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Algoritmica Esercizi su relazioni di ricorrenza

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(1)

Algoritmica

Esercizi su relazioni di ricorrenza

G. Prencipe

giuseppe.prencipe@unipi.it

(2)

Il Master Theorem

Si applica a ricorrenze della forma T(n) = a T(n/b) + f (n)

dove a ≥ 1 , b > 1, e f è asintoticamente positiva

(3)

I tre casi di applicazione

Confronta f (n) con n logba :

1. f (n) = O(n logba – ε ) per qualche costante ε > 0 .

f (n) cresce polinomialmente più lentamente di n logba (di un fattore n ε )

Soluzione: T(n) = Θ(n logba )

T(n) = a T(n/b) + f (n)

(4)

Confronta f (n) con n logba :

2. f (n) = Θ(n logba lg k n) per qualche costante k ≥ 0

f (n) e n logba crescono allo stesso modo

Soluzione: T(n) = Θ(n logba lg k+1 n)

T(n) = a T(n/b) + f (n)

I tre casi di applicazione

Nota: questa è la generalizzazione di

f (n) = Θ(n logba ) → T(n) = Θ(n logba lgn)

(5)

Confronta f (n) con n logba :

3. f (n) = Ω(n logba + ε ) per qualche costante ε > 0

f (n) cresce polinomialmente più veloce di n logba (di un fattore n ε ), e

f (n) soddisfa la condizione che

a f (n/b) ≤ c f (n) per qualche costante c < 1

Soluzione: T(n) = Θ( f (n) ) .

T(n) = a T(n/b) + f (n)

I tre casi di applicazione

(6)

Esercizio 1

T(n) = 4T(n/2) + n

Master Theorem….

(7)

Esercizio 1

T(n) = 4T(n/2) + n

a = 4, b = 2

(8)

Esercizio 1

T(n) = 4T(n/2) + n

a = 4, b = 2 n logba = n 2 e f (n) = n

CASO ????

(9)

Esercizio 1

T(n) = 4T(n/2) + n

a = 4, b = 2 n logba = n 2 e f (n) = n

CASO 1!

(10)

Esercizio 1

T(n) = 4T(n/2) + n

a = 4, b = 2 n logba = n 2 e f (n) = n CASO 1: f (n) = O(n 2 – ε ) per ε = 1

∴ T(n) = Θ(n 2 )

(11)

Esercizio 2

T(n) = 4T(n/2) + n 2

Master Theorem….

(12)

Esercizio 2

T(n) = 4T(n/2) + n 2

a = 4, b = 2 n logba = n 2 e f (n) = n 2

(13)

Esercizio 2

T(n) = 4T(n/2) + n 2

a = 4, b = 2 n logba = n 2 e f (n) = n 2

CASO ????

(14)

Esercizio 2

T(n) = 4T(n/2) + n 2

a = 4, b = 2 n logba = n 2 e f (n) = n 2 CASE 2: f (n) = Θ(n 2 lg 0 n), k = 0

∴ T(n) = Θ(n 2 lg n)

(15)

Esercizio 3

T(n) = 4T(n/2) + n 3

Master Theorem….

(16)

Esercizio 3

T(n) = 4T(n/2) + n 3

a = 4, b = 2 n logba = n 2 e f (n) = n 3

(17)

Esercizio 3

T(n) = 4T(n/2) + n 3

a = 4, b = 2 n logba = n 2 e f (n) = n 3

CASO ????

(18)

Esercizio 3

T(n) = 4T(n/2) + n 3

a = 4, b = 2 n logba = n 2 e f (n) = n 3

CASO 3: f (n) = Ω(n 2 + ε ) per ε = 1

(19)

Esercizio 3

T(n) = 4T(n/2) + n 3

a = 4, b = 2 n logba = n 2 e f (n) = n 3 CASO 3: f (n) = Ω(n 2 + ε ) per ε = 1

….basta così????

(20)

Esercizio 3

T(n) = 4T(n/2) + n 3

a = 4, b = 2 n logba = n 2 e f (n) = n 3 CASO 3: f (n) = Ω(n 2 + ε ) per ε = 1

e 4(n/2) 3 ≤ cn 3 per c = 1/2

∴ T(n) = Θ(n 3 )

a f (n/b) ≤ c f (n) per qualche

costante c < 1

(21)

Esercizio 4

T(n) = 4T(n/2) + n 2 /log n

Risolvere….

(22)

Esercizio 4 Proviamo con il MT….

a = 4, b = 2 n logba = n 2 e f (n) = n 2 /log n

T(n) = 4T(n/2) + n 2 /log n

(23)

Esercizio 4 Proviamo con il MT….

Si può applicare il Master Theorem????

a = 4, b = 2 n logba = n 2 e f (n) = n 2 /log n

T(n) = 4T(n/2) + n 2 /log n

(24)

Esercizio 4

T(n) = 4T(n/2) + n 2 /log n

Proviamo con il MT….

Si può applicare il Master Theorem????

a = 4, b = 2 n logba = n 2 e f (n) = n 2 /log n

n logba = n 2 vs n 2 /log n

(25)

Esercizio 4

T(n) = 4T(n/2) + n 2 /log n

Proviamo con il MT….

Si può applicare il Master Theorem????

a = 4, b = 2 n logba = n 2 e f (n) = n 2 /log n

Quali casi possiamo sicuramente escludere?

n logba = n 2 vs n 2 /log n

(26)

Esercizio 4

T(n) = 4T(n/2) + n 2 /log n

Proviamo con il MT….

Si può applicare il Master Theorem????

a = 4, b = 2 n logba = n 2 e f (n) = n 2 /log n

n 2 /log n = O(n 2 )

Quali casi possiamo sicuramente escludere?

n logba = n 2 vs n 2 /log n

(27)

Esercizio 4

T(n) = 4T(n/2) + n 2 /log n

Proviamo con il MT….

Si può applicare il Master Theorem????

a = 4, b = 2 n logba = n 2 e f (n) = n 2 /log n

Casi 2 e 3 NO!!!!

n logba = n 2 vs n 2 /log n

n 2 /log n = O(n 2 )

(28)

Esercizio 4

T(n) = 4T(n/2) + n 2 /log n

Proviamo con il MT….

Si può applicare il Master Theorem????

a = 4, b = 2 n logba = n 2 e f (n) = n 2 /lg n

n ε ???? log n, ∀ ε > 0

Caso 1 (n 2-ε ), osserva:

n logba = n 2 vs n 2 /log n

(29)

Esercizio 4

T(n) = 4T(n/2) + n 2 /log n

Proviamo con il MT….

Si può applicare il Master Theorem????

a = 4, b = 2 n logba = n 2 e f (n) = n 2 /lg n

n ε = ω(log n), ∀ ε > 0

Caso 1 (n 2-ε ), osserva:

n logba = n 2 vs n 2 /log n

(30)

Esercizio 4

T(n) = 4T(n/2) + n 2 /log n

Proviamo con il MT….

Si può applicare il Master Theorem????

a = 4, b = 2 n logba = n 2 e f (n) = n 2 /lg n

n ε = ω(log n), ∀ ε > 0

n 2 /n ε ???? n 2 /log n

n logba = n 2 vs n 2 /log n

(31)

Esercizio 4

T(n) = 4T(n/2) + n 2 /log n

Proviamo con il MT….

Si può applicare il Master Theorem????

a = 4, b = 2 n logba = n 2 e f (n) = n 2 /lg n

n ε = ω(log n), ∀ ε > 0 n 2 /n ε < n 2 /log n

Caso 1 NO!!!!

n logba = n 2 vs n 2 /log n

(32)

Esercizio 4

T(n) = 4T(n/2) + n 2 /log n

Proviamo con il MT….

Si può applicare il Master Theorem????

a = 4, b = 2 n logba = n 2 e f (n) = n 2 /lg n

n ε = ω(log n), ∀ ε > 0 Nessun Caso!!!!

n logba = n 2 vs n 2 /log n

(33)

Esercizio 4

T(n) = 4T(n/2) + n 2 /log n

E quindi????

(34)

Esercizio 4

T(n) = 4T(n/2) + n 2 /log n

Svolgete….

(35)

Esercizio 4 Svolgete….

4T (n/2) + log n n 2 =

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T (n) =

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(36)

Esercizio 4 Svolgete….

4T (n/2) + log n n 2 =

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4(4T ( n 4 ) + log(n/2) ( n 2 ) 2 ) + log n n 2 =

<latexit sha1_base64="nQgUTqt6nTF1NMUyED8oMR++SH8=">AAACOnicbVDNTgIxGOziH+If6tFLI5hATHB3Q6IeNCRePKIBIQEk3dKFhm5303ZNyGbfy4sv4c2LFw9qvPoAFtigopM0mc7Ml/YbJ2BUKtN8MlILi0vLK+nVzNr6xuZWdnvnRvqhwKSOfeaLpoMkYZSTuqKKkWYgCPIcRhrO8GLsN+6IkNTnNTUKSMdDfU5dipHSUjd7nYflQrlWaLsC4YjHUTkuwkM4vX6rdly8teOozfw+LPAju6hTsxifWTw+g/luNmeWzAngX2IlJAcSVLvZx3bPx6FHuMIMSdmyzEB1IiQUxYzEmXYoSYDwEPVJS1OOPCI70WT3GB5opQddX+jDFZyoPyci5Ek58hyd9JAayHlvLP7ntULlnnQiyoNQEY6nD7khg8qH4yJhjwqCFRtpgrCg+q8QD5DuQ+m6M7oEa37lv6Rul05L1pWdq5wnbaTBHtgHBWCBY1ABl6AK6gCDe/AMXsGb8WC8GO/GxzSaMpKZXfALxucXwuOqkQ==</latexit><latexit sha1_base64="nQgUTqt6nTF1NMUyED8oMR++SH8=">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</latexit><latexit sha1_base64="nQgUTqt6nTF1NMUyED8oMR++SH8=">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</latexit><latexit sha1_base64="nQgUTqt6nTF1NMUyED8oMR++SH8=">AAACOnicbVDNTgIxGOziH+If6tFLI5hATHB3Q6IeNCRePKIBIQEk3dKFhm5303ZNyGbfy4sv4c2LFw9qvPoAFtigopM0mc7Ml/YbJ2BUKtN8MlILi0vLK+nVzNr6xuZWdnvnRvqhwKSOfeaLpoMkYZSTuqKKkWYgCPIcRhrO8GLsN+6IkNTnNTUKSMdDfU5dipHSUjd7nYflQrlWaLsC4YjHUTkuwkM4vX6rdly8teOozfw+LPAju6hTsxifWTw+g/luNmeWzAngX2IlJAcSVLvZx3bPx6FHuMIMSdmyzEB1IiQUxYzEmXYoSYDwEPVJS1OOPCI70WT3GB5opQddX+jDFZyoPyci5Ek58hyd9JAayHlvLP7ntULlnnQiyoNQEY6nD7khg8qH4yJhjwqCFRtpgrCg+q8QD5DuQ+m6M7oEa37lv6Rul05L1pWdq5wnbaTBHtgHBWCBY1ABl6AK6gCDe/AMXsGb8WC8GO/GxzSaMpKZXfALxucXwuOqkQ==</latexit>

T (n) =

<latexit sha1_base64="lAGXaeOUzfys611n7ty4ASveC6o=">AAAB73icbVA9TwJBEJ3DL8Qv1NJmI5hgQ+5o1EJDYmOJCScYuJC9ZQ827O5ddvdMCOFX2FiosfXv2PlvXOAKBV8yyct7M5mZFyacaeO6305ubX1jcyu/XdjZ3ds/KB4ePeg4VYT6JOaxaodYU84k9Q0znLYTRbEIOW2Fo9uZ33qiSrNYNs04oYHAA8kiRrCx0mO5WZHn6BqVe8WSW3XnQKvEy0gJMjR6xa9uPyapoNIQjrXueG5igglWhhFOp4VuqmmCyQgPaMdSiQXVwWR+8BSdWaWPoljZkgbN1d8TEyy0HovQdgpshnrZm4n/eZ3URJfBhMkkNVSSxaIo5cjEaPY96jNFieFjSzBRzN6KyBArTIzNqGBD8JZfXiV+rXpV9e5rpfpNlkYeTuAUKuDBBdThDhrgAwEBz/AKb45yXpx352PRmnOymWP4A+fzB5aIjno=</latexit><latexit sha1_base64="lAGXaeOUzfys611n7ty4ASveC6o=">AAAB73icbVA9TwJBEJ3DL8Qv1NJmI5hgQ+5o1EJDYmOJCScYuJC9ZQ827O5ddvdMCOFX2FiosfXv2PlvXOAKBV8yyct7M5mZFyacaeO6305ubX1jcyu/XdjZ3ds/KB4ePeg4VYT6JOaxaodYU84k9Q0znLYTRbEIOW2Fo9uZ33qiSrNYNs04oYHAA8kiRrCx0mO5WZHn6BqVe8WSW3XnQKvEy0gJMjR6xa9uPyapoNIQjrXueG5igglWhhFOp4VuqmmCyQgPaMdSiQXVwWR+8BSdWaWPoljZkgbN1d8TEyy0HovQdgpshnrZm4n/eZ3URJfBhMkkNVSSxaIo5cjEaPY96jNFieFjSzBRzN6KyBArTIzNqGBD8JZfXiV+rXpV9e5rpfpNlkYeTuAUKuDBBdThDhrgAwEBz/AKb45yXpx352PRmnOymWP4A+fzB5aIjno=</latexit><latexit sha1_base64="lAGXaeOUzfys611n7ty4ASveC6o=">AAAB73icbVA9TwJBEJ3DL8Qv1NJmI5hgQ+5o1EJDYmOJCScYuJC9ZQ827O5ddvdMCOFX2FiosfXv2PlvXOAKBV8yyct7M5mZFyacaeO6305ubX1jcyu/XdjZ3ds/KB4ePeg4VYT6JOaxaodYU84k9Q0znLYTRbEIOW2Fo9uZ33qiSrNYNs04oYHAA8kiRrCx0mO5WZHn6BqVe8WSW3XnQKvEy0gJMjR6xa9uPyapoNIQjrXueG5igglWhhFOp4VuqmmCyQgPaMdSiQXVwWR+8BSdWaWPoljZkgbN1d8TEyy0HovQdgpshnrZm4n/eZ3URJfBhMkkNVSSxaIo5cjEaPY96jNFieFjSzBRzN6KyBArTIzNqGBD8JZfXiV+rXpV9e5rpfpNlkYeTuAUKuDBBdThDhrgAwEBz/AKb45yXpx352PRmnOymWP4A+fzB5aIjno=</latexit><latexit sha1_base64="lAGXaeOUzfys611n7ty4ASveC6o=">AAAB73icbVA9TwJBEJ3DL8Qv1NJmI5hgQ+5o1EJDYmOJCScYuJC9ZQ827O5ddvdMCOFX2FiosfXv2PlvXOAKBV8yyct7M5mZFyacaeO6305ubX1jcyu/XdjZ3ds/KB4ePeg4VYT6JOaxaodYU84k9Q0znLYTRbEIOW2Fo9uZ33qiSrNYNs04oYHAA8kiRrCx0mO5WZHn6BqVe8WSW3XnQKvEy0gJMjR6xa9uPyapoNIQjrXueG5igglWhhFOp4VuqmmCyQgPaMdSiQXVwWR+8BSdWaWPoljZkgbN1d8TEyy0HovQdgpshnrZm4n/eZ3URJfBhMkkNVSSxaIo5cjEaPY96jNFieFjSzBRzN6KyBArTIzNqGBD8JZfXiV+rXpV9e5rpfpNlkYeTuAUKuDBBdThDhrgAwEBz/AKb45yXpx352PRmnOymWP4A+fzB5aIjno=</latexit>

(37)

Esercizio 4 Svolgete….

4T (n/2) + log n n 2 =

<latexit sha1_base64="tWG516WcRFvFrZNpkLQQv6u9cQE=">AAACCHicbVBNS8NAEN34WetX1KOXxVaoCDUJgnpQCl48VmhtoYlls920SzebsLsRSsjVi3/FiwcVr/4Eb/4bt20O2vpg4PHeDDPz/JhRqSzr21hYXFpeWS2sFdc3Nre2zZ3dOxklApMmjlgk2j6ShFFOmooqRtqxICj0GWn5w+ux33ogQtKIN9QoJl6I+pwGFCOlpa4Jy6eNCj9xjuAxdAOBcMrvnSx1WdSHPIOX5a5ZsqrWBHCe2DkpgRz1rvnl9iKchIQrzJCUHduKlZcioShmJCu6iSQxwkPUJx1NOQqJ9NLJJxk81EoPBpHQxRWcqL8nUhRKOQp93RkiNZCz3lj8z+skKjj3UsrjRBGOp4uChEEVwXEssEcFwYqNNEFYUH0rxAOk81A6vKIOwZ59eZ40nepF1b51SrWrPI0C2AcHoAJscAZq4AbUQRNg8AiewSt4M56MF+Pd+Ji2Lhj5zB74A+PzB+yMl4M=</latexit><latexit sha1_base64="tWG516WcRFvFrZNpkLQQv6u9cQE=">AAACCHicbVBNS8NAEN34WetX1KOXxVaoCDUJgnpQCl48VmhtoYlls920SzebsLsRSsjVi3/FiwcVr/4Eb/4bt20O2vpg4PHeDDPz/JhRqSzr21hYXFpeWS2sFdc3Nre2zZ3dOxklApMmjlgk2j6ShFFOmooqRtqxICj0GWn5w+ux33ogQtKIN9QoJl6I+pwGFCOlpa4Jy6eNCj9xjuAxdAOBcMrvnSx1WdSHPIOX5a5ZsqrWBHCe2DkpgRz1rvnl9iKchIQrzJCUHduKlZcioShmJCu6iSQxwkPUJx1NOQqJ9NLJJxk81EoPBpHQxRWcqL8nUhRKOQp93RkiNZCz3lj8z+skKjj3UsrjRBGOp4uChEEVwXEssEcFwYqNNEFYUH0rxAOk81A6vKIOwZ59eZ40nepF1b51SrWrPI0C2AcHoAJscAZq4AbUQRNg8AiewSt4M56MF+Pd+Ji2Lhj5zB74A+PzB+yMl4M=</latexit><latexit sha1_base64="tWG516WcRFvFrZNpkLQQv6u9cQE=">AAACCHicbVBNS8NAEN34WetX1KOXxVaoCDUJgnpQCl48VmhtoYlls920SzebsLsRSsjVi3/FiwcVr/4Eb/4bt20O2vpg4PHeDDPz/JhRqSzr21hYXFpeWS2sFdc3Nre2zZ3dOxklApMmjlgk2j6ShFFOmooqRtqxICj0GWn5w+ux33ogQtKIN9QoJl6I+pwGFCOlpa4Jy6eNCj9xjuAxdAOBcMrvnSx1WdSHPIOX5a5ZsqrWBHCe2DkpgRz1rvnl9iKchIQrzJCUHduKlZcioShmJCu6iSQxwkPUJx1NOQqJ9NLJJxk81EoPBpHQxRWcqL8nUhRKOQp93RkiNZCz3lj8z+skKjj3UsrjRBGOp4uChEEVwXEssEcFwYqNNEFYUH0rxAOk81A6vKIOwZ59eZ40nepF1b51SrWrPI0C2AcHoAJscAZq4AbUQRNg8AiewSt4M56MF+Pd+Ji2Lhj5zB74A+PzB+yMl4M=</latexit><latexit sha1_base64="tWG516WcRFvFrZNpkLQQv6u9cQE=">AAACCHicbVBNS8NAEN34WetX1KOXxVaoCDUJgnpQCl48VmhtoYlls920SzebsLsRSsjVi3/FiwcVr/4Eb/4bt20O2vpg4PHeDDPz/JhRqSzr21hYXFpeWS2sFdc3Nre2zZ3dOxklApMmjlgk2j6ShFFOmooqRtqxICj0GWn5w+ux33ogQtKIN9QoJl6I+pwGFCOlpa4Jy6eNCj9xjuAxdAOBcMrvnSx1WdSHPIOX5a5ZsqrWBHCe2DkpgRz1rvnl9iKchIQrzJCUHduKlZcioShmJCu6iSQxwkPUJx1NOQqJ9NLJJxk81EoPBpHQxRWcqL8nUhRKOQp93RkiNZCz3lj8z+skKjj3UsrjRBGOp4uChEEVwXEssEcFwYqNNEFYUH0rxAOk81A6vKIOwZ59eZ40nepF1b51SrWrPI0C2AcHoAJscAZq4AbUQRNg8AiewSt4M56MF+Pd+Ji2Lhj5zB74A+PzB+yMl4M=</latexit>

4(4T ( n 4 ) + log(n/2) ( n 2 ) 2 ) + log n n 2 =

<latexit sha1_base64="nQgUTqt6nTF1NMUyED8oMR++SH8=">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</latexit><latexit sha1_base64="nQgUTqt6nTF1NMUyED8oMR++SH8=">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</latexit><latexit sha1_base64="nQgUTqt6nTF1NMUyED8oMR++SH8=">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</latexit><latexit sha1_base64="nQgUTqt6nTF1NMUyED8oMR++SH8=">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</latexit>

16T (n/4) + log n/2 4n2 4 + log n n 2 =

<latexit sha1_base64="EnBVE/kHMtOArEvyX8ncFSo0LdE=">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</latexit><latexit sha1_base64="EnBVE/kHMtOArEvyX8ncFSo0LdE=">AAACLXicbVBLSwMxGMzWV62vqkcvwVaoCO1uKT4OSkEEjxVaW+iuJZtm29BsdkmyQln2F3nxr+hB8IFX/4bpA9HWgYRhZj6Sb9yQUalM89VILSwuLa+kVzNr6xubW9ntnVsZRAKTBg5YIFoukoRRThqKKkZaoSDIdxlpuoPLkd+8J0LSgNfVMCSOj3qcehQjpaVO9ioPreN6gZcqh/AI2p5AOJ7cFX5XTuJKksQ2C3qQl8rJT2JsTeQEnsN8J5szi+YYcJ5YU5IDU9Q62We7G+DIJ1xhhqRsW2aonBgJRTEjScaOJAkRHqAeaWvKkU+kE4/XTeCBVrrQC4Q+XMGx+nsiRr6UQ9/VSR+pvpz1RuJ/XjtS3qkTUx5GinA8eciLGFQBHHUHu1QQrNhQE4QF1X+FuI90IUo3nNElWLMrz5NGuXhWtG7KuerFtI002AP7oAAscAKq4BrUQANg8ACewBt4Nx6NF+PD+JxEU8Z0Zhf8gfH1DcEopZg=</latexit><latexit sha1_base64="EnBVE/kHMtOArEvyX8ncFSo0LdE=">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</latexit><latexit sha1_base64="EnBVE/kHMtOArEvyX8ncFSo0LdE=">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</latexit>

T (n) =

<latexit sha1_base64="lAGXaeOUzfys611n7ty4ASveC6o=">AAAB73icbVA9TwJBEJ3DL8Qv1NJmI5hgQ+5o1EJDYmOJCScYuJC9ZQ827O5ddvdMCOFX2FiosfXv2PlvXOAKBV8yyct7M5mZFyacaeO6305ubX1jcyu/XdjZ3ds/KB4ePeg4VYT6JOaxaodYU84k9Q0znLYTRbEIOW2Fo9uZ33qiSrNYNs04oYHAA8kiRrCx0mO5WZHn6BqVe8WSW3XnQKvEy0gJMjR6xa9uPyapoNIQjrXueG5igglWhhFOp4VuqmmCyQgPaMdSiQXVwWR+8BSdWaWPoljZkgbN1d8TEyy0HovQdgpshnrZm4n/eZ3URJfBhMkkNVSSxaIo5cjEaPY96jNFieFjSzBRzN6KyBArTIzNqGBD8JZfXiV+rXpV9e5rpfpNlkYeTuAUKuDBBdThDhrgAwEBz/AKb45yXpx352PRmnOymWP4A+fzB5aIjno=</latexit><latexit sha1_base64="lAGXaeOUzfys611n7ty4ASveC6o=">AAAB73icbVA9TwJBEJ3DL8Qv1NJmI5hgQ+5o1EJDYmOJCScYuJC9ZQ827O5ddvdMCOFX2FiosfXv2PlvXOAKBV8yyct7M5mZFyacaeO6305ubX1jcyu/XdjZ3ds/KB4ePeg4VYT6JOaxaodYU84k9Q0znLYTRbEIOW2Fo9uZ33qiSrNYNs04oYHAA8kiRrCx0mO5WZHn6BqVe8WSW3XnQKvEy0gJMjR6xa9uPyapoNIQjrXueG5igglWhhFOp4VuqmmCyQgPaMdSiQXVwWR+8BSdWaWPoljZkgbN1d8TEyy0HovQdgpshnrZm4n/eZ3URJfBhMkkNVSSxaIo5cjEaPY96jNFieFjSzBRzN6KyBArTIzNqGBD8JZfXiV+rXpV9e5rpfpNlkYeTuAUKuDBBdThDhrgAwEBz/AKb45yXpx352PRmnOymWP4A+fzB5aIjno=</latexit><latexit sha1_base64="lAGXaeOUzfys611n7ty4ASveC6o=">AAAB73icbVA9TwJBEJ3DL8Qv1NJmI5hgQ+5o1EJDYmOJCScYuJC9ZQ827O5ddvdMCOFX2FiosfXv2PlvXOAKBV8yyct7M5mZFyacaeO6305ubX1jcyu/XdjZ3ds/KB4ePeg4VYT6JOaxaodYU84k9Q0znLYTRbEIOW2Fo9uZ33qiSrNYNs04oYHAA8kiRrCx0mO5WZHn6BqVe8WSW3XnQKvEy0gJMjR6xa9uPyapoNIQjrXueG5igglWhhFOp4VuqmmCyQgPaMdSiQXVwWR+8BSdWaWPoljZkgbN1d8TEyy0HovQdgpshnrZm4n/eZ3URJfBhMkkNVSSxaIo5cjEaPY96jNFieFjSzBRzN6KyBArTIzNqGBD8JZfXiV+rXpV9e5rpfpNlkYeTuAUKuDBBdThDhrgAwEBz/AKb45yXpx352PRmnOymWP4A+fzB5aIjno=</latexit><latexit sha1_base64="lAGXaeOUzfys611n7ty4ASveC6o=">AAAB73icbVA9TwJBEJ3DL8Qv1NJmI5hgQ+5o1EJDYmOJCScYuJC9ZQ827O5ddvdMCOFX2FiosfXv2PlvXOAKBV8yyct7M5mZFyacaeO6305ubX1jcyu/XdjZ3ds/KB4ePeg4VYT6JOaxaodYU84k9Q0znLYTRbEIOW2Fo9uZ33qiSrNYNs04oYHAA8kiRrCx0mO5WZHn6BqVe8WSW3XnQKvEy0gJMjR6xa9uPyapoNIQjrXueG5igglWhhFOp4VuqmmCyQgPaMdSiQXVwWR+8BSdWaWPoljZkgbN1d8TEyy0HovQdgpshnrZm4n/eZ3URJfBhMkkNVSSxaIo5cjEaPY96jNFieFjSzBRzN6KyBArTIzNqGBD8JZfXiV+rXpV9e5rpfpNlkYeTuAUKuDBBdThDhrgAwEBz/AKb45yXpx352PRmnOymWP4A+fzB5aIjno=</latexit>

(38)

Esercizio 4 Svolgete….

4T (n/2) + log n n 2 =

<latexit sha1_base64="tWG516WcRFvFrZNpkLQQv6u9cQE=">AAACCHicbVBNS8NAEN34WetX1KOXxVaoCDUJgnpQCl48VmhtoYlls920SzebsLsRSsjVi3/FiwcVr/4Eb/4bt20O2vpg4PHeDDPz/JhRqSzr21hYXFpeWS2sFdc3Nre2zZ3dOxklApMmjlgk2j6ShFFOmooqRtqxICj0GWn5w+ux33ogQtKIN9QoJl6I+pwGFCOlpa4Jy6eNCj9xjuAxdAOBcMrvnSx1WdSHPIOX5a5ZsqrWBHCe2DkpgRz1rvnl9iKchIQrzJCUHduKlZcioShmJCu6iSQxwkPUJx1NOQqJ9NLJJxk81EoPBpHQxRWcqL8nUhRKOQp93RkiNZCz3lj8z+skKjj3UsrjRBGOp4uChEEVwXEssEcFwYqNNEFYUH0rxAOk81A6vKIOwZ59eZ40nepF1b51SrWrPI0C2AcHoAJscAZq4AbUQRNg8AiewSt4M56MF+Pd+Ji2Lhj5zB74A+PzB+yMl4M=</latexit><latexit sha1_base64="tWG516WcRFvFrZNpkLQQv6u9cQE=">AAACCHicbVBNS8NAEN34WetX1KOXxVaoCDUJgnpQCl48VmhtoYlls920SzebsLsRSsjVi3/FiwcVr/4Eb/4bt20O2vpg4PHeDDPz/JhRqSzr21hYXFpeWS2sFdc3Nre2zZ3dOxklApMmjlgk2j6ShFFOmooqRtqxICj0GWn5w+ux33ogQtKIN9QoJl6I+pwGFCOlpa4Jy6eNCj9xjuAxdAOBcMrvnSx1WdSHPIOX5a5ZsqrWBHCe2DkpgRz1rvnl9iKchIQrzJCUHduKlZcioShmJCu6iSQxwkPUJx1NOQqJ9NLJJxk81EoPBpHQxRWcqL8nUhRKOQp93RkiNZCz3lj8z+skKjj3UsrjRBGOp4uChEEVwXEssEcFwYqNNEFYUH0rxAOk81A6vKIOwZ59eZ40nepF1b51SrWrPI0C2AcHoAJscAZq4AbUQRNg8AiewSt4M56MF+Pd+Ji2Lhj5zB74A+PzB+yMl4M=</latexit><latexit sha1_base64="tWG516WcRFvFrZNpkLQQv6u9cQE=">AAACCHicbVBNS8NAEN34WetX1KOXxVaoCDUJgnpQCl48VmhtoYlls920SzebsLsRSsjVi3/FiwcVr/4Eb/4bt20O2vpg4PHeDDPz/JhRqSzr21hYXFpeWS2sFdc3Nre2zZ3dOxklApMmjlgk2j6ShFFOmooqRtqxICj0GWn5w+ux33ogQtKIN9QoJl6I+pwGFCOlpa4Jy6eNCj9xjuAxdAOBcMrvnSx1WdSHPIOX5a5ZsqrWBHCe2DkpgRz1rvnl9iKchIQrzJCUHduKlZcioShmJCu6iSQxwkPUJx1NOQqJ9NLJJxk81EoPBpHQxRWcqL8nUhRKOQp93RkiNZCz3lj8z+skKjj3UsrjRBGOp4uChEEVwXEssEcFwYqNNEFYUH0rxAOk81A6vKIOwZ59eZ40nepF1b51SrWrPI0C2AcHoAJscAZq4AbUQRNg8AiewSt4M56MF+Pd+Ji2Lhj5zB74A+PzB+yMl4M=</latexit><latexit sha1_base64="tWG516WcRFvFrZNpkLQQv6u9cQE=">AAACCHicbVBNS8NAEN34WetX1KOXxVaoCDUJgnpQCl48VmhtoYlls920SzebsLsRSsjVi3/FiwcVr/4Eb/4bt20O2vpg4PHeDDPz/JhRqSzr21hYXFpeWS2sFdc3Nre2zZ3dOxklApMmjlgk2j6ShFFOmooqRtqxICj0GWn5w+ux33ogQtKIN9QoJl6I+pwGFCOlpa4Jy6eNCj9xjuAxdAOBcMrvnSx1WdSHPIOX5a5ZsqrWBHCe2DkpgRz1rvnl9iKchIQrzJCUHduKlZcioShmJCu6iSQxwkPUJx1NOQqJ9NLJJxk81EoPBpHQxRWcqL8nUhRKOQp93RkiNZCz3lj8z+skKjj3UsrjRBGOp4uChEEVwXEssEcFwYqNNEFYUH0rxAOk81A6vKIOwZ59eZ40nepF1b51SrWrPI0C2AcHoAJscAZq4AbUQRNg8AiewSt4M56MF+Pd+Ji2Lhj5zB74A+PzB+yMl4M=</latexit>

4(4T ( n 4 ) + log(n/2) ( n 2 ) 2 ) + log n n 2 =

<latexit sha1_base64="nQgUTqt6nTF1NMUyED8oMR++SH8=">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</latexit><latexit sha1_base64="nQgUTqt6nTF1NMUyED8oMR++SH8=">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</latexit><latexit sha1_base64="nQgUTqt6nTF1NMUyED8oMR++SH8=">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</latexit><latexit sha1_base64="nQgUTqt6nTF1NMUyED8oMR++SH8=">AAACOnicbVDNTgIxGOziH+If6tFLI5hATHB3Q6IeNCRePKIBIQEk3dKFhm5303ZNyGbfy4sv4c2LFw9qvPoAFtigopM0mc7Ml/YbJ2BUKtN8MlILi0vLK+nVzNr6xuZWdnvnRvqhwKSOfeaLpoMkYZSTuqKKkWYgCPIcRhrO8GLsN+6IkNTnNTUKSMdDfU5dipHSUjd7nYflQrlWaLsC4YjHUTkuwkM4vX6rdly8teOozfw+LPAju6hTsxifWTw+g/luNmeWzAngX2IlJAcSVLvZx3bPx6FHuMIMSdmyzEB1IiQUxYzEmXYoSYDwEPVJS1OOPCI70WT3GB5opQddX+jDFZyoPyci5Ek58hyd9JAayHlvLP7ntULlnnQiyoNQEY6nD7khg8qH4yJhjwqCFRtpgrCg+q8QD5DuQ+m6M7oEa37lv6Rul05L1pWdq5wnbaTBHtgHBWCBY1ABl6AK6gCDe/AMXsGb8WC8GO/GxzSaMpKZXfALxucXwuOqkQ==</latexit>

16T (n/4) + log n/2 4n2 4 + log n n 2 =

<latexit sha1_base64="EnBVE/kHMtOArEvyX8ncFSo0LdE=">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</latexit><latexit sha1_base64="EnBVE/kHMtOArEvyX8ncFSo0LdE=">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</latexit><latexit sha1_base64="EnBVE/kHMtOArEvyX8ncFSo0LdE=">AAACLXicbVBLSwMxGMzWV62vqkcvwVaoCO1uKT4OSkEEjxVaW+iuJZtm29BsdkmyQln2F3nxr+hB8IFX/4bpA9HWgYRhZj6Sb9yQUalM89VILSwuLa+kVzNr6xubW9ntnVsZRAKTBg5YIFoukoRRThqKKkZaoSDIdxlpuoPLkd+8J0LSgNfVMCSOj3qcehQjpaVO9ioPreN6gZcqh/AI2p5AOJ7cFX5XTuJKksQ2C3qQl8rJT2JsTeQEnsN8J5szi+YYcJ5YU5IDU9Q62We7G+DIJ1xhhqRsW2aonBgJRTEjScaOJAkRHqAeaWvKkU+kE4/XTeCBVrrQC4Q+XMGx+nsiRr6UQ9/VSR+pvpz1RuJ/XjtS3qkTUx5GinA8eciLGFQBHHUHu1QQrNhQE4QF1X+FuI90IUo3nNElWLMrz5NGuXhWtG7KuerFtI002AP7oAAscAKq4BrUQANg8ACewBt4Nx6NF+PD+JxEU8Z0Zhf8gfH1DcEopZg=</latexit><latexit sha1_base64="EnBVE/kHMtOArEvyX8ncFSo0LdE=">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</latexit>

16T (n/4) + log n/2 n 2 + log n n 2 = . . . = T (n) =

<latexit sha1_base64="lAGXaeOUzfys611n7ty4ASveC6o=">AAAB73icbVA9TwJBEJ3DL8Qv1NJmI5hgQ+5o1EJDYmOJCScYuJC9ZQ827O5ddvdMCOFX2FiosfXv2PlvXOAKBV8yyct7M5mZFyacaeO6305ubX1jcyu/XdjZ3ds/KB4ePeg4VYT6JOaxaodYU84k9Q0znLYTRbEIOW2Fo9uZ33qiSrNYNs04oYHAA8kiRrCx0mO5WZHn6BqVe8WSW3XnQKvEy0gJMjR6xa9uPyapoNIQjrXueG5igglWhhFOp4VuqmmCyQgPaMdSiQXVwWR+8BSdWaWPoljZkgbN1d8TEyy0HovQdgpshnrZm4n/eZ3URJfBhMkkNVSSxaIo5cjEaPY96jNFieFjSzBRzN6KyBArTIzNqGBD8JZfXiV+rXpV9e5rpfpNlkYeTuAUKuDBBdThDhrgAwEBz/AKb45yXpx352PRmnOymWP4A+fzB5aIjno=</latexit><latexit sha1_base64="lAGXaeOUzfys611n7ty4ASveC6o=">AAAB73icbVA9TwJBEJ3DL8Qv1NJmI5hgQ+5o1EJDYmOJCScYuJC9ZQ827O5ddvdMCOFX2FiosfXv2PlvXOAKBV8yyct7M5mZFyacaeO6305ubX1jcyu/XdjZ3ds/KB4ePeg4VYT6JOaxaodYU84k9Q0znLYTRbEIOW2Fo9uZ33qiSrNYNs04oYHAA8kiRrCx0mO5WZHn6BqVe8WSW3XnQKvEy0gJMjR6xa9uPyapoNIQjrXueG5igglWhhFOp4VuqmmCyQgPaMdSiQXVwWR+8BSdWaWPoljZkgbN1d8TEyy0HovQdgpshnrZm4n/eZ3URJfBhMkkNVSSxaIo5cjEaPY96jNFieFjSzBRzN6KyBArTIzNqGBD8JZfXiV+rXpV9e5rpfpNlkYeTuAUKuDBBdThDhrgAwEBz/AKb45yXpx352PRmnOymWP4A+fzB5aIjno=</latexit><latexit sha1_base64="lAGXaeOUzfys611n7ty4ASveC6o=">AAAB73icbVA9TwJBEJ3DL8Qv1NJmI5hgQ+5o1EJDYmOJCScYuJC9ZQ827O5ddvdMCOFX2FiosfXv2PlvXOAKBV8yyct7M5mZFyacaeO6305ubX1jcyu/XdjZ3ds/KB4ePeg4VYT6JOaxaodYU84k9Q0znLYTRbEIOW2Fo9uZ33qiSrNYNs04oYHAA8kiRrCx0mO5WZHn6BqVe8WSW3XnQKvEy0gJMjR6xa9uPyapoNIQjrXueG5igglWhhFOp4VuqmmCyQgPaMdSiQXVwWR+8BSdWaWPoljZkgbN1d8TEyy0HovQdgpshnrZm4n/eZ3URJfBhMkkNVSSxaIo5cjEaPY96jNFieFjSzBRzN6KyBArTIzNqGBD8JZfXiV+rXpV9e5rpfpNlkYeTuAUKuDBBdThDhrgAwEBz/AKb45yXpx352PRmnOymWP4A+fzB5aIjno=</latexit><latexit sha1_base64="lAGXaeOUzfys611n7ty4ASveC6o=">AAAB73icbVA9TwJBEJ3DL8Qv1NJmI5hgQ+5o1EJDYmOJCScYuJC9ZQ827O5ddvdMCOFX2FiosfXv2PlvXOAKBV8yyct7M5mZFyacaeO6305ubX1jcyu/XdjZ3ds/KB4ePeg4VYT6JOaxaodYU84k9Q0znLYTRbEIOW2Fo9uZ33qiSrNYNs04oYHAA8kiRrCx0mO5WZHn6BqVe8WSW3XnQKvEy0gJMjR6xa9uPyapoNIQjrXueG5igglWhhFOp4VuqmmCyQgPaMdSiQXVwWR+8BSdWaWPoljZkgbN1d8TEyy0HovQdgpshnrZm4n/eZ3URJfBhMkkNVSSxaIo5cjEaPY96jNFieFjSzBRzN6KyBArTIzNqGBD8JZfXiV+rXpV9e5rpfpNlkYeTuAUKuDBBdThDhrgAwEBz/AKb45yXpx352PRmnOymWP4A+fzB5aIjno=</latexit>

(39)

Esercizio 4 Svolgete….

4T (n/2) + log n n 2 =

<latexit sha1_base64="tWG516WcRFvFrZNpkLQQv6u9cQE=">AAACCHicbVBNS8NAEN34WetX1KOXxVaoCDUJgnpQCl48VmhtoYlls920SzebsLsRSsjVi3/FiwcVr/4Eb/4bt20O2vpg4PHeDDPz/JhRqSzr21hYXFpeWS2sFdc3Nre2zZ3dOxklApMmjlgk2j6ShFFOmooqRtqxICj0GWn5w+ux33ogQtKIN9QoJl6I+pwGFCOlpa4Jy6eNCj9xjuAxdAOBcMrvnSx1WdSHPIOX5a5ZsqrWBHCe2DkpgRz1rvnl9iKchIQrzJCUHduKlZcioShmJCu6iSQxwkPUJx1NOQqJ9NLJJxk81EoPBpHQxRWcqL8nUhRKOQp93RkiNZCz3lj8z+skKjj3UsrjRBGOp4uChEEVwXEssEcFwYqNNEFYUH0rxAOk81A6vKIOwZ59eZ40nepF1b51SrWrPI0C2AcHoAJscAZq4AbUQRNg8AiewSt4M56MF+Pd+Ji2Lhj5zB74A+PzB+yMl4M=</latexit><latexit sha1_base64="tWG516WcRFvFrZNpkLQQv6u9cQE=">AAACCHicbVBNS8NAEN34WetX1KOXxVaoCDUJgnpQCl48VmhtoYlls920SzebsLsRSsjVi3/FiwcVr/4Eb/4bt20O2vpg4PHeDDPz/JhRqSzr21hYXFpeWS2sFdc3Nre2zZ3dOxklApMmjlgk2j6ShFFOmooqRtqxICj0GWn5w+ux33ogQtKIN9QoJl6I+pwGFCOlpa4Jy6eNCj9xjuAxdAOBcMrvnSx1WdSHPIOX5a5ZsqrWBHCe2DkpgRz1rvnl9iKchIQrzJCUHduKlZcioShmJCu6iSQxwkPUJx1NOQqJ9NLJJxk81EoPBpHQxRWcqL8nUhRKOQp93RkiNZCz3lj8z+skKjj3UsrjRBGOp4uChEEVwXEssEcFwYqNNEFYUH0rxAOk81A6vKIOwZ59eZ40nepF1b51SrWrPI0C2AcHoAJscAZq4AbUQRNg8AiewSt4M56MF+Pd+Ji2Lhj5zB74A+PzB+yMl4M=</latexit><latexit sha1_base64="tWG516WcRFvFrZNpkLQQv6u9cQE=">AAACCHicbVBNS8NAEN34WetX1KOXxVaoCDUJgnpQCl48VmhtoYlls920SzebsLsRSsjVi3/FiwcVr/4Eb/4bt20O2vpg4PHeDDPz/JhRqSzr21hYXFpeWS2sFdc3Nre2zZ3dOxklApMmjlgk2j6ShFFOmooqRtqxICj0GWn5w+ux33ogQtKIN9QoJl6I+pwGFCOlpa4Jy6eNCj9xjuAxdAOBcMrvnSx1WdSHPIOX5a5ZsqrWBHCe2DkpgRz1rvnl9iKchIQrzJCUHduKlZcioShmJCu6iSQxwkPUJx1NOQqJ9NLJJxk81EoPBpHQxRWcqL8nUhRKOQp93RkiNZCz3lj8z+skKjj3UsrjRBGOp4uChEEVwXEssEcFwYqNNEFYUH0rxAOk81A6vKIOwZ59eZ40nepF1b51SrWrPI0C2AcHoAJscAZq4AbUQRNg8AiewSt4M56MF+Pd+Ji2Lhj5zB74A+PzB+yMl4M=</latexit><latexit sha1_base64="tWG516WcRFvFrZNpkLQQv6u9cQE=">AAACCHicbVBNS8NAEN34WetX1KOXxVaoCDUJgnpQCl48VmhtoYlls920SzebsLsRSsjVi3/FiwcVr/4Eb/4bt20O2vpg4PHeDDPz/JhRqSzr21hYXFpeWS2sFdc3Nre2zZ3dOxklApMmjlgk2j6ShFFOmooqRtqxICj0GWn5w+ux33ogQtKIN9QoJl6I+pwGFCOlpa4Jy6eNCj9xjuAxdAOBcMrvnSx1WdSHPIOX5a5ZsqrWBHCe2DkpgRz1rvnl9iKchIQrzJCUHduKlZcioShmJCu6iSQxwkPUJx1NOQqJ9NLJJxk81EoPBpHQxRWcqL8nUhRKOQp93RkiNZCz3lj8z+skKjj3UsrjRBGOp4uChEEVwXEssEcFwYqNNEFYUH0rxAOk81A6vKIOwZ59eZ40nepF1b51SrWrPI0C2AcHoAJscAZq4AbUQRNg8AiewSt4M56MF+Pd+Ji2Lhj5zB74A+PzB+yMl4M=</latexit>

4(4T ( n 4 ) + log(n/2) ( n 2 ) 2 ) + log n n 2 =

<latexit sha1_base64="nQgUTqt6nTF1NMUyED8oMR++SH8=">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</latexit><latexit sha1_base64="nQgUTqt6nTF1NMUyED8oMR++SH8=">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</latexit><latexit sha1_base64="nQgUTqt6nTF1NMUyED8oMR++SH8=">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</latexit><latexit sha1_base64="nQgUTqt6nTF1NMUyED8oMR++SH8=">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</latexit>

16T (n/4) + log n/2 4n2 4 + log n n 2 =

<latexit sha1_base64="EnBVE/kHMtOArEvyX8ncFSo0LdE=">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</latexit><latexit sha1_base64="EnBVE/kHMtOArEvyX8ncFSo0LdE=">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</latexit><latexit sha1_base64="EnBVE/kHMtOArEvyX8ncFSo0LdE=">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</latexit><latexit sha1_base64="EnBVE/kHMtOArEvyX8ncFSo0LdE=">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</latexit>

16T (n/4) + log n/2 n 2 + log n n 2 = . . . =

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2 2k T (n/2 k ) + n 2k 1 i=0 log( 1 n

2i ) =

<latexit sha1_base64="Ikwuj54R7cYzEypRj0yQ+8Ltn64=">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</latexit><latexit sha1_base64="Ikwuj54R7cYzEypRj0yQ+8Ltn64=">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</latexit><latexit sha1_base64="Ikwuj54R7cYzEypRj0yQ+8Ltn64=">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</latexit><latexit sha1_base64="Ikwuj54R7cYzEypRj0yQ+8Ltn64=">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</latexit>

T (n) =

<latexit sha1_base64="lAGXaeOUzfys611n7ty4ASveC6o=">AAAB73icbVA9TwJBEJ3DL8Qv1NJmI5hgQ+5o1EJDYmOJCScYuJC9ZQ827O5ddvdMCOFX2FiosfXv2PlvXOAKBV8yyct7M5mZFyacaeO6305ubX1jcyu/XdjZ3ds/KB4ePeg4VYT6JOaxaodYU84k9Q0znLYTRbEIOW2Fo9uZ33qiSrNYNs04oYHAA8kiRrCx0mO5WZHn6BqVe8WSW3XnQKvEy0gJMjR6xa9uPyapoNIQjrXueG5igglWhhFOp4VuqmmCyQgPaMdSiQXVwWR+8BSdWaWPoljZkgbN1d8TEyy0HovQdgpshnrZm4n/eZ3URJfBhMkkNVSSxaIo5cjEaPY96jNFieFjSzBRzN6KyBArTIzNqGBD8JZfXiV+rXpV9e5rpfpNlkYeTuAUKuDBBdThDhrgAwEBz/AKb45yXpx352PRmnOymWP4A+fzB5aIjno=</latexit><latexit sha1_base64="lAGXaeOUzfys611n7ty4ASveC6o=">AAAB73icbVA9TwJBEJ3DL8Qv1NJmI5hgQ+5o1EJDYmOJCScYuJC9ZQ827O5ddvdMCOFX2FiosfXv2PlvXOAKBV8yyct7M5mZFyacaeO6305ubX1jcyu/XdjZ3ds/KB4ePeg4VYT6JOaxaodYU84k9Q0znLYTRbEIOW2Fo9uZ33qiSrNYNs04oYHAA8kiRrCx0mO5WZHn6BqVe8WSW3XnQKvEy0gJMjR6xa9uPyapoNIQjrXueG5igglWhhFOp4VuqmmCyQgPaMdSiQXVwWR+8BSdWaWPoljZkgbN1d8TEyy0HovQdgpshnrZm4n/eZ3URJfBhMkkNVSSxaIo5cjEaPY96jNFieFjSzBRzN6KyBArTIzNqGBD8JZfXiV+rXpV9e5rpfpNlkYeTuAUKuDBBdThDhrgAwEBz/AKb45yXpx352PRmnOymWP4A+fzB5aIjno=</latexit><latexit sha1_base64="lAGXaeOUzfys611n7ty4ASveC6o=">AAAB73icbVA9TwJBEJ3DL8Qv1NJmI5hgQ+5o1EJDYmOJCScYuJC9ZQ827O5ddvdMCOFX2FiosfXv2PlvXOAKBV8yyct7M5mZFyacaeO6305ubX1jcyu/XdjZ3ds/KB4ePeg4VYT6JOaxaodYU84k9Q0znLYTRbEIOW2Fo9uZ33qiSrNYNs04oYHAA8kiRrCx0mO5WZHn6BqVe8WSW3XnQKvEy0gJMjR6xa9uPyapoNIQjrXueG5igglWhhFOp4VuqmmCyQgPaMdSiQXVwWR+8BSdWaWPoljZkgbN1d8TEyy0HovQdgpshnrZm4n/eZ3URJfBhMkkNVSSxaIo5cjEaPY96jNFieFjSzBRzN6KyBArTIzNqGBD8JZfXiV+rXpV9e5rpfpNlkYeTuAUKuDBBdThDhrgAwEBz/AKb45yXpx352PRmnOymWP4A+fzB5aIjno=</latexit><latexit sha1_base64="lAGXaeOUzfys611n7ty4ASveC6o=">AAAB73icbVA9TwJBEJ3DL8Qv1NJmI5hgQ+5o1EJDYmOJCScYuJC9ZQ827O5ddvdMCOFX2FiosfXv2PlvXOAKBV8yyct7M5mZFyacaeO6305ubX1jcyu/XdjZ3ds/KB4ePeg4VYT6JOaxaodYU84k9Q0znLYTRbEIOW2Fo9uZ33qiSrNYNs04oYHAA8kiRrCx0mO5WZHn6BqVe8WSW3XnQKvEy0gJMjR6xa9uPyapoNIQjrXueG5igglWhhFOp4VuqmmCyQgPaMdSiQXVwWR+8BSdWaWPoljZkgbN1d8TEyy0HovQdgpshnrZm4n/eZ3URJfBhMkkNVSSxaIo5cjEaPY96jNFieFjSzBRzN6KyBArTIzNqGBD8JZfXiV+rXpV9e5rpfpNlkYeTuAUKuDBBdThDhrgAwEBz/AKb45yXpx352PRmnOymWP4A+fzB5aIjno=</latexit>

(40)

Esercizio 4 Svolgete….

4T (n/2) + log n n 2 =

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4(4T ( n 4 ) + log(n/2) ( n 2 ) 2 ) + log n n 2 =

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16T (n/4) + log n/2 4n2 4 + log n n 2 =

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16T (n/4) + log n/2 n 2 + log n n 2 = . . . =

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2 2k T (n/2 k ) + n 2k 1 i=0 log( 1 n

2i ) =

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T (n) =

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[n/2

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k = 1 $ k = log n]

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