (˜ˆฅผ “ค–, NP, Unsolvable, Recursive...)  ฌธ œŠ” 'ž… ฅ— Œ€• ถœ ฅ ––๊ฒŒ ‚˜˜ฌ€ Š”' ผ๊ณ  ถ„ฅ˜• งŒ•œ ๊ฒƒ— Œ€•œ ถ„„„ •˜Š” ๊ฒƒ‹ค. (•„ • งค•˜๊ตฐš”; )

‹คŒ๊ณผ ๊ฐ™€ •Œ๊ณ ฆฌฆ˜ žˆ‹ค
1. input n
2. print n
3. if n == 1 then STOP
4.    if n is odd then n = 3n + 1
5.    else n = n/2
6. GOTO 2

งŒ•ž… ฅœผกœ 22๊ฐ€ ฃผ–กŒ„•Œ ถœ ฅ๊ฐ’€ 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1 ๊ฐ€   ๊ฒƒ‹ค.  •Œ๊ณ ฆฌฆ˜€ ๊ฐ„‹จ• €งŒ n˜ ๊ฐ’ 1กœ ˜– •Œ๊ณ ฆฌฆ˜ ข…ฃŒ €Š” Š” ผ‹ค. •˜€งŒ Š” 0๊ณผ 1000000 ‚ฌ˜ ˆซž, •„‹ˆ ‹ค ” ฐ ˆซž— Œ€•„œ„ n˜ ๊ฐ’ 1 œ‹ค๊ณ  ฆ…˜—ˆ‹ค.

ž… ฅœผกœ 22๊ฐ€ ฃผ–กŒ„•Œ, ถœ ฅ˜Š” ๊ฐ’˜ ˆ˜ n(22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1) Š” 22 16‹ค. ฅผ n— Œ€•œ cycle-length ผ๊ณ  •œ‹ค.

 •ˆ˜ i™€ j — Œ€• ‘ ˆ˜ ‚ฌ— žฌ•˜Š” cycle-length ๊ฐ’“คค‘˜ ตœŒ€๊ฐ’„ ๊ตฌ•  ๊ฒƒ‹ค. ž… ฅ€ •„ž˜™€ ๊ฐ™ •œ ค„— •œ Œ˜  •ˆ˜กœ ฃจ– ธ žˆ‹ค. ถœ ฅ๊ฐ’€  ‘  •ˆ˜ ‚ฌ˜ cycle-length ค‘—„œ ตœŒ€๊ฐ’„ ๊ตฌ•˜Š” ๊ฒƒ‹ค.

ž… ฅ

1 10
100 200
201 210
900 1000

ถœ ฅ

1 10 20
100 200 125
201 210 89
900 1000 174

’€

ž‘„ฑž ‚ฌšฉ–ธ– ๊ฐœฐœ‹œ๊ฐ„ ฝ”“œ ‹ค–‰‹œ๊ฐ„(i=1,j=999999 ๊ธฐ€ 4ˆ †ต๊ณผ)
๊ฐ•ฌ๊ฒฝ Python 1‹œ๊ฐ„ 3N+1Problem/๊ฐ•ฌ๊ฒฝ X
™žฌ„  Python ? 3N+1Problem/™žฌ„  .
๊น€šŒ˜ C++ ? 3N+1Problem/๊น€šŒ˜ .
ฌธฐฝ C++ ? 3N+1Problem/ฌธฐฝ X
๊ตฌž๊ฒธ C ? 3N+1Problem/๊ตฌž๊ฒธ .
‹ žฌ™ C++ 10ถ„ 3N+1Problem/‹ žฌ™ .
Leonardong Python 46ถ„ 3N+1Problem/Leonardong .
๊ณฝ„ธ™˜ C++ ? 3N+1Problem/๊ณฝ„ธ™˜ .
1002 Python 13ถ„ 3N+1Problem/1002 .
1002 Python 30ถ„ 3N+1Problem/1002_2 No-Psyco : 9.25ˆ, With-Psyco : 3.8ˆ
—ˆ•„˜ C++ 1‹œ๊ฐ„ 20ถ„ 3N 1Problem/—ˆ•„˜ .
„˜„ C++ 1‹œ๊ฐ„ 3n+1/„˜„ .
ž„ธƒ HaskellLanguage 30ถ„ —ฌ๊ธฐ .
๊น€ƒ„ญ C++ —„ฒญ..ใ…กใ…œ 3N+1/๊น€ƒ„ญ .

See also BioinfoWiki:AlgorithmQuiz/3Plus1

ฌธ œ 2ƒ„


  • ๊ธฐ˜ ฝ”“œฅผ ˆ˜ ••„œ ๊ฐ€žฅ ฐ Cycle Length ๊ฐ€ •„‹Œ 3ฒˆงธกœ ฐ Cycle Length ฅผ ๊ตฌ•„ธš”.
    ž‘„ฑž ‚ฌšฉ–ธ– ๊ฐœฐœ(ˆ˜ •)‹œ๊ฐ„ ฝ”“œ
    1002 Python 16ถ„(3ถ„) .

“ฐ ˆ“œ

‹ค–‰‹œ๊ฐ„(i=1,j=1000000 ๊ธฐ€ 4ˆ †ต๊ณผ)Š” ŒŒฌ˜ ๊ฒฝšฐ ๊ฐ€Šฅ• Ÿฐ€ ๊ฒ „คš”. ‚˜ฆ„Œ€กœ •Œ๊ณ ฆฌฆ˜„ ๊ฐ•–ˆŠ”ฐ„ 1, 100000— นŒนŒ ๊ฑฐฆฌ‹ˆ...--๊ฐ•ฌ๊ฒฝ


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