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3N+1 Problem

ํ•™ต—„œ ฌดฃŒํ•จ„ ‹ฌž˜ธฐ œ„ํ•ด acm programming contest ธฐถœฌธ œ ํ’€–ดณดŠ”ฐ, ToyProblems —„œ„ ‹คฃฐงŒํ•œ ‰ฌšด ฌธ œ€ žˆธฐ— ด ‡ฒŒ †Œฐœํ•ฉ‹ˆ‹ค. ›ฌธณดธฐ

ด ฌธ œŠ”

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

CS—„œ “žฅํ•˜Š” ฌธ œ˜ ข…ฅ˜Š” —ฌŸฌ€€€ žˆŠ”ฐ (˜ˆ “ค–ด, NP, Unsolvable, Recursive...) ด ฌธ œŠ” 'ž… ฅ— Œ€ํ•ด ถœ ฅด –ด–ปฒŒ ‚˜˜ฌ€ ชจฅดŠ”' ดณ  „ฅ˜ํ• งŒํ•œ ฒƒ— Œ€ํ•œ „„„ ํ•˜Š” ฒƒด‹ค. (ํ•ด„ด • งคํ•˜ตฐš”; )

‹คŒ ฐ™€ •Œณ ฆฌฆ˜ด 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•ฝ ž… ฅœกœ 22€ –ดกŒ„•Œ ถœ ฅฐ’€ 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1 €   ฒƒด‹ค. ด •Œณ ฆฌฆ˜€ „‹จํ•ด ณดด€งŒ n˜ ฐ’ด 1กœ ˜–ด •Œณ ฆฌฆ˜ด ข…ฃŒ €Š” ชจฅดŠ” ด‹ค. ํ•˜€งŒ ดŠ” 0 1000000 ‚ฌด˜ ˆซž, •„‹ˆ ดณด‹ค ” ํฐ ˆซž— Œ€ํ•ด„œ„ n˜ ฐ’ด 1ด œ‹คณ  ฆช…˜—ˆ‹ค.

ž… ฅœกœ 22€ –ดกŒ„•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ด‹ค. ด n— Œ€ํ•œ cycle-length ณ  ํ•œ‹ค.

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

ํ’€ด

ž‘„ž ‚ฌšฉ–ธ–ด ฐœฐœ‹œ„ ฝ”“œ ‹คํ–‰‹œ„(i=1,j=999999 ธฐ€ 4ดˆ ํ†ต)
ฐ•ํฌฒฝ Python 1‹œ„ 3N+1Problem/ฐ•ํฌฒฝ X
ํ™ฉžฌ„  Python ? 3N+1Problem/ํ™ฉžฌ„  .
€ํšŒ˜ C++ ? 3N+1Problem/€ํšŒ˜ .
ฌธณดฐฝ C++ ? 3N+1Problem/ฌธณดฐฝ X
ตฌžฒธ C ? 3N+1Problem/ตฌžฒธ .
‹ žฌ™ C++ 10„ 3N+1Problem/‹ žฌ™ .
Leonardong Python 46„ 3N+1Problem/Leonardong .
ณฝ„ธํ™˜ C++ ? 3N+1Problem/ณฝ„ธํ™˜ .
1002 Python 13„ 3N+1Problem/1002 .
1002 Python 30„ 3N+1Problem/1002_2 No-Psyco : 9.25ดˆ, With-Psyco : 3.8ดˆ
ํ—ˆ•„˜ C++ 1‹œ„ 20„ 3N 1Problem/ํ—ˆ•„˜ .
ด„ํ˜„ C++ 1‹œ„ 3n+1/ด„ํ˜„ .
ž„ธํƒ HaskellLanguage 30„ —ฌธฐ .
€ƒ„ C++ —„ฒญ..ใ…กใ…œ 3N+1/€ƒ„ .

See also BioinfoWiki:AlgorithmQuiz/3Plus1

ฌธ œ 2ํƒ„


  • ธฐกด˜ ฝ”“œ ˆ˜ •ํ•ด„œ €žฅ ํฐ Cycle Length € •„‹Œ 3ฒˆงธกœ ํฐ Cycle Length ตฌํ•ดณด„š”.
    ž‘„ž ‚ฌšฉ–ธ–ด ฐœฐœ(ˆ˜ •)‹œ„ ฝ”“œ
    1002 Python 16„(3„) .

“ฐ ˆ“œ

‹คํ–‰‹œ„(i=1,j=1000000 ธฐ€ 4ดˆ ํ†ต)Š” ํŒŒดฌ˜ ฒฝšฐ €Šฅํ• Ÿฐ€ ชจฅดฒ „š”. ‚˜„Œ€กœ •Œณ ฆฌฆ˜„ ณดฐ•ํ–ˆŠ”ฐ„ 1, 100000— ŒŒ ฆฌ‹ˆ...--ฐ•ํฌฒฝ


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