Haskell でアルゴリズムを抽象化する / 関数型言語で競技プログラミング

Competitive programming with Haskell
Functional Festival 2025 in TOKYO

Transcript

1. )BTLFMM
   ͰΞϧΰϦζϜΛந৅Խ͢Δ ؔ਺ܕݴޠͰڝٕϓϩάϥϛϯά  /BPZB
   *UP
   !OBPZB@JUP
2. ࣗݾ঺հ • גࣜձࣾ Ұٳ ϗςϧɺϨετϥϯͷ8FC༧໿ࣄۀͷձࣾ
   Ͱಇ͍͍ͯ·͢ • झຯͰڝٕϓϩάϥϛϯάΛᅂΜͰ͓Γɺ)BTLFMM
   Ͱࢀઓ͍ͯ͠·͢ • ݱࡏͷϨʔτ͸ਫ৭ 
   Ͱ͢ – ڭՊॻʹग़ͯ͘ΔྨͷΞϧΰϦζϜ͸೉ͳ͘࢖͍͜ͳͤΔϨϕϧ
3. ࿩͍ͨ͜͠ͱ • )BTLFMM ͰڝٕϓϩάϥϛϯάʹࢀՃ͍ͯ͠ΔɻΞϧΰϦζϜΛந৅Խ͢Δͱɺͦͷ࣮૷͕ ࣅͨΑ͏ͳΠϯλϑΣʔεʹͳΔ͜ͱΛܦݧͨ͠ – ߴ֊ؔ਺ͱͯࣸ͠૾ G
   ͱ݁߹ͷೋ߲ԋࢉ͕ύϥϝʔλͱͯ͠Α͘දΕΔ • ͦΕ͸ۮવͳͷ͔ɺ͍΍ɺۮવͰ͸ͳ͍ – )BTLFMM
   ͷࠜఈʹ͋Δ࠶ؼσʔλߏ଄ɺͦΕʹ࠷దͳૢ࡞Ͱ͋Δࣸ૾ͱ৞ΈࠐΈ NBQ
   
   SFEVDF • ࣸ૾ͱ৞ΈࠐΈʹΑΔؔ਺ͷΠϯλϑΣʔε͔ΒΞϧΰϦζϜͷ୅਺తߏ଄͕ݟ͑Δ • ؔ਺ܕϓϩάϥϛϯάɺ)BTLFMM
   ͸ΞϧΰϦζϜΛΑΓந৅౓ߴ͘ଊ͑ΔࢥߟΛิॿͯ͘͠ ΕΔ
4. ໨࣍ • ࣸ૾ NBQ
   Ͱ໰୊Λղ͘ • ྦྷੵ࿨ uuu GPME
   
   TDBOM
   ʹΑΔʮ৞ΈࠐΈʯ • ΞϧΰϦζϜΛந৅Խ͢Δ uuu ೋ෼୳ࡧΛߴ֊ؔ਺Ͱந৅Խ͢Δ • #'4
   Λந৅Խ͢Δuuu ؔ਺ G
   Λʮ͋Δঢ়ଶ͔Β࣍ͷঢ়ଶ΁ͷঢ়ଶભҠʯͱଊ͑Δ • ಈతܭը๏Λ )BTLFMM
   ͰΠϛϡʔλϒϧʹղ͘ uuu
   ঢ়ଶۭؒͷ৞ΈࠐΈɺͦͯ͠୅਺తߏ଄ ͕ݟ͑Δ • ͳͥΞϧΰϦζϜΛந৅Խ͢ΔͱɺNBQ
   
   SFEVDF
   GPME
   ΍୅਺తߏ଄͕
   uuu ؔ਺ܕϓϩά ϥϛϯάɺ)BTLFMM
   ͕ͦΕΛଅ͢
5. ΩʔʹͳΔεϥΠυΛઌʹ
6. ໋ྩܕ
   ୹໋σʔλ
   uuu
   Ұ࣌తͳதؒঢ়ଶΛ܁Γฦ͠ॻ͖׵͑ͯ౴͑ʹ޲͔͏ ؔ਺ܕ Ӭଓσʔλ
   uuu
   ঢ়ଶΛ࣍ͷঢ়ଶ΁ࣸ͢
7. ࣸ૾ͱ݁߹ ू໿
   uuu NBQ
   
   SFEVDF
   GPME • ؔ਺ܕϓϩάϥϛϯάͰ͸ʮࣸ૾ͱ݁߹ ू໿ ʯͷϝϯλϧϞσϧͰ໰୊Λղ͘ • ࣸ૾ͱ݁߹ ू໿
   uuu NBQ
   
   SFEVDF
   GPME • ͳͥ NBQ
   
   SFEVDF
   ͔ – )BTLFMM
   ͷෆมσʔλߏ଄͸୅਺తσʔλܕʹΑΔ࠶ؼσʔλߏ଄ – ࠶ؼσʔλߏ଄ͷૢ࡞ʹ͸ NBQ
   
   SFEVDF – -*41
   ͷ௚ײ͔Βʜ
   ͋ͱͰ
8. #'4
   ʹ౉͍ͯ͠Δؔ਺ G
   ͷҙຯΛߟ͑ͯΈΔ let dist = bfs f (+) (-1) bounds [(1, 0 :: Int)] • f Λهड़͢Δ͚ͩͰ໰୊͕ղ͚Δ͕ɺf ͸Կऀ? • (v -> [(v, e)]) • (ঢ়ଶ -> [(࣍ͷঢ়ଶ, ભҠίετ)]) ͱ͍͏ঢ়ଶભҠͷࣸ૾ ঢ়ଶ͔ΒભҠީิ΁ͷࣸ૾
   ͱߟ͑Δ͜ͱ͕Ͱ͖Δ
9. ݁߹ͷ࢓ํͱঢ়ଶભҠͷؔ਺ ͋ͱॳظঢ়ଶ
   Λએݴ͢Ε͹ɺ%1
   ͕ղ͚Δ main = do [n, wx] <- getInts items <- replicateM n getTuple let dp = accumArrayDP @UArray f max 0 (0, wx) [(0, 0)] items where f (w, acc) (wi, vi) = [(w, acc), (w + wi, acc + vi)] print $ maximum (elems dp)
10. ͜Ε͸ۮવͳͷ͔ • )BTLFMM
    ͰΞϧΰϦζϜΛந৅Խ͢Δͱɺ݁߹ ೋ߲
    ԋࢉɺࣸ૾ ͋ͱॳظ ঢ়ଶ
    ͕ύϥϝʔλԽ͞ΕͯΠϯλϑΣʔεʹදΕΔ • NBQ
    
    SFEVDF • ͦͯ͠ΠϯλϑΣʔε͕ʮ୅਺తߏ଄ΈʯΛଳͼΔ
11. ͳͥͦΕ͕ɺ୅਺తߏ଄ͱ݁ͼͭ͘ͷ͔ • લड़ͷ௨Γ
    ࠶ؼతσʔλߏ଄͸ࣸ૾ͱ݁߹ʹࣗવʹؐݩͰ͖Δ • ঢ়ଶͷʮ఻ൖʯͱʮू໿ʯ͸୅਺తੑ࣭Λඞཁͱ͢Δ – ʮ఻ൖʯ
    ֤ঢ়ଶΛ৽͍͠ঢ়ଶʹࣸ͢ ˠ
    ࣸ૾ – ʮू໿ʯ
    ෳ਺ͷ݁ՌΛҰͭʹ·ͱΊΔ ˠ
    ݁߹ – ͜Ε͕݁߹తͰͳ͚Ε͹࠶ؼɾޮ཰Խ͕೉͍͠ ˠ
    ୅਺తߏ଄ͷཁ੥ ΞϧΰϦζϜΛந৅Խ͢Δͱࣸ૾ͱ݁߹͕ܭࢉͷຊ࣭తͳߏ੒ཁૉͱͯ͠ݱΕΔ ঢ়ଶۭؒΛू߹ͱΈͳ͢ͱɺ୅਺తߏ଄ʢ'VODUPS
    .POPJE
    4FNJSJOHʣʹରԠ͢Δ )BTLFMM
    ͷܕͱߴ֊ؔ਺͸ɺͦͷߏ଄ΛࣗવʹΠϯλϑΣʔεͱͯ͠࿐ग़ͤ͞Δ ந৅Խ͸ʮܭࢉͷ୅਺ʯΛՄࢹԽ͢ΔաఔͰ΋͋Δ
12. ࣸ૾ NBQ
    Ͱ໰୊Λղ͘
13. https://atcoder.jp/contests/abc081/tasks/abc081_b
14. 8 12 40 4 6 20 2 3 10 ۮ਺͔͠ͳ͍ͷͰૢ࡞͢Δ ·ͩۮ਺͔͠ͳ͍ͷͰૢ࡞͢Δ ح਺͕ग़͖ͯͨͷͰऴΘΓ
15. ໋ྩܕϓϩάϥϛϯάͰ࣮૷ uuu ୹໋σʔλߏ଄Λ܁Γฦ͠ॻ͖׵͑ͯ౴͑ΛಘΔ count = 0 while all(a % 2 == 0 for a in as): for i in range(n): as[i] //= 2 count += 1 print(count)
16. ؔ਺ܕ Ӭଓσʔλϓϩάϥϛϯά
    ͳΒʮࣸ૾ NBQ
    Λ܁Γฦ͠ద༻͢Δʯͱߟ͑Δ let res = takeWhile (all even) $ iterate (map (`div` 2)) as print $ length res
17. ؔ਺ద༻ʹΑͬͯ஋ΛಘΔ 
    ؔ਺ʹΑͬͯ஋Λม׵͢Δɾࣸ͢ ࣜ͸ඞͣ໭Γ஋Λฦ͢ɻҾ਺ͷ஋͔Β໭Γ஋ʹ஋Λม׵ͨ͠ɺࣸͨ͠ɺͱݟΔ͜ͱ΋Ͱ͖Δ 𝑓 ؔ਺ܕϓϩάϥϛϯάͱܕγεςϜͷϝϯλϧϞσϧ https://speakerdeck.com/naoya/guan-shu-xing-puroguramingutoxing-sisutemunomentarumoderu
18. ໋ྩܕ
    ୹໋σʔλ
    uuu
    Ұ࣌తͳதؒঢ়ଶΛ܁Γฦ͠ॻ͖׵͑ͯ౴͑ʹ޲͔͏ ؔ਺ܕ Ӭଓσʔλ
    uuu
    ঢ়ଶΛ࣍ͷঢ়ଶ΁ࣸ͢
19. )BTLFMM
    ͰڝٕϓϩάϥϛϯάΛ΍͍ͬͯ͘ɺͱ͍͏͜ͱ͸ • ෆมͳ஋ɺෆมͳσʔλߏ଄ ӬଓσʔλɺӬଓσʔλߏ଄
    Λલఏʹ΍͍ͬͯ͘ • ෆมͳσʔλͷૢ࡞ମܥ uuu NBQ
    
    
    SFEVDF
    
    GPME
    – ৄ͘͠͸͋ͱͰ
20. ྦྷੵ࿨ uuu GPME
    
    TDBOM
    ʹΑΔʮ৞ΈࠐΈʯ
21. https://atcoder.jp/contests/abc305/tasks/abc305_b
22. ۠ؒ࿨ʹ͸ྦྷੵ࿨Λ࢖͏ͱΑ͍ let ds = [3, 1, 4, 1, 5, 9] :: [Int] s = scanl' (+) 0 ds -- [0, 3, 4, 8, 9, 14, 23]
23. ໋ྩతʹ࣮૷͢Δ p, q = input().split() ds = [3, 1, 4, 1, 5, 9] # 累積和 s = [0] * 7 for i in range(6): s[i + 1] = s[i] + ds[i] pi = ord(p) - ord('A') qi = ord(q) - ord('A') print(abs(s[qi] - s[pi]))
24. ໋ྩܕ uuu Ұ࣌తͳঢ়ଶΛ܁Γฦ͠ॻ͖׵͑ͯɺྦྷੵ࿨ͱ͢Δ # 累積和 s = [0] * 7 for i in range(6): s[i + 1] = s[i] + ds[i]
25. ؔ਺ܕͰ࣮૷͢Δ main :: IO () main = do (p, q) <- auto @(Char, Char) let ds = [3, 1, 4, 1, 5, 9] :: [Int] s = listArray @UArray ('A', 'G') $ scanl' (+) 0 ds ans = s ! q - s ! p print $ abs ans
26. ݁߹
    ͷ࠶ؼతͳؔ਺ద༻ uuu ʮ৞ΈࠐΈʯ foldl (+) 0 [3, 1, 4, 1, 5, 9] ==> ((((((0 + 3) + 1) + 4) + 1) + 5) + 9) scanl (+) 0 [3, 1, 4, 1, 5, 9] [ 0 , (0 + 3) , ((0 + 3) + 1) , (((0 + 3) + 1) + 4) , ((((0 + 3) + 1) + 4) + 1) , (((((0 + 3) + 1) + 4) + 1) + 5) , ((((((0 + 3) + 1) + 4) + 1) + 5) + 9) ]
27. վΊͯ )BTLFMM
    Ͱͷྦྷੵ࿨ uuu TDBOM
    ΛΈͯΈΔ let ds = [3, 1, 4, 1, 5, 9] :: [Int] s = scanl' (+) 0 ds -- [0, 3, 4, 8, 9, 14, 23 scanl' :: (b -> a -> b) -> b -> [a] -> [b] • ࠶ؼతʹ݁߹Λద༻͢Δɺͱ͍͏ྦྷੵܭࢉ ৞ΈࠐΈ
    Λந৅Խͨ͠ͷ͕ TDBOM • TDBOM
    ͷΠϯλϑΣʔεʹ͸݁߹ԋࢉ͕ύϥϝʔλͱͯ͠දΕ͍ͯΔ –
    ͳΒྦྷੵ࿨ – NBY
    ͳΒྦྷੵ NBY – NJO
    ͳΒྦྷੵ NJO – YPS
    ͳΒྦྷੵ YPS
28. ࣸ૾ͱ݁߹ ू໿
    uuu NBQ
    
    SFEVDF
    GPME • ؔ਺ܕϓϩάϥϛϯάͰ͸ʮࣸ૾ͱ݁߹ ू໿ ʯͷϝϯλϧϞσϧͰ໰୊Λղ͘ • ࣸ૾ͱ݁߹ ू໿
     NBQ
    
    SFEVDF
    GPME • ͳͥ NBQ
    
    SFEVDF
    ͔ – )BTLFMM
    ͷෆมσʔλߏ଄͸୅਺తσʔλܕʹΑΔ࠶ؼσʔλߏ଄ – ࠶ؼσʔλߏ଄ͷૢ࡞ʹ͸ NBQ
    
    SFEVDF – -*41
    ͷ௚ײ͔Βʜ
    ͋ͱͰ
29. ΞϧΰϦζϜΛந৅Խ͢Δ uuu ೋ෼୳ࡧΛߴ֊ؔ਺Ͱந৅Խ͢Δ
30. https://atcoder.jp/contests/abc409/tasks/abc409_b
32. ୯ௐੑ͕͋ΔͷͰɺڥքΛఆΊΔ͜ͱ͕Ͱ͖Δ 
    
    
    
    
    
     
    Ҏ্ uuu ճ 
    Ҏ্ uuu
    ճ 
    Ҏ্ uuu ճ 
    Ҏ্ uuu
    ճ 
    Ҏ্ uuu ճ 
    Ҏ্ uuu ճ ͜͜·Ͱ৚݅Λຬͨ͢ɺҎ߱͸ຬͨ͞ͳ͍ Y
    Ҏ্ͷཁૉ͕ Y
    ճҎ্දΕΔ͔
33. ೋ෼୳ࡧͰղ͚·͢ɻͰ΋ɺίϯςετதʹೋ෼୳ࡧΛॻ͘ͱόάΒ͕ͤͪ main :: IO () main = do _ <- getInt as <- getInts let binSearch (ok, ng) | abs (ng - ok) == 1 = ok | otherwise = do let m = (ok + ng) `div` 2 count = length $ filter (>= m) as if count >= m then binSearch (m, ng) else binSearch (ok, m) print $ binSearch (0, 10 ^ 18)
34. ຖճॻ͔ͳ͍͍ͯ͘Α͏ɺந৅Խ͠·͢ ˠ
    ߴ֊ؔ਺ G
    ͕දΕΔ -- | 左が true / 右が false で境界を引く bisect2 :: (Integral a) => (a, a) -> (a -> Bool) -> (a, a) bisect2 (ok, ng) f | abs (ng - ok) == 1 = (ok, ng) | f m = bisect2 (m, ng) f | otherwise = bisect2 (ok, m) f where m = (ok + ng) `div` 2 let (ok, _) = bisect2 (0, 10 ^ 18) (¥x -> countBy (>= x) as >= x) print ok
35. ৚݅ؔ਺ G
    ͸ࣸ૾ͱΈͳͤΔ • ೋ෼୳ࡧ͸ʮڥքΛҾ͘৚݅ʯΛؔ਺ G
    Ͱ౉͢Α͏ந৅ԽͰ͖Δ • (a -> Bool) Λʮ஋ ੔਺
    ͔Β ৚݅Λຬ͔ͨ͢Ͳ͏͔
    ΁ͷࣸ૾ʯͱଊ͑Δ͜ͱ͕Ͱ͖Δ • ΞϧΰϦζϜΛந৅Խͨ͠Βͦ͜ʹࣗવͱࣸ૾ G
    ͕දΕͨ bisect2 :: (Integral a) => (a, a) -> (a -> Bool) -> (a, a)
36. #'4
    ෯༏ઌ୳ࡧ
    Λந৅Խ͢Δ ؔ਺ G
    Λʮ͋Δঢ়ଶ͔Β࣍ͷঢ়ଶ΁ͷঢ়ଶભҠʯͱଊ͑Δ
37. https://atcoder.jp/contests/tessoku-book/tasks/math_and_algorithm_an
38. 1 2 4 3 5      6 
39. άϥϑΛʮྡ઀Ϧετʯʹߏ଄Խͯ͠ #'4
    ෯༏ઌ୳ࡧ
    ͢Δ main = do [n, m] <- getInts uvs <- replicateM m getTuple -- 1 => [(2, 1), (4, 1)] という構造の「隣接リスト」にする let g = accumArray @Array (flip (:)) [] (1, n) $ concatMap (¥(u, v) -> [(u, (v, 1)), (v, (u, 1))]) uvs -- 幅優先探索する dist = bfs g [(1, 0)] for_ [1 .. n] $ ¥s -> print $ dist ! s
40. ࢀߟ
    ઌͷ #'4 ͷ࣮૷ bfs :: (Ix v, IArray a [(v, e)], Num e, Eq e) => a v [(v, e)] -> [(v, e)] -> Array v e bfs g v0s = runSTArray $ do dist <- newArray (bounds g) (-1) for_ v0s $ ¥(v0, d0) -> do writeArray dist v0 d0 aux (Seq.fromList [v0 | (v0, _) <- v0s]) dist return dist where aux Empty _ = return () aux (v :<| queue) dist = do acc <- readArray dist v us <- filterM ( ¥(u, _) -> (fmap (== -1) . readArray dist) u ) (g ! v) queue' <- foldForM queue us $ ¥q (u, w) -> do writeArray dist u $! acc + w return $ q |> u aux queue' dist ༨ஊ
    ࢲ͸͜Ε͙Β͍ʹͳΔͱίϯςετ தʹ͸ॻ͖ͨ͘ͳ͍ͷͰϥΠϒϥϦԽ͠· ͕͢ɺ$
    ΍
    1ZUIPO
    Ͱ΍ͬͯΔਓ͸ຖ ճ
    #'4
    ΛιϥͰهड़ͯͨ͠Γ͠·͢
41. ʮάϥϑͷྡ઀ϦετʯͷͨΊͷ࣮૷ʹͳͬͯ͠·͍ͬͯΔ let dist = bfs g [(1, 0)] • #'4
    ͸άϥϑͷྡ઀ϦετͷͨΊ͚ͩͷ୳ࡧΞϧΰϦζϜͰ͸ͳ͍ • ྡ઀Ϧετͷߏ଄ʹґଘ͍ͯ͠ΔՕॴΛύϥϝʔλԽ͠ɺந৅౓Λ্͛Α͏
42. ந৅౓Λ্͛Δ uuu άϥϑͷભҠΛ֎෦͔Β஫ೖͰ͖ΔΑ͏ʹ͢Δ let dist = bfs (g !) (+) (-1) (bounds g) [(1, 0)] • (g !) uuuʮ௖఺W
    ͔ΒḷΕΔ௖఺͸ ʯͱ͍͏ࣸ૾ G – ʮ௖఺ 
    ͔Β͸ɺ௖఺ ̎ ͱ௖఺ 
    ΁ɺͦΕͧΕॏΈ 
    ͰભҠͰ͖ΔʯΛهड़͢Δؔ਺ – f v = g ! v • ڑ཭ͷ݁߹ԋࢉ (+)
43. ೋ࣍ݩάϦουͷ୳ࡧ໰୊Λղ͍ͯΈΔ uuu ಉ࣮͡૷Ͱղ͚Δ͔ https://atcoder.jp/contests/abc308/tasks/abc308_d
45. #'4
    ͷ࣮૷Λม͑Δ͜ͱͳ͘ɺؔ਺ G
    Λهड़͢Δ͚ͩͰ໰୊͕ղ͚Δ main = do [h, w] <- getInts grid <- getCharGrid ((1, 1), (h, w)) let dist = bfs f (+) (-1) (bounds grid) [((1, 1), 0)] where f v = [ (u, 1) | d <- [(1, 0), (0, 1), (-1, 0), (0, -1)], let u = v + d, inRange (bounds grid) u, case (grid ! v, grid ! u) of ('s', 'n') -> True ('n', 'u') -> True ('u', 'k') -> True ('k', 'e') -> True ('e', 's') -> True _ -> False ] printYn $ dist ! (h, w) /= -1 ʮϚε W
    ˠ
    W
    ͔Β౸ୡͰ͖ΔϚε V
    ͷϦετʯ ͱ͍͏ࣸ૾ άϦουͷ্Լࠨӈʹ৚݅Λຬͨ͢ભҠઌ͕͋ΔͳΒ ͦΕΛྻڍ
46. https://atcoder.jp/contests/abc235/tasks/abc235_d Ұݟ͢ΔͱάϥϑͰ΋άϦου΋ͳ͍໰୊ɻछྨͷૢ࡞Λ܁Γฦͯ͠ /
    ʹͰ͖Δ
47. B
    
    
    /
    
    
    ͷ৔߹ 1 3 9 27 81 72 243 18
48. main = do [a, n] <- getInts let bounds = (1, 10 ^ 6 + 1 :: Int) let dist = bfs f (+) (-1) bounds [(1, 0 :: Int)] where f x | x >= 10 && x `mod` 10 /= 0 = [(x', 1) | x' <- [rotate x, a * x], inRange bounds x'] | otherwise = [(a * x, 1) | inRange bounds (a * x)] rotate y = let ys = toDigits 10 y in fromDigits 10 (last ys : init ys) print $ dist ! n ΍͸Γؔ਺ G
    Λهड़͢Δ͜ͱͰ໰୊͕ղ͚Δ
49. վΊͯ #'4
    ʹ౉͍ͯ͠Δؔ਺ G
    ͷҙຯΛߟ͑ͯΈΔ let dist = bfs f (+) (-1) bounds [(1, 0 :: Int)] • f Λهड़͢Δ͚ͩͰ໰୊͕ղ͚Δ͕ɺf ͸Կऀ? • (v -> [(v, e)]) • (ঢ়ଶ -> [(࣍ͷঢ়ଶ, ભҠίετ)]) ͱ͍͏ঢ়ଶભҠͷࣸ૾ ঢ়ଶ͔ΒભҠީิ΁ͷࣸ૾
    ͱߟ͑Δ͜ͱ͕Ͱ͖Δ
50. ࣸ૾ G
    ʹ͍ͭͯߟ͑Δ͏ͪɺ#'4
    ͷϝϯλϧϞσϧ͕Ξοϓσʔτ͞ΕΔ • #'4
    ͸άϥϑΛ୳ࡧ͢ΔΞϧΰϦζϜ • #'4
    ͸άϦουΛ୳ࡧ͢ΔΞϧΰϦζϜ uuu άϦου΋άϥϑͷҰछ • #'4
    ͸ঢ়ଶΛ୳ࡧ͢ΔΞϧΰϦζϜ uuu ঢ়ଶભҠΛάϥϑભҠͱߟ͍͑ͯͬͨΓ͖ͨΓ
51. ༨ஊ
    )BTLFMM Ҏ֎Ͱ΋͜Μͳ෩ʹ #'4
    Λந৅ԽͰ͖Δ • Θ͔Βͳ͍͚Ͳɺ؆୯Ͱ͸ͳͦ͞͏ • ભҠΛʮঢ়ଶભҠͷؔ਺ʯͱ͢Δ͜ͱ͸Ͱ͖Δ • ঢ়ଶۭؒͷߏ଄ ࣍ݩ
    ΛύϥϝʔλԽ͢Δ͜ͱͱɺύϑΥʔϚϯεΛཱ྆͢Δͷ͕೉͍͔͠ ΋ – )BTLFMM
    ͷ "SSBZ
    ͸࣍ݩΛύϥϝʔλԽͰ͖Δ
52. ಈతܭը๏Λ )BTLFMM
    ͰΠϛϡʔλϒϧʹղ͘ ঢ়ଶۭؒͷ৞ΈࠐΈɺͦͯ͠୅਺తߏ଄͕ݟ͑Δ
54. φοϓβοΫ໰୊ͷΑ͋͘ΔϞσϧ uuu ೋ࣍ݩͷάϦου ೋ࣍ݩ഑ྻ
    Ͱߟ͑Δ
55. for (int j = 0; j <= W; ++j) dp[0][j] = 0; for (int i = 0; i < N; ++i) { for (int j = 0; j <= W; ++j) { if (j >= w[i]) dp[i+1][j] = max(dp[i][j-w[i]] + v[i], dp[i][j]); else dp[i+1][j] = dp[i][j]; } } cout << dp[N][W] << endl; ໋ྩతͳ࣮૷ uuu Մมͳೋ࣍ݩ഑ྻΛ༻ҙͯ͠ॻ͖׵͑Δ
56. %1
    Λ͜ͷϞσϧͰߟ͑ͨͱ͖ͷ՝୊ • ೋ࣍ݩͰ͋Ε͹಄ͰΠϝʔδͰ͖Δ͕ɺࡾ࣍ݩʹͳΔͱ΍΍͍͜͠ɻ࢛࣍ݩҎ্͸Πϝʔδ͕೉͍͠
57. %1
    ͷܭࢉͷಛੑ • ෦෼໰୊ॏෳੑͱ෦෼ߏ଄࠷దੑ • ࡶʹ͍͏ͱ – Ұͭલͷঢ়ଶ͚͔ͩΒ࣍ͷঢ়ଶ͕ܭࢉͰ͖Δ ܭࢉաఔͰ࠷ॳͷํͷঢ়ଶ͸͍Βͳ͍ – ͦΕΛ܁Γฦͤ͹࠷దղ͕ٻ·Δ
58. ͜ͷߦ
    ঢ়ଶ
    Λܭࢉ͢Δͷ ʹ͸ɺҰͭલͷߦ Ұͭલͷ ঢ়ଶ
    ͚ͩΘ͔Ε͹͍͍
59. ʮೋ࣍ݩ഑ྻΛॻ͖׵͑ΔʯͰ͸ͳ͘ʮঢ়ଶۭ͕ؒ࣍ͷঢ়ଶʹભҠ͢Δʯͱߟ͑Δ ঢ়ଶۭؒ ભҠ ભҠ ભҠ
60. Ұͭલͷঢ়ଶΛ࣍ͷঢ়ଶʹભҠͤ͞ΔɻͦΕΛ࠶ؼతʹ uuu GPME
    ͡ΌΜ main = do [n, wx] <- getInts items <- replicateM n getTuple -- 初期状態の状態空間 let dp0 = accumArray @UArray max minBound (0, wx) [(0, 0 :: Int)] -- 状態空間を、再帰的に状態遷移させる let dp' = foldl' f dp0 items where f dp (wi, vi) = accum max dp [(w + wi, acc + vi) | (w, acc) <- assocs dp, inRange (bounds dp) (w + wi)] print $ maximum (elems dp) Մม഑ྻΛߋ৽͢Δͱ͍͏໋ ྩతͳ࣮૷Ͱ͸ͳ͘ɺෆมͳ ஋Λ৞ΈࠐΜͰ͍͘ɺͱ͍͏ )BTLFMM
    Β͍࣮͠૷ʹ
61. ໰୊ʹݻ༗ͷ෦෼ΛύϥϝʔλԽ͠ɺGPME
    ʹΑΔ %1
    ܭࢉΛந৅Խ͢Δ -- 畳み込みDP -- ex) accumArrayDP @UArray f max minBound (0, wx) [(0, 0)] wvs accumArrayDP :: ( IArray a e, Ix v, Eq e, Show e, Show v, Show (a v e), Foldable t ) => ((v, e) -> x -> [(v, e')]) -> -- 状態遷移関数 f v / x をみて v の次の遷移可能性を返す (e -> e' -> e) -> -- 緩和の二項演算 e -> -- 初期値 (0, minBound, maxBound, False など) (v, v) -> -- 状態空間の下界、上界 [(v, e')] -> -- 開始時点の状態 t x -> -- 入力 (時間遷移) a v e -- Array or UArray accumArrayDP f combine initial (l, u) v0s xs = let dp = accumArray combine initial (l, u) v0s in foldl' transition dp xs where transition dp x = accumArray combine initial (l, u) $ concatMap (filter (inRange (bounds dp) . fst) . (`f` x)) (assocs dp)
62. φοϓβοΫ໰୊͸͜͏ղ͚Δ main = do [n, wx] <- getInts items <- replicateM n getTuple let dp = accumArrayDP @UArray f max 0 (0, wx) [(0, 0)] items where f (w, acc) (wi, vi) = [(w, acc), (w + wi, acc + vi)] print $ maximum (elems dp)
63. ݁߹ͷ࢓ํͱঢ়ଶભҠͷؔ਺ ͋ͱॳظঢ়ଶ
    Λએݴ͢Ε͹ɺ%1
    ͕ղ͚Δ main = do [n, wx] <- getInts items <- replicateM n getTuple let dp = accumArrayDP @UArray f max 0 (0, wx) [(0, 0)] items where f (w, acc) (wi, vi) = [(w, acc), (w + wi, acc + vi)] print $ maximum (elems dp)
64. %1
    ΋ɺந৅Խͨ͠Β݁߹ͱࣸ૾͕ύϥϝʔλԽ͞Εͨ • ࿩ͷྲྀΕతʹೋ࣍ݩ഑ྻ ˠ
    ঢ়ଶۭؒͷ৞ΈࠐΈɺͱ͍͏Ϟσϧͷస׵Λઌʹߟ͕͑ͨ • ࣮ࡍʹ͸ɺ%1
    ͷந৅ԽΛࢼΈͨΒ GPME
    ͷ࣮૷ʹͳΓɺޙ෇͚ͰҙຯΛߟ͑ͨΒʮঢ়ଶۭؒ ͷ৞ΈࠐΈʯͱ͍͏Ϟσϧʹؾ͕͍ͭͨ • ʮ%1 ΋ NBQ  SFEVDF GPME.BQ ͡Όͳ͍͔ ʜʯ – ࣸ૾ uuu ঢ়ଶͷભҠ – ݁߹ uuu ෳ਺ܦ࿏͔Βಉ͡ঢ়ଶʹྲྀೖͨ͠ͱ͖ɺ஋ΛҰͭʹू໿ ˞ͨͩ͠ɺ͜ͷϞσϧͰղ͚Δͷ͸φοϓβοΫ%1ɻ֝௓ͼ%1
    ͸͜ͷϞσϧͰ͸ղ͚ͳ͍
65. ΠϯλϑΣʔεΛோΊΔͱ୅਺తߏ଄΋ݟ͑ͯདྷΔ uuu %1
    ͸൒؀తߏ଄Λ࣋ͭ let dp = accumArrayDP @UArray f (+) 0 (0, n) [(0, 0)] items f ((v, e) -> x -> [(v, e')]) ঢ়ଶ (v, e) ʹೖྗ x Λ࡞༻ͤ͞ෳ਺ͷભҠઌ (v, e') Λੜ੒͢Δ (࡞༻ తͳ৐๏) (+) (e -> e' -> e) ಉ͡ঢ়ଶʹෳ਺ભҠ͕ू·Δͱ͖ɺ·ͱΊΔ (Ճ๏) 0 e ॳظ஋ (Ճ๏ͷ୯Ґݩ) • %1
    ͸ɺ͋Δঢ়ଶ্ۭؒʹ͓͚ΔϞϊΠυʢࣸ૾ʣ࡞༻ͱɺ൒܈తͳू໿Λ૊Έ߹Θͤͨܭࢉ • GPME.BQ
    ͸
    .POPJE
    Λ࢖͏͕ɺͦΕΛΑΓҰൠԽͯ͠
    4FNJSJOH
    ʹ֦ுͨ͠΋ͷ͕
    %1
    Ͱ͋ΔͱΈͳͤ Δ
66. ந৅ͷߏ଄ ΠϯλϑΣʔε
    ͕ྑ͘ࣅ͍ͯΔ • #'4
    ΋ %1
    ΋ɺந৅తʹ͸ঢ়ଶۭؒʹ஋Λ഑ΓɾूΊΔૢ࡞ͷ্ʹߏங͞ΕͨϞσϧ • #'4
    ΋൒؀తߏ଄ ·ͨ͸ͦͷ֦ு Λ࣋ͭ
    ·ͩͪΌΜͱߟ͑ΒΕ͍ͯ·ͤΜ let dp = accumArrayDP @UArray f (+) 0 (0, n) [(0, 0)] items let dist = bfs f (+) (-1) (0, n) [(1, 0)]
67. f f f f f f (+), max, min, … NBQ SFEVDF
68. ͳͥΞϧΰϦζϜΛந৅Խ͢ΔͱɺNBQ
    
    SFEVDF
    GPME
    ΍୅਺తߏ଄͕ ؔ਺ܕϓϩάϥϛϯάɺ)BTLFMM
    ͕ͦΕΛଅ͢
69. ͠Ό͘ͱΓ๏ • (+) (-) 0 ··· ݁߹ɺٯݩɺ୯Ґݩ → Մ׵ϞϊΠυ • ʮՄ׵ϞϊΠυ্ͷ෦෼۠ؒͷྦྷੵ஋ʯʹରͯ͠ʮ৚݅ f Λຬͨ͢࠷େ۠ؒΛ୳ࡧ͢Δʯ – f ··· ϞϊΠυͷ৞ΈࠐΈʹରͯ͠൑ఆΛ෇͚ͨʮ৚݅෇͖ࣸ૾ʯ let secs = shakutori f (+) (-) 0 as
70. ͜Ε͸ۮવͳͷ͔ • )BTLFMM
    ͰΞϧΰϦζϜΛந৅Խ͢Δͱɺ݁߹ ೋ߲
    ԋࢉɺࣸ૾ ͋ͱॳظ ঢ়ଶ
    ͕ύϥϝʔλԽ͞ΕͯΠϯλϑΣʔεʹදΕΔ • NBQ
    
    SFEVDF • ͦͯ͠ΠϯλϑΣʔε͕ʮ୅਺తߏ଄ΈʯΛଳͼΔ
71. ༨ஊ
    (PPHMF
    ͷ
    .BQ3FEVDF
    
    ͸
    .BQ
    ͱ
    3FEVDF
    ͷ૊Έ߹ΘͤͰ ଟ͘ͷ໰୊Λղ͘͜ͱ͕Ͱ͖Δ͜ͱʹج͍ͮͨฒྻ෼ࢄܭࢉγεςϜ
72. )BTLFMM
    ͸࠶ؼతσʔλߏ଄Λσʔλߏ଄ͷجຊͱ͍ͯ͠Δ data List a = Nil | Cons a (List a) • )BTLFMM
    ͷσʔλߏ଄ uuu ୅਺తσʔλܕʹΑΔ࠶ؼతσʔλߏ଄ • ࠶ؼతσʔλߏ଄ʹదͨ͠࠷খͷૢ࡞͕ NBQ
    ͱ SFEVDF
    GPME – NBQ
    ͸ a -> b Λ֤ཁૉʹద༻͠ɺߏ଄Λอͬͨ··ม׵ ࠶ؼߏ଄ʹର͢Δؔ਺ద༻ͷ࠷খ୯Ґ – SFEVDF
    GPME
    ͸ͦͷߏ଄Λյ͠ͳ͕ΒҰͭͷ஋ʹ৞ΈࠐΉ ߏ଄ΛͨͨΉ࠶ؼతύλʔϯͷ࠷খ୯Ґ
73. ʮࣸ૾ͱ৞ΈࠐΈʯ͸Ͳ͔͜Βདྷͨͷ͔ • -JTQ
    
    ʙ
    ͕Ϧετʹର͢Δ NBQ
    
    SFEVDF
    Ͱɺଟ͘ͷ໰୊Λهड़Ͱ͖Δ͜ͱΛܦݧ తʹൃݟͨ͠ • ؔ਺ܕݴޠͷൃలʹΑΓɺNBQ
    
    SFEVDF
    GPME
    ͸ϦετʹݶΒͳ͍࠶ؼతσʔλߏ଄ʹద ͨ͠ૢ࡞Ͱ͋ΔͱҰൠԽ͞Εͨ • )BTLFMM
    
    ʙ
    ͸ͦΕΒΛཧ࿦͚ͮͯ࠶ߏ੒͠ɺܕΫϥε֊૚ͱͱ΋ʹऔΓࠐΜͩ • 'VODUPS
    'PMEBCMF
    "QQMJDBUJWF
    .POBE
    5SBWFSTBCMF • NBQ
    
    SFEVDF
    GPME
    ͸ )BTLFMM
    ͷʮ࠶ؼʯͱʮߏ଄ԽʯΛ؏֩͘ɺݴޠઃܭͷத৺ʹ͋Δ
74. https://wiki.haskell.org/wikiupload/8/85/TMR-Issue13.pdf
75. )BTLFMM
    ͷෆมͳσʔλߏ଄͸ NBQ
    
    SFEVDF
    GPME
    Ͱૢ࡞͢Δ • Ϧετɺ4FUɺ.BQɺ"SSBZ ͳͲͷෆมσʔλߏ଄͸͍ͣΕ΋ 'PMEBCMF
    ɻ·ͨ 'VODUPS
    Ͱ ͋ͬͨΓɺͦ͏Ͱͳͯ͘΋ NBQ
    Λ͍࣋ͬͯΔ • ͦΕΒΛجૅʹΞϧΰϦζϜΛ࣮૷͠ɺ۩ମΛύϥϝʔλԽ͍ͯ͘͠ͱࣗવͱ NBQ
    ΍ GPME
    ΁ͷҾ਺͕ύϥϝʔλͱͯ͠දΕΔ ͜Ε͕ΞϧΰϦζϜͷந৅ʹ
    G
    ΍
    
    ͷΑ͏ͳؔ਺͕͍ͭ΋දΕΔཧ༝ ӬଓσʔλϓϩάϥϛϯάΛࢤ޲ͨ͠৔߹ͷඞવ ˞
    ඞͣ͠΋͜ͷߏ଄ʹԊΘͳ͍ΞϧΰϦζϜ΍σʔλߏ଄΋ɺ΋ͪΖΜ͋Γ·͢
76. ͳͥͦΕ͕ɺ୅਺తߏ଄ͱ݁ͼͭ͘ͷ͔ • લड़ͷ௨Γ
    ࠶ؼతσʔλߏ଄͸ࣸ૾ͱ݁߹ʹࣗવʹؐݩͰ͖Δ • ঢ়ଶͷʮ఻ൖʯͱʮू໿ʯ͸୅਺తੑ࣭Λඞཁͱ͢Δ – ʮ఻ൖʯ
    ֤ঢ়ଶΛ৽͍͠ঢ়ଶʹࣸ͢ ˠ
    ࣸ૾ – ʮू໿ʯ
    ෳ਺ͷ݁ՌΛҰͭʹ·ͱΊΔ ˠ
    ݁߹ – ͜Ε͕݁߹తͰͳ͚Ε͹࠶ؼɾޮ཰Խ͕೉͍͠ ˠ
    ୅਺తߏ଄ͷཁ੥ ΞϧΰϦζϜΛந৅Խ͢Δͱࣸ૾ͱ݁߹͕ܭࢉͷຊ࣭తͳߏ੒ཁૉͱͯ͠ݱΕΔ ঢ়ଶۭؒΛू߹ͱΈͳ͢ͱɺ୅਺తߏ଄ʢ'VODUPS
    .POPJE
    4FNJSJOHʣʹରԠ͢Δ )BTLFMM
    ͷܕͱߴ֊ؔ਺͸ɺͦͷߏ଄ΛࣗવʹΠϯλϑΣʔεͱͯ͠࿐ग़ͤ͞Δ ந৅Խ͸ʮܭࢉͷ୅਺ʯΛՄࢹԽ͢ΔաఔͰ΋͋Δ
77. )BTLFMM
    ͷந৅ͷɺڝٕϓϩάϥϛϯάʹ͓͚ΔҖྗ • ΞϧΰϦζϜͷந৅ʹग़͖ͯͨࣸ૾΍݁߹͸ʮάϥϑͷભҠʯʮঢ়ଶભҠͷࣸ૾ʯͳͲҙຯ ͚ͮ͢Δ͜ͱ͕Ͱ͖Δ – ͨͩͷύϥϝʔλͰ͸ͳ͘ɺղऍΛՃ͑Δ͜ͱ͕Ͱ͖Δ – ͦͯͦ͠ΕΛ୅਺తߏ଄ͷ໨ͰΈͯɺ਺ֶతੑ࣭Λҙࣝ͢Δ͜ͱ΋Ͱ͖Δ • ڝٕϓϩάϥϛϯάͷ໰୊͕ɺͦͷҙຯʹैͬͯߟ࡯͢Δ͜ͱͰղ͚Δ – ෦෼໰୊Λղ͚ͩ͘Ͱɺશମ͕ղ͚Δ – ͜ͷࢥߟͷϑϨʔϜϫʔΫ͸ಛʹ %1
    ΍άϥϑ୳ࡧ໰୊ͳͲʹ͓͍ͯڧྗͳ෢ثʹͳΔ
78. ໋ྩܕͰΞϧΰϦζϜΛॻ͘ͱ͖ uuu
    ʮͲ͏ಈ͔͔͢ʯ • ؔ৺͸ʮखଓ͖ʯ΍ʮঢ়ଶͷมԽʯʹ޲͘ – ഑ྻΛߋ৽͠ɺม਺Λมߋ͠ͳ͕ΒʮͲ͏΍ͬͯಈ͔͔͢ʯΛߟ͑Δ • Ұ࣌తͳதؒঢ়ଶ ୹໋ͳม਺
    Λ࢖ͬͯʮ࠷ऴঢ়ଶʹͲ͏΋͍͔ͬͯ͘ʯʹूத͢Δ • ΞϧΰϦζϜ͸Ұ࿈ͷ໋ྩͱͯ͠هड़͞ΕΔϨγϐ 🧠 ࢥߟ͸ʮ࣮ߦͷॱংʯʹԊͬͯਐΉɻಈ࡞ΛͳͧΔ͜ͱͰҙຯΛ೺Ѳ͢Δɻ ϓϩηεࢤ޲ɺྲྀΕʹॏ͖Λஔ͘ࢥߟ
79. for (int j = 0; j <= W; ++j) dp[0][j] = 0; for (int i = 0; i < N; ++i) { for (int j = 0; j <= W; ++j) { if (j >= w[i]) dp[i+1][j] = max(dp[i][j-w[i]] + v[i], dp[i][j]); else dp[i+1][j] = dp[i][j]; } } cout << dp[N][W] << endl;
80. ؔ਺ܕͰΞϧΰϦζϜΛॻ͘ͱ͖ uuuʮԿΛҙຯ͍ͯ͠Δ͔ʯ • ؔ৺͸ʮߏ଄ʯ΍ʮҙຯʯʹ޲͘ – ˠ
    ͜ͷ NBQ
    ͸ԿΛ͍ࣸͯ͠Δ
    ͜ͷ GPME
    ͸ͲΜͳԋࢉΛू໿͍ͯ͠Δ • ܭࢉ͸ෆมͳσʔλߏ଄ʹର͢Δࣸ૾ͱ৞ΈࠐΈͱͯ͠ߏ੒͞ΕΔ • ΞϧΰϦζϜ͸ࣸ૾ͱ݁߹ͷ૊Έ͋Θͤͱͯ͠هड़͞ΕΔࣜ 🧠
    ࢥߟ͸ʮߏ଄ͱҙຯʯʹԊͬͯਐΉɻࣜͷߏ੒ΛோΊͯશମ૾Λଊ͑Δɻߏ଄ࢤ޲ɺؔ܎ʹॏ͖Λஔ͘ࢥߟɻ ܭࢉΛྲྀΕͱͯ͠௥͏ͷͰ͸ͳ͘ɺҙຯͷ͋Δߏ੒
    NBQ
    GPME
    ؔ਺߹੒
    ͱͯ͠ଊ͑Δɻ Ұ࿈ͷૢ࡞ΛʮԿΛ͔ͨ͠ʯͰ͸ͳ͘ɺʮͲͷΑ͏ͳҙຯͷ͋Δࣸ૾΍݁߹Λఆ͍ٛͯ͠Δ͔ʯͱݟΔ
81. let dp = accumArrayDP @UArray f max 0 (0, wx) [(0, 0)] items where f (w, acc) (wi, vi) = [(w, acc), (w + wi, acc + vi)] print $ maximum (elems dp)
82. ந৅Խָ͕͍͠ͷ͸Θ͔͚ͬͨͲɺڝϓϩΛ )BTLFMM
    Ͱ΍ΔϝϦοτ͸ • ͋Γ·͢Α
    Ͱ΋ͦΜͳ͜ͱͲ͏Ͱ΋͍͍͡Όͳ͍Ͱ͔͢ɻϩϚϯͰ͢ – ϝϦοτϝϦοτ͏ΔͤʔΜͩΑ – )BTLFMM
    Ͱղ͚ͳ͍໰୊ʹग़ձͬͨ͜ͱ͸ͳ͍ – ʮ)BTLFMM
    ʹΑΔந৅͕ิॿྠʹͳΔʯ͜Ε͚ͩͰ΋े෼ͳϝϦοτ • ΑΓ۩ମతͳϝϦοτ͸ྫ͑͹uuu – )BTLFMM
    ͷ࠶ؼσʔλܕ 
    Ӭଓσʔλߏ଄ ˠ Ӭଓσʔλߏ଄Λલఏʹͨ͠໰୊ͷ෼ղ – ʮӬଓσʔλϓϩάϥϛϯάͱڝٕϓϩάϥϛϯά ʙ )BTLFMM
    Ͱ͕Μ͹Δڝϓϩʯ • IUUQT[FOOEFWOBPZB@JUPBSUJDMFTBCEDBBBC
83. )BTLFMM
    ͛͢ʔͳͱࢥ͏͜ͱ • ࠓ೔࿩ͯ͠ΔΑ͏ͳ͜ͱΛ෼͔ͬͯͯ )BTLFMM
    Λ࢖ͬͯདྷͨΘ͚Ͱ͸ͳ͍ • )BTLFMM
    Λ࢖͍ͬͯͨΒࣗવͱࠓ೔࿩ͨ͠Α͏ͳந৅Խͷ࣮૷ʹͳͬͨ • ͦͷந৅ԽͷҙຯΛߟ͍͑ͯΔ͏ͪʹࠓ೔࿩ͨ͠Α͏ͳߟ࡯ʹࢸͬͨ • )BTLFMM
    Λ΍ͬͯΔͱ͜͏͍͏ܦݧΛԿ౓΋͢Δ – ·ΔͰϓϩάϥϛϯάݴޠͱ͍͏ಓ۩͕ɺΑΓྑ͍ந৅ͱීว΁ͷಓےΛࢦࣔͯ͘͠͠Ε͍ͯΔΑ͏ͳײ͡
84. ࿩ͨ͜͠ͱ • )BTLFMM ͰڝٕϓϩάϥϛϯάʹࢀՃ͍ͯ͠ΔɻΞϧΰϦζϜΛந৅Խ͢Δͱɺͦͷ࣮૷͕ ࣅͨΑ͏ͳΠϯλϑΣʔεʹͳΔ͜ͱΛܦݧͨ͠ – ߴ֊ؔ਺ͱͯࣸ͠૾ G
    ͱ݁߹ͷೋ߲ԋࢉ͕ύϥϝʔλͱͯ͠Α͘දΕΔ • ͦΕ͸ۮવͳͷ͔ɺ͍΍ɺۮવͰ͸ͳ͍ – )BTLFMM
    ͷࠜఈʹ͋Δ࠶ؼσʔλߏ଄ɺͦΕʹ࠷దͳૢ࡞Ͱ͋Δࣸ૾ͱ৞ΈࠐΈ NBQ
    
    SFEVDF • ࣸ૾ͱ৞ΈࠐΈʹΑΔؔ਺ͷΠϯλϑΣʔε͔ΒΞϧΰϦζϜͷ୅਺తߏ଄͕ݟ͑Δ • ؔ਺ܕϓϩάϥϛϯάɺ)BTLFMM
    ͸ΞϧΰϦζϜΛΑΓந৅౓ߴ͘ଊ͑ΔࢥߟΛิॿͯ͘͠ ΕΔ
85. ͓·͚
86. NJTD • ෆมͳσʔλߏ଄ͱ NBQ
    
    SFEVDF
    Ͱશ෦͍͚Δͷ – ͍͍͑ɻύϑΥʔϚϯεͷ؍఺͔Β .VUBCMF
    "SSBZ
    ͕ඞཁͳ৔໘͸͋Γ·͢ • 6OJPO'JOEɺηάϝϯτ໦ɺ஗ԆධՁηάϝϯτ໦ͳͲͷ࣮૷ – .VUBCMF
    "SSBZ
    ͷૢ࡞΋Ϟφυͷݟ஍͔ΒݟΕ͹ NBQ
    
    SFEVDF
    తͳ΋ͷͱͯ͠ଊ͑Δ͜ͱ͸Ͱ ͖Δ͕ɺͦΕΛѻ͏ਓؒͷϝϯλϧϞσϧͱͯ͠͸໋ྩܕతͳૢ࡞ – .VUBCMF
    "SSBZ
    ͸ඇ࠶ؼతͳݻఆαΠζͷઢܗߏ଄Ͱ͋Γɺ୅਺తσʔλܕͰએݴ͞ΕΔ࠶ؼత σʔλߏ଄ͱ͸ҟͳΔ΋ͷ • ೖग़ྗ΍ཚ਺ಉ༷ͷɺ֎ք 3FBM8PSME
    ͷӨڹԼʹ͋Δ෭࡞༻తͳଘࡏ 
    ֎෦ࢿݯ ϝϞϦ
    ͱͷڮ౉͠૷ஔ • .POPJE
    ͱ͔ 4FNJHSPVQ
    ͱ͔ͷܕ࢖࣮ͬͯ૷͠ͳ͍ͷ – ࢲ͸࢖ͬͯ·ͤΜ͕ɺ࢖ͬͯ៉ྷͳந৅Λ࣮૷͍ͯ͠Δ "U$PEFS
    ͷઌഐํ΋͍·͢ – ࢲ͸׳Εͱهड़ͷָ͞Λ༏ઌ͍ͯ͠·͢
87. ܕγεςϜ͸ϓϩάϥϛϯάݴޠͷૢ࡞ମܥ΍දݱྗͦͷ΋ͷΛܗ࡞Δϝλߏ଄