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Apr 12, 2023 277 likes •720 views

r t rr ts rt rrt tr s

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SLIDE 1

❋♦r♠❛❧✐③✐♥❣ t❤❡ ❈♦♥❝✉rr❡♥❝② ❙❡♠❛♥t✐❝s ♦❢ ❛♥ ▲▲❱▼ ❋r❛❣♠❡♥t ❙♦❤❛♠ ❈❤❛❦r❛❜♦rt②✱ ❱✐❦t♦r ❱❛❢❡✐❛❞✐s

▼❛① P❧❛♥❝❦ ■♥st✐t✉t❡ ❢♦r ❙♦❢t✇❛r❡ ❙②st❡♠s ✭▼P■✲❙❲❙✮ ❈●❖ ✷✵✶✼

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SLIDE 2

▲▲❱▼ ❈♦♠♣✐❧❛t✐♦♥ ❈✴❈✰✰ ■❘ ①✽✻ P♦✇❡r

✿

❢♦r♠❛❧✐③❡❞ ❢♦r♠❛❧✐③❡❞ ✐♥❢♦r♠❛❧ ❢r♦♥t❡♥❞ ♦♣t ❝♦❞❡❣❡♥ ▲▲❱▼ ❘❡s✉❧t✿ ▲❛❝❦ ♦❢ ✉♥❞❡rst❛♥❞✐♥❣ ♦❢ t❤❡ ❝♦rr❡❝t♥❡ss ♦❢ t❤❡ tr❛♥s❢♦r♠❛t✐♦♥s

✷

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SLIDE 3

▲▲❱▼ ❈♦♥❝✉rr❡♥❝② ❈♦♠♣✐❧❛t✐♦♥ ❈✶✶ ■❘ ①✽✻ P♦✇❡r ❢♦r♠❛❧✐③❡❞ ❢♦r♠❛❧✐③❡❞ ✐♥❢♦r♠❛❧ ❢r♦♥t❡♥❞ ♦♣t ❝♦❞❡❣❡♥ ❈♦rr❡❝t♥❡ss ♦❢ t❤❡ tr❛♥s❢♦r♠❛t✐♦♥s ✐s ✉♥❝❧❡❛r

✸

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SLIDE 4

▲▲❱▼ ❈♦♥❝✉rr❡♥❝② ❈♦♠♣✐❧❛t✐♦♥ ❈✶✶ ■❘ ①✽✻ P♦✇❡r ❢♦r♠❛❧✐③❡❞ ❢♦r♠❛❧✐③❡❞ ✐♥❢♦r♠❛❧ ❢r♦♥t❡♥❞ ♦♣t ❝♦❞❡❣❡♥ ❈♦rr❡❝t♥❡ss ♦❢ t❤❡ tr❛♥s❢♦r♠❛t✐♦♥s ✐s ✉♥❝❧❡❛r

✸

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SLIDE 5

▲▲❱▼ ❈♦♥❝✉rr❡♥❝② ❈♦♠♣✐❧❛t✐♦♥ ❈✶✶ ■❘ ①✽✻ P♦✇❡r ❢♦r♠❛❧✐③❡❞ ❢♦r♠❛❧✐③❡❞ ✐♥❢♦r♠❛❧ ❢r♦♥t❡♥❞ ♦♣t ❝♦❞❡❣❡♥ ❈♦rr❡❝t♥❡ss ♦❢ t❤❡ tr❛♥s❢♦r♠❛t✐♦♥s ✐s ✉♥❝❧❡❛r

✸

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SLIDE 6

▲✐♠✐t❛t✐♦♥ ♦❢ ▲▲❱▼ ■♥❢♦r♠❛❧ ❈♦♥❝✉rr❡♥❝② t♦♦ ♠❛♥② ♦♣t✳ t♦♦ ❢❡✇ ♦♣t✳ ❜✉❣s ♥♦ ❡❧✐♠✐♥❛t✐♦♥✱ r❡♦r❞❡r✐♥❣ ♦❢ ❛t♦♠✐❝s ▲▲❱▼ ❝♦♠♣✐❧❡r ❱❛❧✐❞ ♦♣t ✐s r❡♠♦✈❡❞ ❜② ♦✈❡r✲r❡str✐❝t✐♦♥ ✐♥ ❜✉❣ ✜①

✹

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SLIDE 7

❚❤✐s ❲♦r❦ ❈✶✶ ■❘ ①✽✻ P♦✇❡r ❢♦r♠❛❧✐③❡❞ ❢♦r♠❛❧✐③❡❞ ✐♥❢♦r♠❛❧ ❢r♦♥t❡♥❞ ♦♣t ❝♦❞❡❣❡♥ ❋♦r♠❛❧✐③❡❞ ❢r❛❣♠❡♥t ♦❢ ▲▲❱▼ ❝♦♥❝✉rr❡♥❝② ✭❡①❝❡♣t ♠♦♥♦t♦♥✐❝✴r❡❧❛①❡❞ ❛❝❝❡ss❡s ❛♥❞ ❢❡♥❝❡s✮ Pr♦✈❡❞ ❝♦rr❡❝t♥❡ss ♦❢ tr❛♥s❢♦r♠❛t✐♦♥s

✺

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SLIDE 8

■♥❢♦r♠❛❧ ▲▲❱▼ ❈♦♥❝✉rr❡♥❝② ■♥❢♦r♠❛❧ t❡①t ✐♥ ▲❛♥❣✉❛❣❡ ❘❡❢❡r❡♥❝❡ ▼❛♥✉❛❧ ❋r❡q✉❡♥t r❡❢❡r❡♥❝❡s t♦ ❈✶✶ ❝♦♥❝✉rr❡♥❝② ✧❚❤✐s ♠♦❞❡❧ ✐s ✐♥s♣✐r❡❞ ❜② t❤❡ ❈✰✰✵① ♠❡♠♦r② ♠♦❞❡❧✳✧ ✧❚❤❡s❡ s❡♠❛♥t✐❝s ❛r❡ ❜♦rr♦✇❡❞ ❢r♦♠ ❏❛✈❛ ❛♥❞ ❈✰✰✵①✱ ❜✉t ❛r❡ s♦♠❡✇❤❛t ♠♦r❡ ❝♦❧❧♦q✉✐❛❧✳✧ ❚❤✐s ✐s ✐♥t❡♥❞❡❞ t♦ ♠❛t❝❤ s❤❛r❡❞ ✈❛r✐❛❜❧❡s ✐♥ ❈✴❈✰✰ . . .✧ . . .

✻

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SLIDE 9

❲❤② ♥♦t ❛❞♦♣t ❈✶✶ ❝♦♥❝✉rr❡♥❝②❄ ❙✉❜t❧❡ ❞✐✛❡r❡♥❝❡s ✲ ❆ ♣r♦❣r❛♠ ❤❛s ✇r✐t❡✲r❡❛❞ r❛❝❡ ♦♥ ♥♦♥✲❛t♦♠✐❝s ❈✶✶✿ t❤❡ ❜❡❤❛✈✐♦r ♦❢ t❤❡ ♣r♦❣r❛♠ ✐s ✉♥❞❡✜♥❡❞ ▲▲❱▼✿ ❞❡✜♥❡❞ ❜❡❤❛✈✐♦r❀ ∗ r❛❝② r❡❛❞ r❡t✉r♥s ✉♥❞❡❢(✉) X = ✶; ✐❢(X) t = ✹; ❡❧s❡ t = ✹; t = ✹ ? : ❈✶✶ ▲▲❱▼ ✗ ✲ ❙❡t ♦❢ ❛❧❧♦✇❡❞ ♦♣t✐♠✐③❛t✐♦♥s ❛r❡ ❞✐✛❡r❡♥t

✼

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SLIDE 10

❋♦r♠❛❧✐③❛t✐♦♥ ❜② ❊✈❡♥t ❙tr✉❝t✉r❡ ✲ Pr♦❣r❛♠ int X = ✵, Y = ✵; a = X; Y = ✶; b = Y ; X = ✶; ✲ ❊✈❡♥t ❙tr✉❝t✉r❡ ❲X✵ ❲Y ✵ ♣r♦❣r❛♠✲♦r❞❡r ❘X✵ r❡❛❞✲❢r♦♠ ❘Y ✵ ❲Y ✶ ❲X✶ ∼ ❘Y ✉ ❝♦♥✢✐❝t r❡❧❛t✐♦♥ ∼ ❘X✉ ❲Y ✶ ❲X✶

✽

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SLIDE 11

❊✈❡♥t ❙tr✉❝t✉r❡ ❈♦♥str✉❝t✐♦♥ int X = ✵, Y = ✵; a = X; Y = ✶; b = Y ; X = ✶; ❲X✵ ❲Y ✵ ♣r♦❣r❛♠✲♦r❞❡r ❘ ✵ r❡❛❞✲❢r♦♠ ❘ ✵ ❲ ✶ ❲ ✶ ❘❆❈❊ ❘ ✉ ❝♦♥✢✐❝t r❡❧❛t✐♦♥ ❘ ✉ ❲ ✶ ❲ ✶

✾

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SLIDE 12

❊✈❡♥t ❙tr✉❝t✉r❡ ❈♦♥str✉❝t✐♦♥ int X = ✵, Y = ✵; a = X; Y = ✶; b = Y ; X = ✶; ❲X✵ ❲Y ✵ ♣r♦❣r❛♠✲♦r❞❡r ❘X✵ r❡❛❞✲❢r♦♠ ❘ ✵ ❲ ✶ ❲ ✶ ❘❆❈❊ ❘ ✉ ❝♦♥✢✐❝t r❡❧❛t✐♦♥ ❘ ✉ ❲ ✶ ❲ ✶

✾

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SLIDE 13

❊✈❡♥t ❙tr✉❝t✉r❡ ❈♦♥str✉❝t✐♦♥ int X = ✵, Y = ✵; a = X; Y = ✶; b = Y ; X = ✶; ❲X✵ ❲Y ✵ ♣r♦❣r❛♠✲♦r❞❡r ❘X✵ r❡❛❞✲❢r♦♠ ❘Y ✵ ❲ ✶ ❲ ✶ ❘❆❈❊ ❘ ✉ ❝♦♥✢✐❝t r❡❧❛t✐♦♥ ❘ ✉ ❲ ✶ ❲ ✶

✾

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SLIDE 14

❊✈❡♥t ❙tr✉❝t✉r❡ ❈♦♥str✉❝t✐♦♥ int X = ✵, Y = ✵; a = X; Y = ✶; b = Y ; X = ✶; ❲X✵ ❲Y ✵ ♣r♦❣r❛♠✲♦r❞❡r ❘X✵ r❡❛❞✲❢r♦♠ ❘Y ✵ ❲Y ✶ ❲X✶ ❘❆❈❊ ❘ ✉ ❝♦♥✢✐❝t r❡❧❛t✐♦♥ ❘ ✉ ❲ ✶ ❲ ✶

✾

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SLIDE 15

❊✈❡♥t ❙tr✉❝t✉r❡ ❈♦♥str✉❝t✐♦♥ int X = ✵, Y = ✵; a = X; Y = ✶; b = Y ; X = ✶; ❲X✵ ❲Y ✵ ♣r♦❣r❛♠✲♦r❞❡r ❘X✵ r❡❛❞✲❢r♦♠ ❘Y ✵ ❲Y ✶ ❲X✶ ❘❆❈❊ ❘ ✉ ❝♦♥✢✐❝t r❡❧❛t✐♦♥ ❘ ✉ ❲ ✶ ❲ ✶

✾

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SLIDE 16

❊✈❡♥t ❙tr✉❝t✉r❡ ❈♦♥str✉❝t✐♦♥ int X = ✵, Y = ✵; a = X; Y = ✶; b = Y ; X = ✶; ❲X✵ ❲Y ✵ ♣r♦❣r❛♠✲♦r❞❡r ❘X✵ r❡❛❞✲❢r♦♠ ❘Y ✵ ❲Y ✶ ❲X✶ ❘❆❈❊ ∼ ❘Y ✉ ❝♦♥✢✐❝t r❡❧❛t✐♦♥ ❘ ✉ ❲ ✶ ❲ ✶

✾

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SLIDE 17

❊✈❡♥t ❙tr✉❝t✉r❡ ❈♦♥str✉❝t✐♦♥ int X = ✵, Y = ✵; a = X; Y = ✶; b = Y ; X = ✶; ❲X✵ ❲Y ✵ ♣r♦❣r❛♠✲♦r❞❡r ❘X✵ r❡❛❞✲❢r♦♠ ❘Y ✵ ❲Y ✶ ❲X✶ ❘❆❈❊ ∼ ❘Y ✉ ❝♦♥✢✐❝t r❡❧❛t✐♦♥ ∼ ❘X✉ ❲ ✶ ❲ ✶

✾

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SLIDE 18

❊✈❡♥t ❙tr✉❝t✉r❡ ❈♦♥str✉❝t✐♦♥ int X = ✵, Y = ✵; a = X; Y = ✶; b = Y ; X = ✶; ❲X✵ ❲Y ✵ ♣r♦❣r❛♠✲♦r❞❡r ❘X✵ r❡❛❞✲❢r♦♠ ❘Y ✵ ❲Y ✶ ❲X✶ ❘❆❈❊ ∼ ❘Y ✉ ❝♦♥✢✐❝t r❡❧❛t✐♦♥ ∼ ❘X✉ ❲Y ✶ ❲X✶

✾

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SLIDE 19

Pr♦❣r❛♠ ❇❡❤❛✈✐♦r int X = ✵, Y = ✵; a = X; Y = ✶; b = Y ; X = ✶; a = b = ✶ ? ✓ ✵ ✵ ✶ ✶ ✵ ✵ ✶ ✶

✶✵

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SLIDE 20

Pr♦❣r❛♠ ❇❡❤❛✈✐♦r int X = ✵, Y = ✵; a = X; Y = ✶; b = Y ; X = ✶; a = b = ✶ ? ✓ int X = ✵, Y = ✵; a = X; Y = ✶; b = Y ; X = ✶; ❀ int X = ✵, Y = ✵; Y = ✶; a = X; X = ✶; b = Y ;

✶✵

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SLIDE 21

❊①❡❝✉t✐♦♥ ❢r♦♠ ❊✈❡♥t ❙tr✉❝t✉r❡ int X = ✵, Y = ✵; a = X; Y = ✶; b = Y ; X = ✶; ❲X✵ ❲Y ✵ ❘X✵ ❘Y ✵ ❲Y ✶ ❲X✶ ∼ ❘Y ✉ ∼ ❘X✉ ❲Y ✶ ❲X✶

✉ ✶✱ ✉ ✶

✶✶

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SLIDE 22

❊①❡❝✉t✐♦♥ ❢r♦♠ ❊✈❡♥t ❙tr✉❝t✉r❡ int X = ✵, Y = ✵; a = X; Y = ✶; b = Y ; X = ✶; ❲X✵ ❲Y ✵ ❘X✵ ❘Y ✵ ❲Y ✶ ❲X✶ ∼ ❘Y ✉ ∼ ❘X✉ ❲Y ✶ ❲X✶

✉ ✶✱ ✉ ✶

✶✶

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SLIDE 23

❊①❡❝✉t✐♦♥ ❢r♦♠ ❊✈❡♥t ❙tr✉❝t✉r❡ int X = ✵, Y = ✵; a = X; Y = ✶; b = Y ; X = ✶; ❲X✵ ❲Y ✵ ❘X✵ ❘Y ✵ ❲Y ✶ ❲X✶ ∼ ❘Y ✉ ∼ ❘X✉ ❲Y ✶ ❲X✶

a = ✉ = ✶✱ b = ✉ = ✶

✶✶

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SLIDE 24

❆s♣❡❝ts ♦❢ ❊✈❡♥t ❙tr✉❝t✉r❡ ✲ Pr♦♣♦s❡❞ ❢♦r♠❛❧✐③❛t✐♦♥ ❤❛♥❞❧❡s ▼❡♠♦r② ♦♣❡r❛t✐♦♥s✿ ❧♦❛❞✱ st♦r❡✱ ❈❆❙ ▼❡♠♦r② ♦r❞❡rs✿ ♥♦♥✲❛t♦♠✐❝✱ ❛❝q✉✐r❡✱ r❡❧❡❛s❡✱ ❛❝q✉✐r❡❴r❡❧❡❛s❡✱ s❡q✉❡♥t✐❛❧❧② ❝♦♥s✐st❡♥t ✭❙❈✮ ✲ Pr❡s❡r✈❡s ❝♦♥s✐st❡♥❝② ❛t ❡❛❝❤ ❝♦♥str✉❝t✐♦♥ st❡♣ ✲ ▼✉❧t✐♣❧❡ ❝♦♥s✐st❡♥t ❡✈❡♥t str✉❝t✉r❡s ♣❡r ♣r♦❣r❛♠

✶✷

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SLIDE 25

❚r❛♥s❢♦r♠❛t✐♦♥ ❈♦rr❡❝t♥❡ss ❈✶✶ ■❘ ①✽✻ P♦✇❡r ❢r♦♥t❡♥❞ ♦♣t ❝♦❞❡❣❡♥ ❇❡❤❛✈✐♦r(Ptgt) ⊆ ❇❡❤❛✈✐♦r(Psrc) ❇❡❤❛✈✐♦r✳ ✜♥❛❧ ✈❛❧✉❡s ♦❜s❡r✈❡❞ ✐♥ ❡❛❝❤ ❧♦❝❛t✐♦♥ ❇❡❤❛✈✐♦r ❇❡❤❛✈✐♦r

✶✸

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SLIDE 26

❚r❛♥s❢♦r♠❛t✐♦♥ ❈♦rr❡❝t♥❡ss ❈✶✶ ■❘ ①✽✻ P♦✇❡r ❢r♦♥t❡♥❞ ♦♣t ❝♦❞❡❣❡♥ ❇❡❤❛✈✐♦r(Ptgt) ⊆ ❇❡❤❛✈✐♦r(Psrc) ❇❡❤❛✈✐♦r✳ ✜♥❛❧ ✈❛❧✉❡s ♦❜s❡r✈❡❞ ✐♥ ❡❛❝❤ ❧♦❝❛t✐♦♥ ⇑ ❇❡❤❛✈✐♦r(Gtgt) ⊆ ❇❡❤❛✈✐♦r(Gsrc)

✶✸

slide-27
SLIDE 27

▲▲❱▼ ❊❧✐♠✐♥❛t✐♦♥ ❖♣t✐♠✐③❛t✐♦♥s ▲▲❱▼ ♣❡r❢♦r♠s t❤❡s❡ ❡❧✐♠✐♥❛t✐♦♥s ❆❞❥❛❝❡♥t r❡❛❞ ❛❢t❡r r❡❛❞✴✇r✐t❡ ❡❧✐♠✐♥❛t✐♦♥ a = Xo; b = X♥❛; ❀ a = Xo; b = a; Xo = v; b = X♥❛; ❀ Xo = v; b = v; ❆❞❥❛❝❡♥t ♦✈❡r✇r✐tt❡♥ ✇r✐t❡ ❡❧✐♠✐♥❛t✐♦♥ X♥❛ = v ′; X♥❛ = v; ❀ X♥❛ = v; ◆♦♥✲❛❞❥❛❝❡♥t ♦✈❡r✇r✐tt❡♥ ✇r✐t❡ ❡❧✐♠✐♥❛t✐♦♥ X♥❛ = v ′; ❈; X♥❛ = v; ❀ ❈; X♥❛ = v;

✇❤❡r❡ r❡❧✲❛❝q✲♣❛✐r / ∈ ❈

✶✹

slide-28
SLIDE 28

❆❧s♦ Pr♦✈❡❞✳✳✳ ▲▲❱▼ ❞♦❡s ◆❖❚ ♣❡r❢♦r♠ t❤❡s❡ ❡❧✐♠✐♥❛t✐♦♥s ❆❞❥❛❝❡♥t r❡❛❞ ❛❢t❡r r❡❛❞✴✇r✐t❡ ❡❧✐♠✐♥❛t✐♦♥ a = X❛❝q; b = X❛❝q; ❀ a = X❛❝q; b = a; a = Xs❝; b = X(❛❝q|s❝); ❀ a = Xs❝; b = a; Xr❡❧ = v; b = X❛❝q; ❀ Xr❡❧ = v; b = v; Xs❝ = v; b = X(❛❝q|s❝); ❀ Xs❝ = v; b = v; ❆❞❥❛❝❡♥t ♦✈❡r✇r✐tt❡♥ ✇r✐t❡ ❡❧✐♠✐♥❛t✐♦♥ Xr❡❧ = v ′; Xr❡❧ = v; ❀ Xr❡❧ = v; X(r❡❧|s❝) = v ′; Xs❝ = v; ❀ Xs❝ = v; ◆♦♥✲❛❞❥❛❝❡♥t r❡❛❞ ❛❢t❡r ✇r✐t❡ ❡❧✐♠✐♥❛t✐♦♥

♥❛

❈

♥❛ ♥❛

❈

✇❤❡r❡ r❡❧✲❛❝q✲♣❛✐r ❈

✶✺

slide-29
SLIDE 29

❆❧s♦ Pr♦✈❡❞✳✳✳ ▲▲❱▼ ❞♦❡s ◆❖❚ ♣❡r❢♦r♠ t❤❡s❡ ❡❧✐♠✐♥❛t✐♦♥s ❆❞❥❛❝❡♥t r❡❛❞ ❛❢t❡r r❡❛❞✴✇r✐t❡ ❡❧✐♠✐♥❛t✐♦♥ a = X❛❝q; b = X❛❝q; ❀ a = X❛❝q; b = a; a = Xs❝; b = X(❛❝q|s❝); ❀ a = Xs❝; b = a; Xr❡❧ = v; b = X❛❝q; ❀ Xr❡❧ = v; b = v; Xs❝ = v; b = X(❛❝q|s❝); ❀ Xs❝ = v; b = v; ❆❞❥❛❝❡♥t ♦✈❡r✇r✐tt❡♥ ✇r✐t❡ ❡❧✐♠✐♥❛t✐♦♥ Xr❡❧ = v ′; Xr❡❧ = v; ❀ Xr❡❧ = v; X(r❡❧|s❝) = v ′; Xs❝ = v; ❀ Xs❝ = v; ◆♦♥✲❛❞❥❛❝❡♥t r❡❛❞ ❛❢t❡r ✇r✐t❡ ❡❧✐♠✐♥❛t✐♦♥ X♥❛ = v; ❈; a = X♥❛; ❀ X♥❛ = v; ❈; a = v;

✇❤❡r❡ r❡❧✲❛❝q✲♣❛✐r / ∈ ❈

✶✺

slide-30
SLIDE 30

▲▲❱▼ ❘❡♦r❞❡r✐♥❣s ▲▲❱▼ ♣❡r❢♦r♠s✭✮ t❤❡s❡ r❡♦r❞❡r✐♥❣s a; b ❀ b; a ↓ a \ b → (❙t|▲❞)♥❛ ❙tr❡❧ ▲❞❛❝q ▲❞s❝ ❯(❛❝q❴r❡❧|s❝) (❙t|▲❞)♥❛

  • ✲
  • ✲

❙tr❡❧

  • ✲

✲ ✲ ✲ ❙ts❝

  • ✲

✲ ✲ ✲ ▲❞❛❝q ✲ ✲ ✲ ✲ ✲ ❯(❛❝q❴r❡❧|s❝) ✲ ✲ ✲ ✲ ✲ Xr❡❧ = v; Y♥❛ = v ′; ❀ Y♥❛ = v ′; Xr❡❧ = v❀

  • ✶✻
slide-31
SLIDE 31

▲▲❱▼ ❘❡♦r❞❡r✐♥❣s ▲▲❱▼ r❡str✐❝ts✭×✮ t❤❡s❡ r❡♦r❞❡r✐♥❣s a; b ❀ b; a ↓ a \ b → (❙t|▲❞)♥❛ ❙tr❡❧ ▲❞❛❝q ▲❞s❝ ❯(❛❝q❴r❡❧|s❝) (❙t|▲❞)♥❛

  • ×
  • ×

❙tr❡❧

  • ×

✲ ✲ × ❙ts❝

  • ×

✲ × × ▲❞❛❝q × × × × × ❯(❛❝q❴r❡❧|s❝) × × × × × Y♥❛ = v ′; Xr❡❧ = v; ❀ Xr❡❧ = v; Y♥❛ = v ′❀ ×

✶✼

slide-32
SLIDE 32

❆❧s♦ ❆♥❛❧②③❡❞✳✳✳ ▲▲❱▼ ❞♦❡s ◆❖❚ ♣❡r❢♦r♠ t❤❡s❡ r❡♦r❞❡r✐♥❣s a; b ❀ b; a ↓ a \ b → (❙t|▲❞)♥❛ ❙tr❡❧ ▲❞❛❝q ▲❞s❝ ❯(❛❝q❴r❡❧|s❝) (❙t|▲❞)♥❛

  • ×
  • ×

❙tr❡❧

  • ×
  • ×

❙ts❝

  • ×
  • ×

× ▲❞❛❝q × × × × × ❯(❛❝q❴r❡❧|s❝) × × × × × Xr❡❧ = v; t = Y❛❝q; ❀ t = Y❛❝q; Xr❡❧ = v❀

  • ✶✽
slide-33
SLIDE 33

❈✶✶ t♦ ▲▲❱▼ ▼❛♣♣✐♥❣ ❈♦rr❡❝t♥❡ss ❈✶✶ ■❘ ①✽✻ P♦✇❡r ❝❧❛♥❣ ✲ ▲▲❱▼ ❤❛s ♦♣❡r❛t✐♦♥s ✭▲❞✴❙t✴❈❆❙✮ ❛♥❞ ♠❡♠♦r② ♦r❞❡rs ✭♥❛✴r❡❧✴❛❝q✴❛❝q❴r❡❧✴❙❈✮ s✐♠✐❧❛r t♦ ❈✶✶✳ ✲ ▲▲❱▼ ♠♦❞❡❧ ✐s str♦♥❣❡r t❤❛♥ ❈✶✶✳

✶✾

slide-34
SLIDE 34

▲▲❱▼ t♦ ❆r❝❤✐t❡❝t✉r❡ ▼❛♣♣✐♥❣ ❈♦rr❡❝t♥❡ss ❈✶✶ ■❘ ①✽✻ P♦✇❡r ❝♦❞❡❣❡♥ (▲▲❱▼ ❀ ①✽✻/P♦✇❡r) = (❈✶✶ ❀ ①✽✻/P♦✇❡r) Pr♦✈❡❞ ❝♦rr❡❝t♥❡ss ♦❢ t❤❡s❡ ♠❛♣♣✐♥❣s ▲▲❱▼ t♦ ❙❈ ▲▲❱▼ t♦ ❙P♦✇❡r ❊♥s✉r❡ ❝♦rr❡❝t♥❡ss ♦❢ ▲▲❱▼ ❀ ①✽✻✴P♦✇❡r ✭r❡s✉❧ts ❢r♦♠ ▲❛❤❛✈ ✫ ❱❛❢❡✐❛❞✐s✳ ❋▼✬✶✻✮

✷✵

slide-35
SLIDE 35

❲❤❛t✬s ▼♦r❡ ✐♥ ❚❤❡ P❛♣❡r ❊✈❡♥t str✉❝t✉r❡ ❝♦♥str✉❝t✐♦♥ r✉❧❡s ❈♦♥s✐st❡♥❝② ❝♦♥str❛✐♥ts ❉❛t❛ r❛❝❡ ❢r❡❡❞♦♠ ✭❉❘❋✮ t❤❡♦r❡♠s ▼♦r❡ tr❛♥s❢♦r♠❛t✐♦♥s ❙♣❡❝✉❧❛t✐✈❡ ❧♦❛❞ ❙tr❡♥❣t❤❡♥✐♥❣ ♠❡♠♦r② ♦r❞❡r ♦❢ ❛❝❝❡ss❡s Pr♦♦❢s✿ ❤tt♣✿✴✴♣❧✈✳♠♣✐✲s✇s✳♦r❣✴❧❧✈♠❝s✴

✷✶

slide-36
SLIDE 36

❲❤❛t✬s ▼♦r❡ ✐♥ ❚❤❡ P❛♣❡r ❊✈❡♥t str✉❝t✉r❡ ❝♦♥str✉❝t✐♦♥ r✉❧❡s ❈♦♥s✐st❡♥❝② ❝♦♥str❛✐♥ts ❉❛t❛ r❛❝❡ ❢r❡❡❞♦♠ ✭❉❘❋✮ t❤❡♦r❡♠s ▼♦r❡ tr❛♥s❢♦r♠❛t✐♦♥s ❙♣❡❝✉❧❛t✐✈❡ ❧♦❛❞ ❙tr❡♥❣t❤❡♥✐♥❣ ♠❡♠♦r② ♦r❞❡r ♦❢ ❛❝❝❡ss❡s Pr♦♦❢s✿ ❤tt♣✿✴✴♣❧✈✳♠♣✐✲s✇s✳♦r❣✴❧❧✈♠❝s✴

✷✶

slide-37
SLIDE 37

❲❤❛t✬s ▼♦r❡ ✐♥ ❚❤❡ P❛♣❡r ❊✈❡♥t str✉❝t✉r❡ ❝♦♥str✉❝t✐♦♥ r✉❧❡s ❈♦♥s✐st❡♥❝② ❝♦♥str❛✐♥ts ❉❛t❛ r❛❝❡ ❢r❡❡❞♦♠ ✭❉❘❋✮ t❤❡♦r❡♠s ▼♦r❡ tr❛♥s❢♦r♠❛t✐♦♥s ❙♣❡❝✉❧❛t✐✈❡ ❧♦❛❞ ❙tr❡♥❣t❤❡♥✐♥❣ ♠❡♠♦r② ♦r❞❡r ♦❢ ❛❝❝❡ss❡s Pr♦♦❢s✿ ❤tt♣✿✴✴♣❧✈✳♠♣✐✲s✇s✳♦r❣✴❧❧✈♠❝s✴

✷✶

slide-38
SLIDE 38

❲❤❛t✬s ▼♦r❡ ✐♥ ❚❤❡ P❛♣❡r ❊✈❡♥t str✉❝t✉r❡ ❝♦♥str✉❝t✐♦♥ r✉❧❡s ❈♦♥s✐st❡♥❝② ❝♦♥str❛✐♥ts ❉❛t❛ r❛❝❡ ❢r❡❡❞♦♠ ✭❉❘❋✮ t❤❡♦r❡♠s ▼♦r❡ tr❛♥s❢♦r♠❛t✐♦♥s ❙♣❡❝✉❧❛t✐✈❡ ❧♦❛❞ ❙tr❡♥❣t❤❡♥✐♥❣ ♠❡♠♦r② ♦r❞❡r ♦❢ ❛❝❝❡ss❡s Pr♦♦❢s✿ ❤tt♣✿✴✴♣❧✈✳♠♣✐✲s✇s✳♦r❣✴❧❧✈♠❝s✴

✷✶

slide-39
SLIDE 39

❲❤❛t✬s ▼♦r❡ ✐♥ ❚❤❡ P❛♣❡r ❊✈❡♥t str✉❝t✉r❡ ❝♦♥str✉❝t✐♦♥ r✉❧❡s ❈♦♥s✐st❡♥❝② ❝♦♥str❛✐♥ts ❉❛t❛ r❛❝❡ ❢r❡❡❞♦♠ ✭❉❘❋✮ t❤❡♦r❡♠s ▼♦r❡ tr❛♥s❢♦r♠❛t✐♦♥s ❙♣❡❝✉❧❛t✐✈❡ ❧♦❛❞ ❙tr❡♥❣t❤❡♥✐♥❣ ♠❡♠♦r② ♦r❞❡r ♦❢ ❛❝❝❡ss❡s Pr♦♦❢s✿ ❤tt♣✿✴✴♣❧✈✳♠♣✐✲s✇s✳♦r❣✴❧❧✈♠❝s✴

✷✶

slide-40
SLIDE 40

❈♦♥❝❧✉s✐♦♥s ✫ ❋✉t✉r❡ ❉✐r❡❝t✐♦♥s ✲ ❈♦♥tr✐❜✉t✐♦♥s ❈✶✶ ■❘ ①✽✻ P♦✇❡r ❋♦r♠❛❧✐③❡❞ ❉❘❋ ❚❤❡♦r❡♠s ❝❧❛♥❣ ♦♣t ❝♦❞❡❣❡♥ ❝♦❞❡❣❡♥ ✲ ❋✉t✉r❡✿ ❡①t❡♥❞ t❤❡ ▲▲❱▼ ❝♦♥❝✉rr❡♥❝② ♠♦❞❡❧ ❲✐t❤ r❡❧❛①❡❞ ❛❝❝❡ss❡s ❛♥❞ ❢❡♥❝❡s Pr♦✈❡✴❞✐s♣r♦✈❡ ♠♦r❡ ♦♣t✐♠✐③❛t✐♦♥s ▼❡❝❤❛♥✐③❡ t❤❡ ❢♦r♠❛❧✐③❛t✐♦♥ ❚❤❛♥❦ ❨♦✉ ✦

✷✷

slide-41
SLIDE 41

❇❛❝❦✉♣ ❙❧✐❞❡s

✷✸

slide-42
SLIDE 42

❊①❛♠♣❧❡s int X = ✵, Y = ✵; a = X; Y = ✶; b = Y ; X = ✶; a = b = ✶ ✭▲❇✮ int X = ✵, Y = ✵; a = X; ✐❢(a == ✶) Y = ✶; b = Y ; ✐❢(b == ✶) X = ✶; a = b = ✶ ✗ ✭❈❨❈✮

✷✹

slide-43
SLIDE 43

▲▲❱▼ ✈s ❈✶✶ ▲▲❱▼

❬❲X✵, ❲Y ✵❪ ❘X✵ ❘Y ✵ ❲Y ✶ ❲Y ✶ ∼ ❘Y ✉ ❲X✶ ∼ ❲Y ✶ ❘X✉ ❲Y ✶ ✭▲❇✮ ❬❲X✵, ❲Y ✵❪ ❘X✵ ❘Y ✵ ✭❈❨❈✮

❈✶✶

❬❲X✵, ❲Y ✵❪ ❘Y ✶ ❲X✶ ❘X✶ ❲Y ✶ ✭▲❇ ✫ ❈❨❈✮

✷✺

slide-44
SLIDE 44

❙♣❡❝✉❧❛t✐✈❡ ▲♦❛❞ ▲▲❱▼ ♣❡r❢♦r♠s s♣❡❝✉❧❛t✐✈❡ ❧♦❛❞ X = ✶; ✐❢(flag){ a = X; } ❀ X = ✶; t = X; // ✉♥❞❡❢ ✐❢(flag){ a = t; }

✷✻