Upgrade to Pro
— share decks privately, control downloads, hide ads and more …
Speaker Deck
Features
Speaker Deck
PRO
Sign in
Sign up for free
Search
Search
一般グラフの最大マッチング
Search
yosupo
March 26, 2017
3
2.1k
一般グラフの最大マッチング
yosupo
March 26, 2017
Tweet
Share
More Decks by yosupo
See All by yosupo
Grundy
yosupo
1
3.1k
Featured
See All Featured
Principles of Awesome APIs and How to Build Them.
keavy
126
17k
10 Git Anti Patterns You Should be Aware of
lemiorhan
PRO
656
60k
How to Think Like a Performance Engineer
csswizardry
25
1.8k
Typedesign – Prime Four
hannesfritz
42
2.7k
4 Signs Your Business is Dying
shpigford
184
22k
Keith and Marios Guide to Fast Websites
keithpitt
411
22k
Understanding Cognitive Biases in Performance Measurement
bluesmoon
29
1.8k
The Web Performance Landscape in 2024 [PerfNow 2024]
tammyeverts
8
720
Six Lessons from altMBA
skipperchong
28
3.9k
実際に使うSQLの書き方 徹底解説 / pgcon21j-tutorial
soudai
PRO
181
54k
Designing Experiences People Love
moore
142
24k
Easily Structure & Communicate Ideas using Wireframe
afnizarnur
194
16k
Transcript
Ұൠάϥϑͷ ࠷େϚονϯά ాɹߊฏ
Ұൠ࠷େϚονϯάͱͳΜͧ w άϥϑ͕༩͑ΒΕΔͷͰɺล͕࠷େͷϚονϯά ΛٻΊ͍ͯͩ͘͞ w ϚονϯάͱɺάϥϑͷลΛɺͲͷลಉ࢜ Λڞ༗͠ͳ͍Α͏ʹ͍͔ͭ͘બΜͩͷͰ͢ w ͳ͓ɺ͜ͷߨٛͰجຊతʹάϥϑ࿈͔݁ͭ୯७ ͳͷͱ͠·͢
Ϛονϯάͷྫ
ϚονϯάͰͳ͍ྫ
lҰൠz࠷େϚονϯά w ͳΜͰzҰൠzͱ͍͍ͭͯΔͷʁ w ࣮ɺ༩͑ΒΕΔάϥϑΛೋ෦άϥϑʹݶఆ͢Δͱ ͬͱָͳʹͳΓ·͢ ڈͷߨٛͰͬͨʁ w ͜Ε͕ೋ෦࠷େϚονϯάͱݺΕ͍ͯͯɺ༩͑Β
ΕΔάϥϑ͕ҰൠάϥϑʹͳΔͱҰൠ࠷େϚονϯ άͰ͢
ܭࢉྔ w 0 7? ۪ͳ࣮ ΘΓ͔͠؆୯ w 0 7?
಄ྑ࣮͘ &ENPOETͷՖղΞϧΰϦ ζϜ ͜͜·ͰΓ·͢ w 0 㲋7 & 46(0* ࠓճΓ·ͤΜ
ࢀߟจݙ w ߹ͤ࠷దԽୈೋ൛ #ίϧς+ϑΟʔήϯஶ ઙઙହ ਔখஉฏా༁ ؙળग़൛ฏ
࣍ ᶃ .૿Ճύε ᶄ ด࿏Λ௵͢ ᶅ 0 7? ᶆ
0 7? લ ᶇ 0 7? ޙ
ᶃ.૿Ճύε
ᶃͷॏཁϙΠϯτ άϥϑͱϚονϯάʹ͍ͭͯ .૿Ճύε͕͋Δ 㱻࠷େϚονϯάͰͳ͍
.૿Ճύε w άϥϑͱϚονϯά͕༩͑ΒΕΔ w ҎԼͷ݅Λຬͨ͢ͷ͕.૿Ճύε w ͕͞ح w ྆ͷ͕ϚονϯάʹΘΕ͍ͯͳ͍ w
ύεͷล͕Ϛονϯάʹɺ ؚ·Εͳ͍ ؚΉ ؚ·Εͳ͍ ؚΉ ʜ ؚ·Εͳ͍
.૿Ճύεͷྫ
ॏཁϙΠϯτ .૿Ճύε͕͋Δ 㱻࠷େϚονϯάͰͳ͍ ͜ΕΛࣔ͢
ॏཁϙΠϯτ w .૿Ճύε͕͋Δ 㱺࠷େϚονϯάͰͳ͍ w ࠷େϚονϯάͰͳ͍ 㱺.૿Ճύε͕͋Δ
ॏཁϙΠϯτ w .૿Ճύε͕͋Δ 㱺࠷େϚονϯάͰͳ͍ w ࠷େϚονϯάͰͳ͍ 㱺.૿Ճύε͕͋Δ
.૿Ճύε͕͋Δ㱺࠷େϚονϯάͰͳ͍ w ͬͪ͜؆୯ w .૿Ճύε ؚ·Εͳ͍ ؚΉ ؚ·Εͳ͍ ؚΉ ʜ
ؚ·Εͳ͍ ͳͷͰɺ͜ΕΛ ؚΉ ؚ·Εͳ͍ ؚΉ ؚ·Εͳ͍ ʜ ؚΉ ʹ͢Δ w ͜ΕͰϚονϯά͕૿ͤͨͷͰ0,
ྫ
ॏཁϙΠϯτ w .૿Ճύε͕͋Δ 㱺࠷େϚονϯάͰͳ͍ w ࠷େϚονϯάͰͳ͍ 㱺.૿Ճύε͕͋Δ
࠷େϚονϯάͰͳ͍㱺.૿Ճύε͕͋Δ w ࣮ͬͪ͜؆୯ w άϥϑͱ࠷େͰͳ͍Ϛονϯά.Λߟ͑ɺ. ʹ૿Ճύε͕ଘࡏ͢Δ͜ͱΛࣔ͢ɻ͜͜Ͱɺͦͷά ϥϑͷ࠷େϚονϯάΛ ͳΜͰ͍͍ͷͰબͼ . ͱ͢Δɻ
w &.YPS.Λߟ͑Δ &ɺ.͔.ͷͲͬͪ ͔ʹؚ͚ͩ·ΕΔลͷू߹
ྫ . .
ྫ . . .?.
w &ʹͲΜͳੑ࣭͕͋Δ͔ʁ w ͯ͢ͷͷ࣍d 㲎. .ͱʹ͔࣍ w ͭ·Γύε͔αΠΫϧ͔͠ͳ͍ w
࣍ͷ͔Βݩ.ͱݩ.ͷล͕ຊͣͭ w ߋʹɺݩ.ͷลݩ.ͷลΑΓଟ͍ w ͭ·Γɺඞͣ. . . ʜ .ͱ͍͏ύε͕ଘࡏ͢Δ ˠ͜Εɺ.ͷ.૿Ճύε
ॏཁϙΠϯτ ࠶ܝ .૿Ճύε͕͋Δ 㱻࠷େϚονϯάͰͳ͍
ᶄด࿏Λ௵͢
ͦͦ w ᶃͰɺάϥϑͷ.૿ՃύεΛൃݟͰ͖ΕϚον ϯά͕૿ͤͯϋοϐʔͱ͍͏͜ͱ͕Θ͔ͬͨ w దʹൃݟ͠Α͏ͱ͢ΔͱͲ͏ͳΔͩΖ͏ʁ
؆୯ͳ w άϥϑͱT U͕༩͑ΒΕ·͢ w T͔ΒUͷύεΛൃݟ͍ͯͩ͘͠͞
ղ๏ w EGT όοΫτϥοΫ w ୳ࡧͨ͠Λ͏୳ࡧ͠ͳ͍Α͏ʹͨ͠ Β 0 7
w άϥϑͱϚονϯά͕༩͑ΒΕ·͢ w .૿ՃύεΛݟ͚͍ͭͯͩ͘͞
ղ๏ w EGT όοΫτϥοΫ w ελʔτɺΰʔϧϚονϯάʹͬͯͳ͍ w ୳ࡧͨ͠ Ϛονϯάͷล͔
Λ͏୳ࡧ ͠ͳ͍Α͏ʹͨ͠Β 0 7 w Λ લͬͨͷϚονϯά ͱ લ ͬͨͷϚονϯάͰͳ͍ ʹഒՃ͢Δͱߟ͑ ΒΕΔ
ྫ
ྫ ͳΜͩ͜Εʜͨ·͛ͨͳ͋
ղ๏JTӕ
Կ͕͍͚ͳ͔ͬͨͷ͔ w ղ๏ͰɺΛछྨʹഒՃͯ͠EGT͍ͯ͠Δ w ͜ͷछྨͷΛ྆ํ͍ͬͯΔύεͱ͍͏ͷΛ ݟ͚ͭͯ͠·͏ɻ w ͜ΕΛഒՃͨ͠ޙͳΒύεʹͳ͍ͬͯΔ͕ɺ ݩͷάϥϑʹ͢ͱด࿏͕ੜ·Εͯ͠·͏
w ͜ͷEGTͩͱɺ.૿Ճύε͚ͩΛਖ਼֬ʹݟ͚ͭΒΕ ΔΘ͚Ͱແ͍ w ͰɺଟগͷใಘΒΕΔ w ͠ɺݟ͚ͭͨͷ͕ύεͰແ͍ ด࿏͕͋ͬ ͨ ͱͨ͠ΒҎԼͷܗ͕ಘΒΕΔ
ۮຊ ด࿏ͷ͞ح
w ด࿏ͷ͞حˠΛഒՃͨ݁͠Ռύεʹͳ Δ͔Β w ࠷ॳͷχϣϩͷ͕͞ۮˠด࿏ͷҰ൪࠷ޙͷล ϚονϯάʹΘΕ͍ͯͳ͍ล ۮຊ ด࿏ͷ͞ح
͜ΕΛͲ͏͢Δʁ
None
ʁʁʁ w ࣮͜͏͍͏ด࿏௵ͯ͠ɺz࠷େϚονϯά͔ Ͳ͏͔zมΘΒͳ͍ w ด࿏Λݟ͚ͭͨΒɺ௵͢ˠϚονϯάΛ૿͢ˠ ͢ɺͱݴ͏͜ͱΛߦ͑Α͍ w ௵ͨ݁͠ՌͷάϥϑͰϚονϯά͕૿ͤͨΒඞͣ ݩͷάϥϑͰϚονϯά͕૿ͤΔ
w ˢ͜͏͍͏ܗͷด࿏Λ௵ͯ͠ɺz࠷େϚονϯά ͔Ͳ͏͔zมΘΒͳ͍ w ͜ΕΛࣔ͢ w ۮຊɺด࿏ͷ͞حɹΊͪΌͪ͘Όॏཁ ۮຊ ด࿏ͷ͞ح
લ४උ ͜ΕΛ
લ४උ ͜͏
݁Ռ ح ্ਤͷΑ͏ʹɺ ࠷ॳͷχϣϩͷ͕͞ͷ߹͚ͩߟ͑Εྑ͍
௵͢લ͕࠷େϚονϯά 㱻௵͢ޙ͕࠷େϚονϯά ͜ΕΛࣔ͢
௵͢લ͕࠷େϚονϯάͰͳ͍ 㱻௵͢ޙ͕࠷େϚονϯάͰͳ͍
௵͢લ͕࠷େϚονϯάͰͳ͍ 㱺௵͢ޙ͕࠷େϚονϯάͰͳ͍ ௵͢ޙ͕࠷େϚονϯάͰͳ͍ 㱺௵͢લ͕࠷େϚονϯάͰͳ͍
௵͢લ͕࠷େϚονϯάͰͳ͍ 㱺௵͢ޙ͕࠷େϚονϯάͰͳ͍ ௵͢ޙ͕࠷େϚονϯάͰͳ͍ 㱺௵͢લ͕࠷େϚονϯάͰͳ͍
ᶃΛ͔ͭ͏ ௵͢લʹ.૿Ճύε͕͋Δ 㱺௵͢ޙʹ.૿Ճύε͕͋Δ
w ௵͢લͷάϥϑʹ.૿Ճύε͕͋ΔͱԾఆ͢Δ w ͜Ε͕௵ͨͪ͢Λͬͯͳ͔ͬͨΒવ௵ͨ͠ޙʹ ͋Δ w ௵ͨ͠ͷ͏ͪͲΕ͔ΛͬͯͨΒʁ w ·ͣɺ௵ͨͨͪ͠ͷ͏ͪɺϚονϯάʹͬͯͳ͍ ݸ͚ͩͳͷͰɺύεͷͷ͏ͪͲ͔ͬͪ௵͢
Ͱແ͍ w ͔ͦ͜ΒύεΛݟ͍ͯ͘ͱɺͲ͔͜Ͱ௵͢ʹͿ͔ͭΔ
w ύεΛݟͯߦ͘ͱ͍͔ͭ௵͢ͷ͏ͪͲΕ͔͕ग़ͯ͘ Δ w ͚ͩͲ௵ͨͪ͢ɺͯ͢௵͢ಉ࢜ͰϚονϯ άͯ͠ΔPSϚονϯάͯ͠ͳ͍ w Αͬͯɺ௵͢ʹzϚονϯάͯ͠ͳ͍ลzͰೖΓࠐΉ w ͱ͜ΖͰ௵ͨ͠ޙϚονϯάʹͬͯͳ͍ʹͳΔ
w Αͬͯɺͦ͜ͰύεΛଧͪΕɺ௵ͨ͠ޙͷάϥϑͰ .૿ՃύεͱͳΔ
ࣔͤͨ ௵͢લʹ.૿Ճύε͕͋Δ 㱺௵͢ޙʹ.૿Ճύε͕͋Δ ͭ·Γ ௵͢લ͕࠷େϚονϯάͰͳ͍ 㱺௵͢ޙ͕࠷େϚονϯάͰͳ͍
௵͢લ͕࠷େϚονϯάͰͳ͍ 㱺௵͢ޙ͕࠷େϚονϯάͰͳ͍ ௵͢ޙ͕࠷େϚονϯάͰͳ͍ 㱺௵͢લ͕࠷େϚονϯάͰͳ͍
w ·ͣɺ௵͢ͱ͖ʹඞͣϚονϯάͷຊ ด࿏ͷ ͞ ݸݮΔ w ٯʹɺ௵ͨ͠ޙͷάϥϑͷϚονϯά͕༩͑ΒΕΕ ɺ ด࿏ͷ͞ ݸ૿͑ͨϚονϯάΛݩͷά
ϥϑͰߏஙͰ͖Δ w ௵ͨ͠Λͬͯͳ͔ͬͨΒͦͷ··͢ w ͬͯͯɺݩͷάϥϑͰͷͦͷϚονϯάʹͬ ͯΔҎ֎Λ͚ͬͭ͘Δ
͜͏ͳͬͨͱͨ͠Β
͜͏
͜͏ͳͬͨͱͨ͠Β
͜͏
w ௵ͨ݁͠Ռ͕࠷େϚονϯά͡Όແ͍ͱ͢Δ w ௵ͨ݁͠ՌͰͷ࠷େϚονϯάΛߟ͑ͯɺͦΕΛ ͢͜ͱʹΑΓɺݩͷάϥϑͰͷݩʑͷϚονϯάΑ Γຊͷଟ͍Ϛονϯά͕ಘΒΕΔ w ͭ·ΓݩͷάϥϑͰ࠷େϚονϯάͰແ͍
ࣔͤͨ ௵͢ޙ͕࠷େϚονϯάͰͳ͍ 㱺௵͢લ͕࠷େϚονϯάͰͳ͍
ࣔͤͨ ௵͢લ͕࠷େϚονϯάͰͳ͍ 㱻௵͢ޙ͕࠷େϚονϯάͰͳ͍
ࣔͤͨ ௵͢લ͕࠷େϚονϯά 㱻௵͢ޙ͕࠷େϚονϯά
0 7? ΞϧΰϦζϜ
0 7? w طʹ͔͍ͬͯΔਓ͍Δ͔ʁ w άϥϑͱϚονϯάΛ༩͑ͯɺϚονϯάΛ૿͠ ͯฦ͕ؔ͢࡞ΕΕྑ͍ ͜ΕΛ૿͑ͳ͘ͳΔ· Ͱݺͼଓ͚Δ
0 7? w ؔͷதɺ w దʹ.૿ՃύεΛ୳ͦ͏ͱ͢Δ w ͳ͔ͬͨΒ͏࠷େϚονϯάͳͷͰ0, w ݟ͚ͭͨͷ͕ύεͩͬͨΒϚονϯάΛͦΕͰ૿ͤ0,
w ด࿏͕͋ͬͨΒʁ w ด࿏Λ௵ͨ͋͠ͱͷάϥϑͱϚονϯάΛҾʹɺ࠶ؼ తʹ͜ͷؔΛݺͿˠ෮ݩͯ͠SFUVSO
ܭࢉྔ w ·ͣɺҰ൪֎ଆͰؔΛݺͿճ͕0 7 w ؔͷதͰ࠶ؼతʹ0 7 ճ͙Β͍ؔΛݺͿ ด
࿏Λ௵͢ʹݸͣͭݮΔ w ͦͷதͰɺ.૿ՃύεΛݟ͚ͭΑ͏ͱ͢Δͷ ʹ0 7 & 0 7? w ݁Ռͱͯ͠ɺ0 7?
0 7? લ
લJTԿ w FENPOETͷՖղΞϧΰϦζϜͰɺ w άϥϑͱϚονϯά͕༩͑ΒΕͨ࣌ʹϚονϯά Λ૿ͯ͠ฦؔ͢Λ࡞Γɺ0 7 ճݺͿ w ·ͰมΘΓ·ͤΜ
w ͜ͷؔΛɺ࠶ؼతʹؔΛݺͿͷΛΊΔ͜ͱ ʹΑΓ0 7? ʹ͠·͢
લJTԿ w ͔͠͠ɺ͍͖ͳΓϚονϯάΛ0 7? Ͱ૿͢ͷ ͍͠ w ͱΓ͋͑ͣ࠷େϚονϯά͔Ͳ͏͔͚ͩΛ0 7? Ͱఆ͢Δ͜ͱΛߟ͑·͢
w .૿ՃύεΛ෮ݩ͢Δύʔτ͕͔ͳΓ͍͠ʜ
0 7? w 0 7? ൛ʹແବͳͱ͜Ζͳ͍ͩΖ͏͔ʁ w .૿ՃύεΛൃݟ͠Α͏ͱͯ͠ɺحͷαΠΫϧ͕ ͋ͬͨΒ௵͢ˡ͜͜·ͰΑ͍ w
ͦͷ͋ͱɺ·͔ͨΒEGTΛ࢝ΊΔͷ͕ແବ w EGTΛ͠ͳ͕ΒɺحͷαΠΫϧ͕͋ͬͨΒద࣌௵ ͯ͘͠ɺΈ͍ͨͳײ͡ͰΕ͏·͍͜ͱճEGT ͢Δ͚ͩͰͲ͏ʹ͔ͳΒͳ͍ͩΖ͏͔
0 7? w ୳ࡧΛ࡞͍ͬͯ͘ w ࠜϚονϯάʹΘΕ͍ͯͳ͍ͨͪ
w ϚονϯάʹΘΕ͍ͯͳ͍ͨͪਂ͞ w ਂ͕͞ۮͷΛۮɺحͷΛحͱݺͿ w ۮͱࢠΛͭͳ͙ลɺϚονϯάʹΘΕ͍ͯͳ ͍ล w حͱࢠΛͭͳ͙ลɺϚονϯάʹΘΕ͍ͯΔ
ล
͜͏͍͏ײ͡ͷΛ࡞͍ͬͯ͘ ۮ ح ۮ ح ۮ
୳ࡧ w ۮ͔Βੜ͑ΔลΛݟ͍ͯ͘ w ลͷ૬खͷछྨʹΑΓɺύλʔϯʹ߹͚͢Δ w ʹݱΕ͍ͯͳ͍ˠ૬खͱɺͦͷϚονϯάઌΛʹ Ճ͢Δ w حˠԿ͠ͳ͍
w ҧ͏ͷۮˠʁʁ w ಉ͡ͷۮˠʁʁ
ҧ͏ͷۮͷ߹ ۮ ح ۮ ح ۮ
͜Εͱ͔ ۮ ح ۮ ح ۮ
͜Εͱ͔ ۮ ح ۮ ح ۮ
͜Εͱ͔ ۮ ح ۮ ح ۮ
ҧ͏ͷۮͷ߹ w ลͷࠨӈΛY Zͱ͢Δͱɺ YͷͷࠜdYͷύε Y Z ZdZͷͷࠜͷύε
ɺ.૿Ճύεʹͳͬ ͍ͯΔ w Αͬͯɺҧ͏ͷۮಉ࢜Λͭͳ͙ล͕͋ͬͨΒͦ Ε࠷େϚονϯάͰແ͍
ಉ͡ͷۮͷ߹ ۮ ح ۮ ح ۮ
͜Εͱ͔ ۮ ح ۮ ح ۮ
͜Εͱ͔ ۮ ح ۮ ح ۮ
͜Εͱ͔ ۮ ح ۮ ح ۮ
ಉ͡ͷͷ߹ w YͱZΛܨ͍ͰΔͱ͢Δ w ࣮ɺMDB Y Z [ͱ͢Δͱɺ Yd[dZ ͱ
Y Z ͔ΒͳΔด࿏ɺ௵ͯ͠ྑ͍ด࿏ ʹͳ͍ͬͯΔ w ͳͷͰɺಉ͡ͷۮಉ࢜Λͭͳ͙ล͕ ͋ͬͨΒ௵͢ Y Z [
௵ͯ͠ྑ͍ด࿏ ࠶ܝ ۮຊ ด࿏ͷ͞ح
w ͜ΕΒΛ܁Γฦ͢ͱɺ͍͔ͭ.૿Ճύε͕ݟ͔ͭΔ͔ɺ͘͠ ɺߋʹۮͱͭͳ͕Δลͷઌ͕ح͚ͩʹͳΔ w ۮͱͭͳ͕Δลͷઌ͕ح͚ͩͳͷͰɺۮͷ͏ͪϚονϯάʹ ͑ΔͷͷݸحͷݸҎԼ w ͨͩحશͯۮͱશͯϚονϯά͍ͯ͠Δ w ͔͠ϚονϯάʹΘΕ͍ͯͳ͍શͯۮ
w Αͬͯ͜ΕҎ্Ϛονϯά૿ͤͳ͍ w Αͬͯ͜͏ͳΔ·Ͱ܁Γฦͤྑ͍ w ͜ΕͳΒదʹΔͱ0 7? Ͱ࠷େϚονϯά͔ఆͰ͖·͢
0 7? ޙ
ޙ w ࠷େϚονϯά͔0 7? Ͱఆ͢ΔͷΘΓ͔͠ ؆୯ w ͚ͩͲ࣮ࡍ૿ͦ͏ͱ͢Δͱɺେมʜ w ૿ՃύεΛ͏·͘෮ݩͰ͖ΔΑ͏ʹ͠ͳ͍͚ͯ͘
ͳ͍
૿Ճύεͷ෮ݩ w ૿Ճύε͕ඞཁʹͳΔͷɺҧ͏ͷۮಉ࢜Λͭ ͳ͙ล͕ݟ͔ͭͬͨ࣌ w ͭ·Γɺͷۮʹ͍ͭͯͦͷ͔Β࢝·Γɺࠜ ͰऴΘΔΑ͏ͳɺzϚονϯάʹͬͯΔ ͬͯͳ ͍ ͬͯΔ
ͬͯͳ͍ ʜ ͬͯͳ͍zύε͕෮ ݩͰ͖ΕΑ͍
૿Ճύεͷ෮ݩ w ͬͯΔ ͬͯͳ͍ ʜ ͬͯͳ͍ͱ͍͏ύεͷ෮ݩ͕ ͍ͨ͠ w ϚονϯάʹͬͯΔลͱ͍͏ͷ͝ͱʹҰҙʹఆ· Δ
w Ϛονϯάʹͬͯͳ͍ลɺ͜ΕͲΕΛબ͍ ͍ΜͩΖ͏ʁ ˠٯʹɺʹ͍ͭͯ͜ͷz࣍ʹ͏͖Ϛονϯάʹͬ ͯͳ͍ลͲΕ͔zΛมʹ࣋ͬͯɺ͏·͘ཧ͢Εʁ
૿Ճύεͷ෮ݩ w ҎԼͷछྨͷมΛߟ͑Δ w NU V VͱϚονϯάͯ͠Δ NBUDI w
OY V Vͱͷؒʹล͋Δ͚ͲɺϚονϯάͯ͠ͳ ͍ͷ͏ͪͲΕ͔ͭ OFYU
NU OYͷ੍ w ҙͷۮVʹ͍ͭͯɺ w NU V OY NU V
NU OY NU V OY NU OY NU V ʜ OY NU ʜ V ʜ w ͕ɺzV͔Β࢝·ΓɺͦͷͷࠜͰऴΘΔύεzͱͳ ΔΑ͏ʹ͍ͨ͠ w ͜͏ͳΔΑ͏ʹOY V Λཧ͢ΕΑ͍
ະଓͷՃ w ͜Ε؆୯ w OY V ͭͳ͙Ͱ0, w W͔ΒTUBSU͢Δͱύεɺ w
W V ͭͳ͙ dͱͳΔ ۮ V W ͭͳ͙
Λ௵͢ w ͜Εେม w ·ͣۮ͕શ෦ݸͷ߹ V W
Λ௵͢ w ͜͏͢ΕΑͦ͞͏ʁ V W
Λ௵͢ w ۮͷαΠζ͕શ෦ͷͱ͖ɺ ·ͣVdMDBͱWdMDBͷύεΛٻ ΊΔ w ͦͷύε্ͷMDBҎ֎ͷۮYʹͭ ͍ͯ OY Y
ͦͷύεͷݸ༿ଆ ʹ͢Δ w ࣮ࡍۮ͕αΠζͰͳ͍ͨ Ίɺେม V W
Λ௵͢ V W -$"
͜͏ͯ͠ V W
͜͏ V W
Λ௵͢ w VͱW͔Β࢝·Δ.૿ՃύεΛ࡞Δ w -$" ͭͷύε͕௨Δɺ࠷ࠜʹ͍ۙۮ ΛٻΊΔ w -$"·ͰͷɺϚονϯάʹ௨Βͳ͍ลΛํʹҠಈͰ ͖ΔΑ͏ʹ͢Δ
V W͔ΒۮճਐΜͩYʹ͍ͭͯɺY ͷॴଐ͢Δۮ͕-$"Ҏ্Ͱͳ͚ΕɺOY Y ύεͷ ݸલ w -$"Ҏ্ͳͷɺલਤͷΑ͏ʹɺV͔ΒͷύεͱW͔Βͷ ύε-$"ͷதͰަΘΔ͜ͱ͕͋Δ͔Β
NU OYͷ੍ ࠶ܝ w ҙͷۮVʹ͍ͭͯɺ w NU V OY NU
V NU OY NU V OY NU OY NU V ʜ OY NU ʜ V ʜ w ͕ɺzV͔Β࢝·ΓɺͦͷͷࠜͰऴΘΔύεzͱͳ ΔΑ͏ʹ͍ͨ͠ w Λ௵ͨ͋͠ͱ͜ΕΛຬ͍ͨͯ͠Δ͔ʁ
NU OYͷ੍ w ·ͣɺ-$"ͷࢠ -$"আ͘ ͚ͩߟ͑Εྑ͍ w V͔ΒͱW͔Βͷύεʹؚ·ΕΔશͯ0, w ͦΕҎ֎ɺͲ͔͜ͰV͔ΒͱW͔ΒͷύεʹͿͭ
͔Δ͕ɺͿ͔ͭͬͨΒύεͷ͚ͩΛͬͯ-$" ·ͰӡΕΔͷͰ0,
.૿ՃύεΛ૿͢ w ҧ͏ͷۮΛͭͳ͙߹ w ྆ํͷ͔ΒύεΛ࡞ͬͯɺదʹ૿ͤ0, w Ҏ্ΑΓɺ0 7? ͰϚονϯά͕૿ͤΔ͜ͱ͕ Θ͔ͬͨ
͜ΕͰ0 7? ͕ग़དྷ·ͨ͠