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r rs tr sttt r strt Prr

  1. ❙❡♠✐♥❛r ❙❡r✐❡s ❙✸ ✲ ■▼❉❊❆ ❙♦❢t✇❛r❡ ■♥st✐t✉t❡ ❋❛✐❧✉r❡ ❚❛❜❧❡❞ ❈♦♥str❛✐♥t ▲♦❣✐❝ Pr♦❣r❛♠♠✐♥❣ ❜② ■♥t❡r♣♦❧❛t✐♦♥ ❆✉t❤♦rs✿ ●r❛❡♠❡ ●❛♥❣❡✱ ❏♦r❣❡ ❆✳ ◆❛✈❛s✱ P❡t❡r ❙❝❤❛❝❤t❡✱ ❍❛r❛❧❞ ❙ø♥❞❡r❣❛❛r❞✱ ❛♥❞ P❡t❡r ❏✳ ❙t✉❝❦❡② ✭❯♥✐✈❡rs✐t② ♦❢ ▼❡❧❜♦✉r♥❡ ✲ ■❈▲P✬✶✸✮ ❙♣❡❛❦❡r✿ ❏♦❛q✉í♥ ❆r✐❛s ❍❡rr❡r♦ ▼❛❞r✐❞✱ ◆♦✈❡♠❜❡r ✷✵✶✹ ❏♦❛q✉í♥ ❆r✐❛s ❍❡rr❡r♦ ❙❡♠✐♥❛r ❙❡r✐❡s ❙✸ ✶✶ ♥♦✈❡♠❜❡r ✷✵✶✹ ✶ ✴ ✶✻

  2. ❙❡♠✐♥❛r ❙❡r✐❡s ❙✸ ✲ ■▼❉❊❆ ❙♦❢t✇❛r❡ ■♥st✐t✉t❡ ❋❛✐❧✉r❡ ❚❛❜❧❡❞ ❈♦♥str❛✐♥t ▲♦❣✐❝ Pr♦❣r❛♠♠✐♥❣ ❜② ■♥t❡r♣♦❧❛t✐♦♥ ❆✉t❤♦rs✿ ●r❛❡♠❡ ●❛♥❣❡✱ ❏♦r❣❡ ❆✳ ◆❛✈❛s✱ P❡t❡r ❙❝❤❛❝❤t❡✱ ❍❛r❛❧❞ ❙ø♥❞❡r❣❛❛r❞✱ ❛♥❞ P❡t❡r ❏✳ ❙t✉❝❦❡② ✭❯♥✐✈❡rs✐t② ♦❢ ▼❡❧❜♦✉r♥❡ ✲ ■❈▲P✬✶✸✮ ❙♣❡❛❦❡r✿ ❏♦❛q✉í♥ ❆r✐❛s ❍❡rr❡r♦ ✷✵✵✷ ✲ ▼❙❝ ❆r❝❤✐t❡❝t✉r❡ ❲♦r❦✐♥❣ ❛s ❛r❝❤✐t❡❝t ✭✷✵✵✵✲✷✵✶✵✮ ✷✵✶✹ ✲ ❇❙❝ ❈♦♠♣✉t❡r ❙❝✐❡♥❝❡ ❲♦r❦✐♥❣ ❛t t❤❡ ■▼❉❊❆ ❙♦❢t✇❛r❡ ■♥st✐t✉t❡ ✭✷✵✶✸✲t♦❞❛②✮ ▼❛❞r✐❞✱ ◆♦✈❡♠❜❡r ✷✵✶✹ ❏♦❛q✉í♥ ❆r✐❛s ❍❡rr❡r♦ ❙❡♠✐♥❛r ❙❡r✐❡s ❙✸ ✶✶ ♥♦✈❡♠❜❡r ✷✵✶✹ ✷ ✴ ✶✻

  3. ■♥❞❡① ▼♦t✐✈❛t✐♦♥✳ ❋❛✐❧✉r❡ ❚❛❜❧❡❞ ❈♦♥str❛✐♥t Pr♦❣r❛♠♠✐♥❣ ❜② ■♥t❡r♣♦❧❛t✐♦♥✳ ❊①❛♠♣❧❡✳ P❡r❢♦r♠❛♥❝❡✳ ■♥t❡r♣♦❧❛♥t ✐♥ ❋❚❈▲P ❁❃ Pr♦❥❡❝t✐♦♥ ✐♥ ❚❈▲P✳ ❏♦❛q✉í♥ ❆r✐❛s ❍❡rr❡r♦ ❙❡♠✐♥❛r ❙❡r✐❡s ❙✸ ✶✶ ♥♦✈❡♠❜❡r ✷✵✶✹ ✸ ✴ ✶✻

  4. ▼♦t✐✈❛t✐♦♥ ❈♦♠❜✐♥❡ ❜❡♥❡✜ts ♦❢ ❝♦♥str❛✐♥ts ❛♥❞ t❛❜❧✐♥❣ ✐♥ Pr♦❧♦❣✳ ❏♦❛q✉í♥ ❆r✐❛s ❍❡rr❡r♦ ❙❡♠✐♥❛r ❙❡r✐❡s ❙✸ ✶✶ ♥♦✈❡♠❜❡r ✷✵✶✹ ✹ ✴ ✶✻

  5. ▼♦t✐✈❛t✐♦♥ ❈♦♠❜✐♥❡ ❜❡♥❡✜ts ♦❢ ❝♦♥str❛✐♥ts ❛♥❞ t❛❜❧✐♥❣ ✐♥ Pr♦❧♦❣✳ ❲✐t❤ ❝♦♥str❛✐♥ts✳ ◮ ❘❡❞✉❝❡ s❡❛r❝❤ tr❡❡✳ ❄ − s ♦ ❧ ✉ t ✐ ♦ ♥ s ✭❳✮ ✱ ❳ ❃ ✵ ✳ ❄ − ❳ ✳ ❃✳ ✵ ✱ s ♦ ❧ ✉ t ✐ ♦ ♥ s ✭❳✮ ✳ ❏♦❛q✉í♥ ❆r✐❛s ❍❡rr❡r♦ ❙❡♠✐♥❛r ❙❡r✐❡s ❙✸ ✶✶ ♥♦✈❡♠❜❡r ✷✵✶✹ ✹ ✴ ✶✻

  6. ▼♦t✐✈❛t✐♦♥ ❈♦♠❜✐♥❡ ❜❡♥❡✜ts ♦❢ ❝♦♥str❛✐♥ts ❛♥❞ t❛❜❧✐♥❣ ✐♥ Pr♦❧♦❣✳ ❲✐t❤ t❛❜❧✐♥❣✳ ◮ ❆✈♦✐❞ r❡❝♦♠♣✉t❛t✐♦♥s✳ ◮ ❊♥s✉r❡ t❡r♠✐♥❛t✐♦♥ ❢♦r ✏❜♦✉♥❞❡❞ t❡r♠ s✐③❡✑ ♣r♦❣r❛♠s✳ ❡❞❣❡ ✭ ✶ ✱ ✷ ✮ ✳ ❡❞❣❡ ✭ ✷ ✱ ✶ ✮ ✳ r ❡ ❛ ❝ ❤ ✭❳✱❨✮ ✿ − ❡❞❣❡ ✭❳✱ ❩✮ ✱ r ❡ ❛ ❝ ❤ ✭❩ ✱❨✮ ✳ r ❡ ❛ ❝ ❤ ✭❳✱❨✮ ✿ − ❡❞❣❡ ✭❳✱❨✮ ✳ ❏♦❛q✉í♥ ❆r✐❛s ❍❡rr❡r♦ ❙❡♠✐♥❛r ❙❡r✐❡s ❙✸ ✶✶ ♥♦✈❡♠❜❡r ✷✵✶✹ ✹ ✴ ✶✻

  7. ▼♦t✐✈❛t✐♦♥ ❈♦♠❜✐♥❡ ❜❡♥❡✜ts ♦❢ ❝♦♥str❛✐♥ts ❛♥❞ t❛❜❧✐♥❣ ✐♥ Pr♦❧♦❣✳ ❲✐t❤ t❛❜❧✐♥❣✳ ◮ ❆✈♦✐❞ r❡❝♦♠♣✉t❛t✐♦♥s✳ ◮ ❊♥s✉r❡ t❡r♠✐♥❛t✐♦♥ ❢♦r ✏❜♦✉♥❞❡❞ t❡r♠ s✐③❡✑ ♣r♦❣r❛♠s✳ ❡❞❣❡ ✭ ✶ ✱ ✷ ✮ ✳ 1. reach(1,Y). ❡❞❣❡ ✭ ✷ ✱ ✶ ✮ ✳ r ❡ ❛ ❝ ❤ ✭❳✱❨✮ ✿ − 2. edge(1,Z), reach(Z,Y). ❡❞❣❡ ✭❳✱ ❩✮ ✱ Z=2 r ❡ ❛ ❝ ❤ ✭❩ ✱❨✮ ✳ 3. reach(2,Y). r ❡ ❛ ❝ ❤ ✭❳✱❨✮ ✿ − ❡❞❣❡ ✭❳✱❨✮ ✳ 4. edge(2,Z), reach(Z,Y). Z=1 5. reach(1,Y). ... ❏♦❛q✉í♥ ❆r✐❛s ❍❡rr❡r♦ ❙❡♠✐♥❛r ❙❡r✐❡s ❙✸ ✶✶ ♥♦✈❡♠❜❡r ✷✵✶✹ ✹ ✴ ✶✻

  8. ▼♦t✐✈❛t✐♦♥ ❈♦♠❜✐♥❡ ❜❡♥❡✜ts ♦❢ ❝♦♥str❛✐♥ts ❛♥❞ t❛❜❧✐♥❣ ✐♥ Pr♦❧♦❣✳ ❲✐t❤ t❛❜❧✐♥❣✳ ◮ ❆✈♦✐❞ r❡❝♦♠♣✉t❛t✐♦♥s✳ ◮ ❊♥s✉r❡ t❡r♠✐♥❛t✐♦♥ ❢♦r ✏❜♦✉♥❞❡❞ t❡r♠ s✐③❡✑ ♣r♦❣r❛♠s✳ ❡❞❣❡ ✭ ✶ ✱ ✷ ✮ ✳ 1. reach(1,Y). ❡❞❣❡ ✭ ✷ ✱ ✶ ✮ ✳ r ❡ ❛ ❝ ❤ ✭❳✱❨✮ ✿ − 3. edge(1,Z), reach(Z,Y). 13. edge(1,Y). ❡❞❣❡ ✭❳✱ ❩✮ ✱ Z=2 Y=2 r ❡ ❛ ❝ ❤ ✭❩ ✱❨✮ ✳ 4. reach(2,Y). 14. edge(1,2). r ❡ ❛ ❝ ❤ ✭❳✱❨✮ ✿ − ❡❞❣❡ ✭❳✱❨✮ ✳ 6. edge(2,Z), reach(Z,Y). 8. edge(2,1). Z=1 ❙✉❜❣♦❛❧ ❆♥s✇❡rs 7. reach(1,Y). ✶✵✳ ❨ ❂ ✶ ✷✳ r❡❛❝❤✭✶✱❨✮ ✶✺✳ ❨ ❂ ✷ Y=1 Y=2 ✶✽✳ ❈♦♠♣❧❡t❡ 11. reach(1,1). 16. reach(1,2). ✾✳ ❨ ❂ ✶ ✺✳ r❡❛❝❤✭✷✱❨✮ ✶✼✳ ❨ ❂ ✷ 12. fail . ✶✽✳ ❈♦♠♣❧❡t❡ ❏♦❛q✉í♥ ❆r✐❛s ❍❡rr❡r♦ ❙❡♠✐♥❛r ❙❡r✐❡s ❙✸ ✶✶ ♥♦✈❡♠❜❡r ✷✵✶✹ ✹ ✴ ✶✻

  9. ▼♦t✐✈❛t✐♦♥ ❈♦♠❜✐♥❡ ❜❡♥❡✜ts ♦❢ ❝♦♥str❛✐♥ts ❛♥❞ t❛❜❧✐♥❣ ✐♥ Pr♦❧♦❣✳ Pr❡✈✐♦✉s ✐♠♣❧❡♠❡♥t❛t✐♦♥s✳ ❈♦♥str❛✐♥t ▼❡♠♦✐♥❣✱ ❛♣♣❧✐❝❛❜❧❡ t♦ ❝♦♥str❛✐♥t ❉❛t❛❧♦❣✳ ✶ ❚❤❡ t❛❜❧✐♥❣ ❢❡❛t✉r❡s ♦❢ ❳❙❇ s✉♣♣♦rts ❝♦♥str❛✐♥ts✳ ✷ ❚❛❜❧❡❞ ❈♦♥str❛✐♥t ❍❛♥❞❧✐♥❣ ❘✉❧❡s ✐♠♣❧❡♠❡♥t❡❞ ✐♥ ❳❙❇✳ ✸ ❚❛❜❧❡❞ ❈♦♥str❛✐♥t ▲♦❣✐❝ Pr♦❣r❛♠♠✐♥❣ ✭❚❈▲P✮ ❢♦r ❞✐s❡q✉❛❧✐t② ❛♥❞ ✹ ❞✐✛❡r❡♥❝❡ ❝♦♥str❛✐♥ts✳ ❏♦❛q✉í♥ ❆r✐❛s ❍❡rr❡r♦ ❙❡♠✐♥❛r ❙❡r✐❡s ❙✸ ✶✶ ♥♦✈❡♠❜❡r ✷✵✶✹ ✺ ✴ ✶✻

  10. ❋❛✐❧✉r❡ ❚❛❜❧❡❞ ❈♦♥str❛✐♥t ▲♦❣✐❝ Pr♦❣r❛♠♠✐♥❣ ❜② ■♥t❡r♣♦❧❛t✐♦♥ ■t ❧❡❛r♥s ❢r♦♠ ❢❛✐❧❡❞ ❞❡r✐✈❛t✐♦♥s✳ ✶ ❚❤❡ ❢❛✐❧✉r❡ ❛❧❣♦r✐t❤♠ ❛✈♦✐❞s r❡❝♦♠♣✉t❡ r❡❞✉♥❞❛♥t ❢❛✐❧❡❞ ❞❡r✐✈❛t✐♦♥s✳ ✷ ■♥ ♣r❡s❡♥❝❡ ♦❢ r❡❝✉rs✐✈❡ ❝❧❛✉s❡s ✐t ✉s❡s ✐t❡r❛t✐✈❡ ❞❡❡♣❡♥✐♥❣ s❡❛r❝❤✿ ✸ ◮ ■♥ ❡❛❝❤ ✐t❡r❛t✐♦♥ ♣r♦❞✉❝❡s ❛ ❢❛✐❧❡❞ ❞❡r✐✈❛t✐♦♥s✳ ◮ ▲♦♦❦s ❢♦r ✐♥✈❛r✐❛♥t t♦ st♦♣ t❤❡ s❡❛r❝❤✳ ❆✈❛✐❧❛❜❧❡ ❛t ❤tt♣✿✴✴❝♦❞❡✳❣♦♦❣❧❡✳❝♦♠✴♣✴❢t❝❧♣ ❏♦❛q✉í♥ ❆r✐❛s ❍❡rr❡r♦ ❙❡♠✐♥❛r ❙❡r✐❡s ❙✸ ✶✶ ♥♦✈❡♠❜❡r ✷✵✶✹ ✻ ✴ ✶✻

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