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競プロのすすめ

 競プロのすすめ

社内勉強会で競技プログラミングを広めるために作成した資料を社外用に加工したもの

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uya116

June 17, 2022
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  1. ࣮ࡍʹ΍ͬͯΈΑ͏ʢͦͷ̍ʣ Q1. ͋Δ੔਺ N ͕༩͑ΒΕΔͷͰ N ͷ໿਺Λ͢΂ͯग़ྗ͍ͯͩ͘͠͞ɻ 
 ɹɹͨͩ͠ N

    ͸ 1 Ҏ্ 10^12 ҎԼ ྫʣN = 100 ͷͱ͖ 
 1, 2, 4, 5, 10, 20, 25, 50, 100 5
  2. ࣮ࡍʹ΍ͬͯΈΑ͏ʢͦͷ̍ʣ Q1. N ͷ໿਺Λ͢΂ͯग़ྗ͍ͯͩ͘͠͞ɻͨͩ͠ N ͸ 1 Ҏ্ 10^12 ҎԼ

    ◦ N ͕Ͳͷ਺ͰׂΔ͜ͱ͕Ͱ͖Δ͔ 1 ͔Β N ·Ͱͷ਺Ͱࢼ͢ 6 for i in 1ʙN if ( N % i == 0 ) print( i )ɹ← i ͰׂΓ੾ΕͨΒ i ͸ N ͷ໿਺
  3. ࣮ࡍʹ΍ͬͯΈΑ͏ʢͦͷ̍ʣ Q1. N ͷ໿਺Λ͢΂ͯग़ྗ͍ͯͩ͘͠͞ɻͨͩ͠ N ͸ 1 Ҏ্ 10^12 ҎԼ

    ◦ N ͕Ͳͷ਺ͰׂΔ͜ͱ͕Ͱ͖Δ͔ 1 ͔Β N ·Ͱͷ਺Ͱࢼ͢ ਖ਼͍͠౴͑͸ग़ྗ͞ΕΔ͕ɺ 
 ڝϓϩͰ͸ϓϩάϥϜͷ࣮ߦ࣌ؒʹ੍ݶ͕͋Δʢ2ඵҎ಺ͳͲʣͨΊ͜ΕͰ͸NG • ίϯϐϡʔλ͸ 1 ඵʹ 10^8 ճܭࢉͰ͖Δ • ࠓճͷ໰୊Ͱ͸ N ͕࠷େ 10^12 ͷ৔߹ 10000ඵʢ3࣌ؒऑʣ͔͔ͬͯ͠·͏ • Ͱ͸Ͳ͏͢Δ͔ʁ΋ͬͱޮ཰ྑ͘ܭࢉͰ͖ͳ͍͔ߟ͑ͯΈΔ 7 for i in 1ʙN if ( N % i == 0 ) print( i )ɹ← i ͰׂΓ੾ΕͨΒ i ͸ N ͷ໿਺
  4. ࣮ࡍʹ΍ͬͯΈΑ͏ʢͦͷ̍ʣ Q1. N ͷ໿਺Λ͢΂ͯग़ྗ͍ͯͩ͘͠͞ɻͨͩ͠ N ͸ 1 Ҏ্ 10^12 ҎԼ

    A. N ͕Ͳͷ਺ͰׂΔ͜ͱ͕Ͱ͖Δ͔ 1 ͔Β √N ·Ͱͷ਺Ͱࢼ͢ for i in 1ʙ√Nɹ← N / i ΋Ұॹʹग़ྗ͢Δ͜ͱͰ √N ·ͰͰ͢΂ͯͷ໿਺͕ἧ͏ if ( N % i == 0 ) print( i )ɹ← i ͰׂΓ੾ΕͨΒ i ͸ N ͷ໿਺ if ( N / i != i ) print( N / i )ɹ← i ͰׂΓ੾ΕͨΒ N / i ΋ N ͷ໿਺ • N ͕࠷େ 10^12 ͷ৔߹Ͱ΋ϧʔϓճ਺͸ 10^6 • ίϯϐϡʔλ͕ 1 ඵʹ 10^8 ճܭࢉ͢Δͱͯ͠ 1ඵҎ಺ʹܭࢉ͕ऴΘΔ ྫ͑͹ɺ100ͷ໿਺ΛٻΊΔͱ͖ 100͕5ͰׂΓ੾ΕΔͳΒ100͸20(=100/5)Ͱ΋ׂΓ੾ΕΔ 8
  5. ࣮ࡍʹ΍ͬͯΈΑ͏ʢͦͷ̎ʣ Q2. ৽γεςϜʹ N ਓͷϢʔβΛొ࿥͠·͢ɻ 
 ɹɹʢೖྗ͸ N ݸͷ ID

    ͱر๬Ϣʔβ໊ͷ૊ʣ 
 ಉ͡Ϣʔβ໊͸ొ࿥Ͱ͖ͣ ID ͷখ͍͞Ϣʔβ͕༏ઌ͞Ε·͢ɻ 
 ɹɹر๬ͷϢʔβ໊Ͱొ࿥Ͱ͖ͳ͍Ϣʔβͷ ID Λग़ྗ͍ͯͩ͘͠͞ɻ 
 ɹɹͨͩ͠ N ͸ 1 Ҏ্ 10^6 ҎԼ ྫʣӈਤ ͷͱ͖ 
 ɹɹID ͕ 3, 4, 6 ͷϢʔβ͸ر๬ͷ ID ͕ొ࿥Ͱ͖ͳ͍ 9 ID ر๬Ϣʔβ໊ 1 aaa 2 bbb 3 aaa 4 aaa 5 ccc 6 ccc
  6. ࣮ࡍʹ΍ͬͯΈΑ͏ʢͦͷ̎ʣ Q2. ر๬ͷϢʔβ໊Ͱొ࿥Ͱ͖ͳ͍Ϣʔβͷ ID Λग़ྗ͍ͯͩ͘͠͞ɻ 
 N ͸ 1 Ҏ্

    10^6 ҎԼ ◦ ֤Ϣʔβʹ͍ͭͯͦΕΑΓ ID ͕খ͍͞ϢʔβΛ͢΂ͯ֬ೝ for i in 1ʙNɹ← ࠓͷର৅Ϣʔβ for j in 1ʙ(i - 1)ɹ← ର৅ϢʔβΑΓID͕খ͍͞Ϣʔβ if ( username[ i ] == username[ j ] ) flag = 1ɹ← Ϣʔβ໊͕ඃ͍ͬͯͨΒνΣοΫ if (flag == 1) print( i ) 10 ID ر๬Ϣʔβ໊ 1 aaa 2 bbb 3 aaa 4 aaa 5 ccc 6 ccc
  7. ࣮ࡍʹ΍ͬͯΈΑ͏ʢͦͷ̎ʣ Q2. ر๬ͷϢʔβ໊Ͱొ࿥Ͱ͖ͳ͍Ϣʔβͷ ID Λग़ྗ͍ͯͩ͘͠͞ɻ 
 N ͸ 1 Ҏ্

    10^6 ҎԼ ◦ ֤Ϣʔβʹ͍ͭͯͦΕΑΓ ID ͕খ͍͞ϢʔβΛ͢΂ͯ֬ೝ for i in 1ʙNɹ← ࠓͷର৅Ϣʔβ for j in 1ʙ(i - 1)ɹ← ର৅ϢʔβΑΓID͕খ͍͞Ϣʔβ if ( username[ i ] == username[ j ] ) flag = 1ɹ← Ϣʔβ໊͕ඃ͍ͬͯͨΒνΣοΫ if (flag == 1) print( i ) 11 ID ر๬Ϣʔβ໊ 1 aaa 2 bbb 3 aaa 4 aaa 5 ccc 6 ccc ͜Ε΋ਖ਼͍͠౴͑͸ग़ྗ͞ΕΔ͕ɾɾɾ • N ͷೋॏϧʔϓ͕͋ΔͨΊ N ͕࠷େ 10^6 ͷ৔߹ɺܭࢉྔ͸ 10^12 • 1 ඵʹ 10^8 ճܭࢉͰ͖Δͱͯ͠ 10000ඵʢ3࣌ؒऑʣ͔͔ͬͯ͠·͏ • ଞʹԿ͔ྑ͍ํ๏͸ͳ͍͔ߟ͑ͯΈΔ
  8. ࣮ࡍʹ΍ͬͯΈΑ͏ʢͦͷ̎ʣ Q2. ر๬ͷϢʔβ໊Ͱొ࿥Ͱ͖ͳ͍Ϣʔβͷ ID Λग़ྗ͍ͯͩ͘͠͞ɻ 
 N ͸ 1 Ҏ্

    10^6 ҎԼͷ੔਺ A. ࿈૝഑ྻʢC++ͳΒmap, PythonͳΒdictʣΛ࢖͏ for i in 1ʙNɹ← ࠓͷର৅Ϣʔβ if (used[ username[ i ] ]) print( i )ɹ← ࿈૝഑ྻͷ஋͕ true ͳΒ͢Ͱʹ࢖ΘΕ͍ͯΔϢʔβ໊ used[ username[ i ] ] == trueɹ← ͢Ͱʹ࢖ͬͨϢʔβ໊Λ࿈૝഑ྻʹϢʔβ໊ΛΩʔͱͯ͠ه࿥ 12 ID ر๬Ϣʔβ໊ 1 aaa 2 bbb 3 aaa 4 aaa 5 ccc 6 ccc • ࿈૝഑ྻͷ֤஋ʹΞΫηε͢Δࡍͷܭࢉྔ͸ logN • τʔλϧͷܭࢉྔ͸ NlogNʹͳΓɺ࠷େ 10^6 ͷ৔߹ɺܭࢉྔ͸໿ 10^7 • ίϯϐϡʔλ͕ 1 ඵʹ 10^8 ճܭࢉ͢Δͱͯ͠ 1ඵҎ಺ʹܭࢉ͕ऴΘΔ
  9. Q3. ௕͞ L cmͷ๮ͷ্Λ N ඖͷΞϦ͕ 1cm/ඵͰา͍͍ͯΔɻ 
 ΞϦ͸ޓ͍ʹͿ͔ͭΔͱ޲͖Λม͑ͯ൓ରํ޲ʹา͖ͩ͠ɺ 


    ๮ͷ୺ʹ౸ୡ͢Δͱ๮͔ΒམͪΔ 
 ࠷ޙͷΞϦ͕๮͔ΒམͪΔ·Ͱʹ͔͔Δ࣌ؒ͸Կඵ͔ʁ 13 p1 p2 p3 p4 0 L ࣮ࡍʹ΍ͬͯΈΑ͏ʢͦͷ̏ʣ
  10. ࣮ࡍʹ΍ͬͯΈΑ͏ʢͦͷ̏ʣ Q3. ࠷ޙͷΞϦ͕๮͔ΒམͪΔ·Ͱʹ͔͔Δ࣌ؒ͸Կඵ͔ʁ ◦ ੺͸੨ͱҐஔ X1 ͰͿ͔ͭͬͯ୺·ͰߦͬͯམͪΔ 
 ੨͸ԫͱҐஔ X2

    ͰͿ͔ͭͬͯ੺ͱҐஔ X1 ͰͿ͔ͭͬͯɾɾ 
 ྘ʹҐஔ X3 ͰͿ͔ͭͬͯ໭͖ͬͯͨԫͱҐஔ X4 ͰͿ͔ͭͬͯɾɾɾ 
 ԫ͸੨ͱҐஔ X2 ͰͿ͔ͭͬͯ྘ͱҐஔ X3 ͰͿ͔ͭͬͯɾɾ 
 ੺ʹҐஔ X1 ͰͿ͔ͭͬͯ໭͖ͬͯͨ੨ͱҐஔ X4 ͰͿ͔ͭͬͯɾɾɾ 14
  11. ࣮ࡍʹ΍ͬͯΈΑ͏ʢͦͷ̏ʣ Q3. ࠷ޙͷΞϦ͕๮͔ΒམͪΔ·Ͱʹ͔͔Δ࣌ؒ͸Կඵ͔ʁ ◦ ੺͸੨ͱҐஔ X1 ͰͿ͔ͭͬͯ୺·ͰߦͬͯམͪΔ 
 ੨͸ԫͱҐஔ X2

    ͰͿ͔ͭͬͯ੺ͱҐஔ X1 ͰͿ͔ͭͬͯɾɾ 
 ྘ʹҐஔ X3 ͰͿ͔ͭͬͯ໭͖ͬͯͨԫͱҐஔ X4 ͰͿ͔ͭͬͯɾɾɾ 
 ԫ͸੨ͱҐஔ X2 ͰͿ͔ͭͬͯ྘ͱҐஔ X3 ͰͿ͔ͭͬͯɾɾ 
 ੺ʹҐஔ X1 ͰͿ͔ͭͬͯ໭͖ͬͯͨ੨ͱҐஔ X4 ͰͿ͔ͭͬͯɾɾɾ • ΞϦͷಈ͖Λͦͷ··γϛϡϨʔτ͍ͯ͘͠ͱେมɾɾɾ • ΋ͬͱγϯϓϧʹͰ͖ͳ͍͔ߟ͑ͯΈΔ 15
  12. ࣮ࡍʹ΍ͬͯΈΑ͏ʢͦͷ̏ʣ Q3. ࠷ޙͷΞϦ͕๮͔ΒམͪΔ·Ͱʹ͔͔Δ࣌ؒ͸Կඵ͔ʁ A. Ϳ͔ͭͬͯ޲͖Λม͑Δͷͱ͢Εҧ͏ͷ͸݁Ռͱͯ͠ಉ͡ 17 ans = 0 for

    i in 1ʙNɹ← ֤ΞϦ if (ӈ޲͖) t = L - p[i]ɹ if (ࠨ޲͖) t = p[i] ans = max(ans, t)ɹ← ࠷େΛߋ৽ print(ans) 0 p1 p2 p3 p4 L ֤ΞϦΛಠཱͯ͠ߟ͑Ε͹Α͍
  13. 1. ·ͣ͸աڈ໰ΛԿ໰͔΍ͬͯΈΔ ◦ AtCoder ʹొ࿥ͨ͠Β࣍ʹ΍Δ͜ͱ ʙ ͜Ε͚ͩղ͚͹े෼ಆ͑Δʂաڈ໰ਫ਼બ 10 ໰ ʙ

    https://qiita.com/drken/items/fd4e5e3630d0f5859067#%E7%AC%AC-6-%E5%95%8F--abc- 088-b---card-game-for-two-200-%E7%82%B9 ◦ AtCoder ProblemsʢAtCoderͷΞΧ΢ϯτͱ࿈ܞͯ͠ղ͍ͨ໰୊Λ؅ཧͰ͖Δʣ https://kenkoooo.com/atcoder/#/table/ 2. ׳Ε͖ͯͨΒϦΞϧλΠϜͰίϯςετʹग़ͯΈΑ͏ 3. ࠷ۙ͸ڝϓϩʹؔ࿈ͨ͠ຊ΋ͨ͘͞Μग़͍ͯΔͷͰಡΜͰΈΔͷ΋͓͢͢Ί ڝϓϩΛ͸͡ΊͨΒ 24