Algoritmi e strutture dati - Schema algoritmi

INSERTION SELECTION SORT

SORT im

in PE

①(m)

MI Oluz)

2) n

INSERTION-SORT (A) Selection-Son(a)

length

for A

length

to A =

jz2 . .

Key for to

Atj] jc-1 1

m

<

- -

smallest

ic -j 1 ↓

- for

While to

iz-j

key

Ali]

iso and +1 m

> if Ati]

Ati Atsmallest]

1] Ali] <

+ - smallesti

ic-i 1

- A

Ali Ismallest]

1] ATj]

exchange

Key < >

<

+ -

ALGORITMI RICORSIVI

MERGE MERGE MERGE-SORT

SORT Onlg

MERGE

Merge-Sort r)

(A pir) (A p g

, ,

,

,

if Mr a 1

p j

+

per 1

- - -

for

r)/2] Keptor

[(p q

m2 r

-

q + -

for

g)

(A RIj]

if ([i]

toms

ic-1

MERGE-SORT p

, , Alp

([i] i -1] Atk]

MERGE-SORT(A ([i]

r) < +

- <

1

+ -

a ,

, for to ic i

w) j-1

(A M2 + 1

MERGE -

g

p

, ,

, j]

Rtj] Alg REj]

else

<- Atk]

+ <

LIMs 2

1 -

+ j 1

jk +

RIM2 11-0

+

i 1 QUICK-SORT

PARTITION

QUICKSORT O(m) MI-MEO(m Ign) PEE(m2)

Quiersort RANDOMED-QUICKSort (A pir)

pir)

(A , ,

if

if per

par (A pir)

(A r) gl-RANDOMIZED-PARTITION

PARTITION

9 p ,

- ,

, (A P19-1)

(A RANDOMIZED-QUICKSORT

1)

QUICKSORT q

p - ,

, , RANDOMIZED-QuickSort (A r)

r)

(A

QUICKSORT gra

1

+

a , ,

, , RANDOMIZED

PARTITION PARTITION pir)

(A

(A r)

p - ,

,

, RANDOM(pir)

Atr] in

X

- Atr] Ati)

exchange

i <

p >

1

< -

- r)

(A

for to return PARTITION

r-s

j p

p

<- , ,

Atj]

if X

i

ic 1

+

- A[j]

A[i] <

Atite] Atr]

< >

-

return i +1

FATTORIALE

FATT(N)

N

if 1

=

retun 1

else FATT(N-1)

return NX RADIX-SORT

COUNTING-SORT ⑦(d(k

k)

k) Alm

(A m))

COUNTING-SORT RADIX-Sort (A d)

B +

+

, ,

,

KI tod

Clo for

sia ic-1

nuovo array

un

...

for perordinare

to stabile

R ordinamento

ic-o array

usa

A cifra

sulla

C[i] < i

O length

to

for A

jco .

CIA[j]] CIAlj]]

< 1

+

-

l

for to

ic-1

C[i] Cli] Cli 1]

< +

- -

length

for jcA downto 1

.

BICIATj7]] AIj]

< -

CIAtj]] -1

CIA[j]] <

-

TABELLE DIRETTO

INAMENTO

DIRECT-ADDRESS DIRECT-ADDRESS-DELETE

x) (T

INSERT(T X)

,

- ,

Key] Key]

TIx TIx NIL

< X <

-

-

.

HASH

HASH-SEARCH (T (T

k) HASH-Insert k)

, ,

ic il 0

O - i)

jc-h(k

repeat

repeat ,

i)

h(k TIjT

if

jz- NIL

=

, Tj]

A

if K

TIj] <-

= return

return j

j else

i ic-i +1

i 1

< + until

TIj]

until in

ori

Nic m

m

=

= overflow"

table

"hash

return NIL error

ALBERI TREE-SEARCH

TREE-INsERT (X

(T z) te)

, ,

if K Key

NIL

y) X

NIL

X or

= =

- T root return

X- X

. if

while Key

X

NIL

= <

X . (X left

return k)

TREF-SEARCH

=X

Y ,

.

(X h)

right

if return

else

Key

Key Tree-search

X

z . ,

.

. left

7 X

X .

right

else X . TRAPIANTO (T v)

Y

z P( u

- ,

. ,

if if

NIL

y NIL

= U p =

.

T root z T root -V

-

. .

Key Key

elseif elseif left

z <y. p

v u

=

. . .

left left =

. z

y v

p

u .

.

else right else right

z

y. v

U p .

.

if VENIL p

U

<

p

v - .

.

TREE-DELETE (T z)

,

left

if NIL

z =

. right)

(T Z

TRAPIANTO z

, , .

elseif right = N

z. (T left

TRAPIANTO z

z

, , . right)

(z

else TREE-MINIMUM

Y <

- .

if +z

y p

. (T right)

TRAPIANTO Y y

, ,

right right

<

-z

Y . .

right pzy

y . . y]

(T

TRAPIANTO z ,

,

left

left

y <z

. .

left ps-y

y .

.

STRUTTURE DATI AUMENTATE

OS-RANK

OS-SELECT (T x)

(X i) ,

, left

left size

X

1 =

r 1

size

rc X + +

.

.

. .

if i y X

r

= while root

T

return y

X .

if

elseif right

icr y X p

= .

.

(x i) left

left

OS-Select

return r< 1

size

+

r +

p

y .

. .

.

,

(X -r)

right

OS-SELECT

else return i y p

yc

-

, ,

. return r DINAMICA

PROGRAMMAZIONE

TOP-DOWN

MEMOIZED-CUT-ROD(pim)

r[o

Sia n] un nuovo array

...

ton

feric-o

r[i]c-- Rod-Aux(pim r)

MEMOlZED-CuT-

return ,

MemozED-CuT-Rod-Aux (p r)

m

. ,

r[m]

if O

> rIm]

return

if 0

n = 0

97

else q--x

for ic-stom r))

(q (p

pti] i

MEMORED-CUT-ROD-Aux

q n

max + -

1 , ,

r[m] = a

return a

BOTTOM-UP

Bottom-Up-CUT-Rod (p m)

.

Sia ro m] array

un nuovo

...

r[0] 0

for ton

jl-1

q--

for ic-sto j r[g-i])

(9 pliT

97 max +

.

rij) a

rin]

return

MST

GENERIC-MST (G w)

,

A-D albero

while forma di

A connessione

un

non è

v)

(n che

trova A

sicuro

un arco per

,

A-AuS(u v))

,

A

return