Flip Distance de triangulations convexes ani jiriw jiginni ye NP-Complete ye

daminɛ : Gɛlɛya dogolen sigida minnu bɛ i n' a fɔ u ka nɔgɔn

A filɛli fɔlɔ la, jatebɔ jateminɛcogo cɛɲiw ani jagokɛlaw ka baarakɛminɛnw sigicogo modulari i n’a fɔ Mewayz, o bɛ se ka kɛ i n’a fɔ diɲɛw tɛ kelen ye. Kelen bɛ kuma jatebɔ daliluw kan minnu tɛ ye; tɔ kelen ni baarakɛcogo, kunnafonidilanw ani kumaɲɔgɔnya nɔgɔyali ye. Nka, n’i y’a lajɛ ka ɲɛ, i bɛ fɛn dɔ jira min bɛ ɲɔgɔn fɛ: gɛlɛyaw ɲɛnabɔli. I n’a fɔ jagokɛlaw bɛ baara kɛ ni modulu systems ye cogo min na walasa ka taabolo gɛlɛnw tila ka kɛ yɔrɔw ye minnu bɛ se ka ɲɛnabɔ, ɔridinatɛri dɔnnikɛlaw bɛ gɛlɛyaw sɛgɛsɛgɛ u kɛtɔ ka baara jɔnjɔnw faamuya minnu bɛ jamana dɔ sɛmɛntiya ka kɛ jamana wɛrɛ ye. Kɔsa in na, dalilu jɔnjɔn min b'a Jira ko "Flip Distance of Convex Triangulations" ni "Tree Rotation" jatebɔ ye NP-dafalen ye, o ye o hakilina yɛrɛ ɲinini jugu ye. A b’a jira ko hali sigida minnu sigilen don kosɛbɛ, sira ɲuman sɔrɔli jamana fila ni ɲɔgɔn cɛ, o bɛ se ka kɛ gɛlɛya ye min bɛ mɔgɔ kabakoya. Plateformes i n’a fɔ Mewayz, minnu bɛ ɲɛtaa sɔrɔ baarakɛcogo gɛlɛnw ɲɛnabɔli la, nin jatebɔ tiɲɛ in bɛ lase sariyakolo jɔnjɔn dɔ ma : sigicogo hakilitigi ye fɛnba ye walasa ka gɛlɛyaw ɲɛminɛ.

hakilila kolomaw faamuyali : kɛrɛ saba ni jiginni

Walisa ka nin jaabi in nafa faamuya , an ka kan ka ntolatannaw faamuya fɔlɔ . kɛrɛ saba sɔgɔlen ye poligoni sɔgɔlen tilacogo ye ka kɛ kɛrɛ saba ye ni diagonalw ja ye minnu tɛ ɲɔgɔn cɛ a kuncɛw ni ɲɔgɔn cɛ. Baara jɔnjɔn min bɛ Kɛ o kɛrɛ saba sugu kan o ye "flip" ye, o kɔrɔ dɔrɔn ye ka 'kɔnɔna kelen Bɔ k'a Blà 'kɔnɔna tɔ kelen nɔ na min bɛ Kɛ 'kɔnɔna naani na min bɛ Kɛ ni kɛrɛ saba fla ye minnu bɛ ɲɔgɔn kɛrɛfɛ. Nin ye fɛn fitinin ye, sigida la, min bɛ kɛrɛ saba tiɲɛnen dɔ sɛmɛntiya ka kɛ dɔ wɛrɛ ye.

o cogo kelen na , jiri binna ye kunnafonidilan ye min bɛ sigi senkan , node kelen-kelen bɛɛ bɛ se den fila ma min kɔnɔ . jiri jiginni ye baara ye min bɛ jiri in jɔcogo Changer k’a sɔrɔ a bɛ a sigicogo danma mara, ka node dɔ n’a bangebaga "yɛrɛyɛrɛ" cogo ɲuman na walasa ka jiri balansi kokura. Flip ni rotation fila bɛɛ ye fɛn fɔlɔw ye minnu bɛ Kɛ k’u ka jɔcogo kelen-kelen bɛɛ Labɛn kokura.

Flip distance ani rotation distance gɛlɛya

Cɛmancɛ ɲininkali in ka nɔgɔn nanbarako la : ni kɛrɛ saba fila (walima jiri fila fila) dira, flip (walima jiginni) hakɛ fitinin min ka kan ka kɛ walasa ka kelen sɛmɛntiya ka kɛ tɔ kelen ye, o hakɛ fitinin ye mun ye ? O jateden fitinin in bɛ Weele ko flip distance walima rotation distance. San tan caman kɔnɔ, jatebɔ gɛlɛya min tun bɛ o yɔrɔjan fitinin in jatebɔ la, o tun ye gɛlɛya dafalenba ye. Hali n’a ka nɔgɔn ka flip walima rotation kɛ, ka o baara ninnu kɛcogo ɲuman sɔrɔ walasa ka laɲini kɛrɛnkɛrɛnnen dɔ sɔrɔ, o ye gɛlɛya wɛrɛ ye pewu. A bɛ tali kɛ modulu kelen-kelen bɛɛ lasegincogo dɔnni na sistɛmu kɔnɔ i n’a fɔ Mewayz, nka n’i ma kɛ ni bolodacogo jɛlen ye min bɛ se ka kɛ sababu ye ka porozɛ baarakɛcogo bɛɛ labɛn kokura teliya la ka bɔ a daminɛ cogo la ka se a sɔrɔcogo ɲininen ma.

• Sigida taamaw , diɲɛ gɛlɛya : baara kelen-kelen bɛɛ ka nɔgɔn , nka ɲɔgɔndan min ka kan ka kɛ walasa ka fɛn caman tigɛli ɲuman kɛ , o bɛ na ni diɲɛnatigɛ kɔlɔlɔw ye .
• Sɛbɛnni minnu bɛ se ka kɛ : cɛmancɛ jamana minnu bɛ se ka kɛ, olu hakɛ bɛ bonya kosɛbɛ, o b’a to fanga jugu ɲinini tɛ se ka kɛ misalibaw la.
• Jɛɲɔgɔnya : Yɛlɛma donna sigida yɔrɔ dɔ la , o bɛ se ka nɔ bila lamaga sɔrɔlenw na yɔrɔ wɛrɛ la , ka dantigɛliw ka web gɛlɛn dɔ da .

NP-dafalen dalilu n' a nɔfɛkow

Dalilu min sɔrɔla kɔsa in na, o bɛ ɲininkali in ɲɛnabɔ k'a jɛya : flip distance jatebɔ kɛrɛ saba konvexe fila cɛ (ani ni bɛnkan dɔnnen ye , jiri fila ni ɲɔgɔn cɛ jiginni janya ) o ye NP-dafalen ye O b’a bila gɛlɛya gɛlɛnw cɛma minnu tɔgɔ bɔra kosɛbɛ ɔridinatɛri dɔnniya la, i n’a fɔ Feerekɛla taamakɛla ka gɛlɛya. Algoritmɛ ɲuman dɔnnen tɛ yen min bɛ Se ka nin gɛlɛya in misali bɛɛ ɲɛnabɔ joona, wa a dalen b’a la ko o si tɛ yen. O hakilila-jɔ-ko in bɛ na ni nɔ ye min bɛ se ka kɛ. A b’a fɔ ɲininikɛlaw ye k’u ka kan k’u sinsin gɛrɛgɛrɛli algorisimuw labɛnni kan walima fura ɲumanw labɛnni kan ko kɛrɛnkɛrɛnnenw kama, sanni u ka fɛɛrɛ kelen ɲini.

Nin tiɲɛni in bɛ tiɲɛ jɔnjɔn dɔ sinsin : kɛlɛli dɔgɔya sira min bɛ sigicogo ɲuman fila ni ɲɔgɔn cɛ, a ka c’a la, o yɔrɔ ka jan kosɛbɛ, hali sigida minnu bɛ mara sariya nɔgɔmanw fɛ.

O kɔrɔ ye min ye modulu sitɛmuw la i n' a fɔ Mewayz

k'a sɔrɔ Mewayz tɛ baara kɛ ni kɛrɛ saba ye , sariya min yeelen bɔra nin jatebɔ sɔrɔli in fɛ , o nafa ka bon kosɛbɛ . Jagokɛlaw ka OS modulariw bɛɛ ye labɛnni ni u labɛncogo kura ye—donanw moduluw, poroze pankurunw, kumaɲɔgɔnya siraw ani otomatiki baarakɛcogo. NP-dafalen sɔrɔlen ye ntalen barikama ye jago taabolo ɲɛnabɔli gɛlɛya danbe la. A b’a jira ko ni sistɛmuw bɛ ka bonya u bonya la ani u ni ɲɔgɔn cɛ jɛɲɔgɔnya la, ka fɛɛrɛ dafalen sɔrɔ min bɛ se ka kɛ ka fɛnw labɛn kokura, o bɛ se ka kɛ gɛlɛya ye min tɛ se ka ɲɛnabɔ. O de y’a to Mewayz bɛ sinsin modularite intuitif kan ani dilancogo min bɛ ɲɛminɛ baarakɛlaw fɛ. Sani a k’a ɲini ka ɲɛnabɔli gɛlɛya dɔ ɲɛnabɔ min ka gɛlɛn kosɛbɛ, min tɛ se ka kɛ, min bɛ se ka kɛ, Mewayz bɛ jɔlifɛnw ni yecogo jɛlen di, ka fanga di ekipuw ma, u ka se ka fɛn caman Changements hakilitigiw, minnu bɛ caya ka taa a fɛ. Plateforme in jɔcogo b’a jira ko sira ɲuman bɛ sɔrɔ tuma caman na iterasiyɔn teliyalen ni hadamaden ka faamuyali fɛ, jatebɔ raw dɔrɔn tɛ.

Kunnafoni na, flip ni rotation distance ka NP-dafalen ka ca ni arcane result ye jatebɔ jateminɛ na. O ye kalan ye gɛlɛyako la min bɛ fɔ ka bɔ kunnafonidilanw na minnu tɛ fɛn ye, ka taa a bila bi jago gɛlɛya jɔnjɔnw na. A b’an hakili jigin ko sigida min bɛ i n’a fɔ Mewayz, o fanga tɛ sɔrɔ ɲɛnabɔli gɛlɛya bɛɛ ɲɛnabɔli la cogo dafalen na, nka a bɛ sɔrɔ ka sigida dɔ di min bɛ se ka sɛgɛsɛgɛ, min bɛ kɛnɛya, min b’a to baarakɛlaw bɛ se ka gɛlɛyaw ɲɛnabɔ ka ɲɛ, “flip” hakilitigi kelen a waati kelen na.

Ɲininkali minnu bɛ kɛ tuma caman na

daminɛ : Gɛlɛya dogolen sigida minnu bɛ i n' a fɔ u ka nɔgɔn

A filɛli fɔlɔ la, jatebɔ jateminɛcogo cɛɲiw ani jagokɛlaw ka baarakɛminɛnw sigicogo modulari i n’a fɔ Mewayz, o bɛ se ka kɛ i n’a fɔ diɲɛw tɛ kelen ye. Kelen bɛ kuma jatebɔ daliluw kan minnu tɛ ye; tɔ kelen ni baarakɛcogo, kunnafonidilanw ani kumaɲɔgɔnya nɔgɔyali ye. Nka, n’i y’a lajɛ ka ɲɛ, i bɛ fɛn dɔ jira min bɛ ɲɔgɔn fɛ: gɛlɛyaw ɲɛnabɔli. I n’a fɔ jagokɛlaw bɛ baara kɛ ni modulu systems ye cogo min na walasa ka taabolo gɛlɛnw tila ka kɛ yɔrɔw ye minnu bɛ se ka ɲɛnabɔ, ɔridinatɛri dɔnnikɛlaw bɛ gɛlɛyaw sɛgɛsɛgɛ u kɛtɔ ka baara jɔnjɔnw faamuya minnu bɛ jamana dɔ sɛmɛntiya ka kɛ jamana wɛrɛ ye. Kɔsa in na, dalilu jɔnjɔn min b'a Jira ko "Flip Distance of Convex Triangulations" ni "Tree Rotation" jatebɔ ye NP-dafalen ye, o ye o hakilina yɛrɛ ɲinini jugu ye. A b’a jira ko hali sigida minnu sigilen don kosɛbɛ, sira ɲuman sɔrɔli jamana fila ni ɲɔgɔn cɛ, o bɛ se ka kɛ gɛlɛya ye min bɛ mɔgɔ kabakoya. Plateformes i n’a fɔ Mewayz, minnu bɛ ɲɛtaa sɔrɔ baarakɛcogo gɛlɛnw ɲɛnabɔli la, nin jatebɔ tiɲɛ in bɛ lase sariyakolo jɔnjɔn dɔ ma : sigicogo hakilitigi ye fɛnba ye walasa ka gɛlɛyaw ɲɛminɛ.

hakilila kolomaw faamuyali : kɛrɛ saba ni jiginni

Walisa ka nin jaabi in nafa faamuya , an ka kan ka ntolatannaw faamuya fɔlɔ . Kɛrɛ saba-saba-yɔrɔ-ko ye fɛɛrɛ ye min bɛ kɛ ka poligoni sɔgɔlen tila ka kɛ kɛrɛ saba ye ni diagonals (daɲɛw) ja ye minnu tɛ ɲɔgɔn cɛ a kuncɛw ni ɲɔgɔn cɛ. Baara jɔnjɔn min bɛ Kɛ o kɛrɛ saba sugu kan o ye "flip" ye, o kɔrɔ dɔrɔn ye ka 'kɔnɔna kelen Bɔ k'a Blà 'kɔnɔna tɔ kelen nɔ na min bɛ Kɛ 'kɔnɔna naani na min bɛ Kɛ ni kɛrɛ saba fla ye minnu bɛ ɲɔgɔn kɛrɛfɛ. Nin ye fɛn fitinin ye, sigida la, min bɛ kɛrɛ saba tiɲɛnen dɔ sɛmɛntiya ka kɛ dɔ wɛrɛ ye.

Flip distance ani rotation distance gɛlɛya

Cɛmancɛ ɲininkali in ka nɔgɔn nanbarako la : ni kɛrɛ saba fila (walima jiri fila fila) dira, flip (walima jiginni) hakɛ fitinin min ka kan ka kɛ walasa ka kelen sɛmɛntiya ka kɛ tɔ kelen ye, o hakɛ fitinin ye mun ye ? O jateden fitinin in bɛ Weele ko flip distance walima rotation distance. San tan caman kɔnɔ, jatebɔ gɛlɛya min tun bɛ o yɔrɔjan fitinin in jatebɔ la, o tun ye gɛlɛya dafalenba ye. Hali n’a ka nɔgɔn ka flip walima rotation kɛ, ka o baara ninnu kɛcogo ɲuman sɔrɔ walasa ka laɲini kɛrɛnkɛrɛnnen dɔ sɔrɔ, o ye gɛlɛya wɛrɛ ye pewu. A bɛ tali kɛ modulu kelen-kelen bɛɛ lasegincogo dɔnni na sistɛmu kɔnɔ i n’a fɔ Mewayz, nka n’i ma kɛ ni bolodacogo jɛlen ye min bɛ se ka kɛ sababu ye ka porozɛ baarakɛcogo bɛɛ labɛn kokura teliya la ka bɔ a daminɛ cogo la ka se a sɔrɔcogo ɲininen ma.

NP-dafalen dalilu n' a nɔfɛkow

Dalilu min sɔrɔla kɔsa in na, o bɛ ɲininkali in ɲɛnabɔ k’a jɛya : flip distance jatebɔ kɛrɛ saba jɛlen fila ni ɲɔgɔn cɛ (ani ni bɛnkan dɔnta ye, jiri fila ni ɲɔgɔn cɛ jiginni janya) o ye NP-dafalen ye. O b’a bila gɛlɛya gɛlɛnw cɛma minnu tɔgɔ bɔra kosɛbɛ ɔridinatɛri dɔnniya la, i n’a fɔ Feerekɛla taamakɛla ka gɛlɛya. Algoritmɛ ɲuman dɔnnen tɛ yen min bɛ Se ka nin gɛlɛya in misali bɛɛ ɲɛnabɔ joona, wa a dalen b’a la ko o si tɛ yen. O hakilila-jɔ-ko in bɛ na ni nɔ ye min bɛ se ka kɛ. A b’a fɔ ɲininikɛlaw ye k’u ka kan k’u sinsin gɛrɛgɛrɛli algorisimuw labɛnni kan walima fura ɲumanw labɛnni kan ko kɛrɛnkɛrɛnnenw kama, sanni u ka fɛɛrɛ kelen ɲini.

O kɔrɔ ye min ye modulu sitɛmuw la i n' a fɔ Mewayz

k'a sɔrɔ Mewayz tɛ baara kɛ ni kɛrɛ saba ye , sariya min yeelen bɔra nin jatebɔ sɔrɔli in fɛ , o nafa ka bon kosɛbɛ . Jagokɛlaw ka OS modulariw bɛɛ ye labɛnni ni u labɛncogo kura ye—donanw moduluw, poroze pankurunw, kumaɲɔgɔnya siraw ani otomatiki baarakɛcogo. NP-dafalen sɔrɔlen ye ntalen barikama ye jago taabolo ɲɛnabɔli gɛlɛya danbe la. A b’a jira ko ni sistɛmuw bɛ ka bonya u bonya la ani u ni ɲɔgɔn cɛ jɛɲɔgɔnya la, ka fɛɛrɛ dafalen sɔrɔ min bɛ se ka kɛ ka fɛnw labɛn kokura, o bɛ se ka kɛ gɛlɛya ye min tɛ se ka ɲɛnabɔ. O de y’a To Mewayz bɛ sinsin modulari intuitif (modularité intuitif) kan ani dilancogo min bɛ ɲɛminɛ baarakɛlaw fɛ. Sani a k’a ɲini ka ɲɛnabɔli gɛlɛya dɔ ɲɛnabɔ min ka gɛlɛn kosɛbɛ, min tɛ se ka kɛ, min bɛ se ka kɛ, Mewayz bɛ jɔlifɛnw ni yecogo jɛlen di, ka fanga di ekipuw ma, u ka se ka fɛn caman Changements hakilitigiw, minnu bɛ caya ka taa a fɛ. Plateforme in jɔcogo b’a jira ko sira ɲuman bɛ sɔrɔ tuma caman na iterasiyɔn teliyalen ni hadamaden ka faamuyali fɛ, jatebɔ raw dɔrɔn tɛ.