Algoritmos - Taller 1 (2011-II)

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Lfjeynqbe} ” Qlffky <

Kaznh Fkehlyae Iecýy|{k I{nqylje 9;::1<

Albnlh Anl Akpnpkye 9;::;9

<. l. ]klh ~ `{hmnehk} l}nhqýqnmlbkhqk he hkjlqnpl}( [}lhae fl ak`nhnmnýh iì}nml ak

fl heqlmnýh & akb{k}qyk |{k (

]{wehnkhae |{k ~ |{k ( Wey ak`nhnmnýh }k }lik |{k

ksn}qkh qlfk} |{k # . ( Lf anpnany

qeae} fe} qîybnhe} khqyk }k eiqnkhk?

(

Mebe & }k akikh k}mejky ~ qlfk} |{k ⁁ ~ ( ]k }nj{k {h

ylehlbnkhqe }nbnfly kh kf ml}e ak (

i. µK} 5 µK} 5

]n khqehmk}

Ak k}qe }k mehmf{~k |{k }n }k k}mejk

Kh kf ml}e ak }k qnkhk

Wey fe qlhqe }k mehmf{~k |{k

m. [}k {h ìyief ak ykm{y}nýh wlyl akqkybnhly {hl i{khl meql l}nhqýqnml }{wkyney wlyl fl

ykm{yykhmnl ⌏⌄ ( [}k kf bîqeae ak }{}qnq{mnýh wlyl pkyn`nmly fl yk}w{k}ql(

Mebe ⌏⌄

& fl meql }{wkyney ak qlbinîh }nypk wlyl ⌏

⌄



∜

[}lhae kf bîqeae ak }{}qnq{mnýh?Cl~ |{k wyeily |{k ( L}{bnkhae |{k wlyl ~

⌏⌄

⌏⌄

K}qe he akb{k}qyl fl cnwýqk}n} nha{mqnpl( Wey fe qlhqe cl~ |{k ykèylyfl?

L}{bnkhae meh ~

⌏⌄

⌏⌄ ⌏

⌄ ⌏⌄ ⌏

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]n ~

a. [qnfnmk kf bîqeae blk}qye wlyl eiqkhky kf fnbnqk l}nhqýqnme ak fl} }nj{nkhqk} ykm{yykhmnl}?

l(

Khqehmk}&

i( ∟

Khqehmk}&

m(

Khqehmk}&

a(

Khqehmk}&



k. Kf wye`k}ey Mlk}ly ak}kl ak}lyyeffly {h lfjeynqbe wlyl b{fqnwfnmly blqynmk} |{k }kl

l}nhqýqnmlbkhqk bl} yìwnae |{k kf lfjeynqbe ak ]qyl}}kh( ]{ lfjeynqbe {}lyl kf bîqeae

‖anpnak ~ meh|{n}qlyl}‒& anpnankhae mlal blqynz kh wnkzl} ak qlblüe

& ~ fe} wl}e} ak

anpnany ~ mebinhly qeblylh {h qnkbwe ( Îf hkmk}nql akqkybnhly m{lhqe}

}{iwyeifkbl} akik mykly }{ lfjeynqbe wlyl }{wkyly kf lfjeynqbe ak ]qyl}}kh( ]n }{

lfjeynqbe mykl }{iwyeifkbl}& khqehmk} fl ykm{yykhmnl wlyl kf qnkbwe ak kokm{mnýh

k} ( µM{ìf k} kf plfey khqkye bl} jylhak ak wlyl |{k kf

lfjeynqbe akf wye`k}ey Mlk}ly }kl l}nhqýqnmlbkhqk bl} yìwnae |{k kf lfjeynqbe ak

]qyl}}kh5

Fl ykm{yykhmnl akf lfjeynqbe ak ]qyl}}kh k} ( [}lhae kf qkeykbl

blk}qye meh ~ }k pk |{k meh & wey

fe qlhqe ( Wlyl |{k kf lfjeynqbe akf wye`k}ey Mlk}ly }kl bkoey |{k kf lfjeynqbe

ak ]qyl}}kh& }{ meql }{wkyney akik }ky bkhey |{k & l}â |{k lwfnmlhae kf qkeykbl blk}qye

kh fl ykm{yykhmnl akf lfjeynqbe ak Mlk}ly }k eiqnkhk

( K}qe }k nj{lfl meh kf

|{k }k

eiq{pe kh kf lfjeynqbe ak ]qyl}}kh& |{kalhae l}â ( Ak}wkolhae }k eiqnkhk

( Qeblhae {h }k mehmf{~k |{k akik }ky bkhey ak 1>(

9. Alae kf }nj{nkhqk }k{aemýanje?

ak` bn}qkyne#h.? n` h 62<?

ykq{yh n2< zcnfk n 62;?

n2n$< bn}qkyne#h%9.

èy o nh ylhjk#<&h.? èy d nh ylhjk#n&o.?

wynhq *hlal*

l. Wflhqkk {hl km{lmnýh ak ykm{yykhmnl wlyl Q#h.& kf qnkbwe |{k qebl fl `{hmnýh bn}qkyne#h.?

i. Akqkybnhk kf mebweyqlbnkhqe l}nhqýqnme ak Q#h. o{}qn`nmlhae ak blhkyl akqlfflal?

K}ql `{hmnýh ak ykm{yykhmnl k}ql kswyk}lal kh qîybnhe} kh fe} m{lfk} w{kak }ky lwfnmlae kf

Qkeykbl Blk}qye& khqehmk} qkhkbe} |{k?

]kjÿh kf qkeykbl blk}qye weakbe} akmny |{k? ]n # . & khqehmk}&

& kh k}qk ml}e (

Wey qlhqe?



# .

=. Kf lfjeynqbe wlyl kf ]kfkmqneh ]eyq k} kf }nj{nkhqk?

ak` }kfkmqnehU}eyq#L.? < èy n nh ylhjk#7&#fkh#L."<..? 9 d2n= èy o nh ylhjk ##n$<.&fkh#L..? 1 n`#LToR6LTdR.? ; d2o0 LTdR&LTnR2LTnR&LTdR

l. Ak`nhl {h nhplynlhqk ak mnmfe wlyl kf lfjeynqbe ]kfkmqneh ]eyq(

[h Nhplynlhqk ak mnmfe lakm{lae wlyl kf lfjeynqbe }kyâl?

Kf lyykjfe eyakhlae LTR khqyk fl we}nmnýh 7 ~ fl we}nmnýh n

Nhnmnlfnzlmnýh? LT7R k}ql eyakhlae& ~l |{k we}kk {h }efe kfkbkhqeKokm{mnýh? LT7†nR k}ql eyakhlae ~l |{k }k qebl kf bkhey kfkbkhqe kf lyykjfe LTn$<†hR ~

}k mefeml kh fl we}nmnýh n(

@nhlfnzlmnýh? n }k khm{khqyl meh plfey h& wey qlhqe kf lyykjfe LT7†nR ~l }k cl eyakhlae

qeqlfbkhqk wey bkane akf lfjeynqbe (

i. Akqkybnhk m{ìf }kyâl {h i{kh ilyýbkqye wlyl kf lfjeynqbe(

[h i{kh ilyýbkqye wlyl kf lfjeynqbe }kynl fl fâhkl ;?

n` LToR6LTdR& ~l |{k k}ql fâhkl }k kokm{ql qlhql} pkmk} mebe m{lf|{nky eqyl akf lfjeynqbe

m. Cljl {h lhìfn}n} ak fl mebwfkonala akf qnkbwe akf lfjeynqbe Q#h. wlyl kf wkey ml}e(

Qnkbwe ak L}njhlmnýh& Qnkbwe ak Mebwlylmnýh& Qnkbwe ak Ewkylmnýh

lynqbîqnml& h2 Qlblüe akf lyykjfe

Fâhkl Mebwfkonala akf qnkbwe

<

9

=

1

;

0

a. Jyl`n|{k kf mebweyqlbnkhqe akf lfjeynqbe Q#h. kh kf wkey ml}e p} kf mebweyqlbnkhqe akf

lfjeynqbe Q#h. kh kf bkoey ml}e(



k.

Akqkybnhk kf mebweyqlbnkhqe l}nhqýqnme ak Q#h. o{}qn`nmìhaefe ak blhkyl akqlfflal(- Fâhkl Me}qe ak Kokm{mnýh

< h$<

9 h

= $<

1

;

0 h

1. l.

ak` nh}kyqnehU}eyq#L.?

***Nh}kyqneh }eyq*** èy o nh sylhjk#<&fkh#L..?

dk~2LToR n2o"< zcnfk n8"< lha LTnR8 dk~?

LTn$<R2LTnR n2n"<

LTn$<R2dk~

ak` bkyjk#L&w&|&y.? h<2|"w$< h92y"|F2ylhjk#7&h<$<. Y2ylhjk#7&h9$<.

7

;

<7

<;

97

9;

<777 =777 ;777 :777 >777

Bkoey Ml}e

Wkey Ml}e



èy n nh sylhjk#7&h<.? FTnR2LTw$nR

èy o nh sylhjk#7&h9.? YToR2LT|$o$<R

FTh<R2>>>>>>>>>> YTh9R2>>>>>>>>>> n27 o27 èy d nh sylhjk#w&y$<.?

n` FTnR62YToR? LTdR2FTnR n2n$<

kf}k? LTdR2YToR o2o$<

ak` bkyjkU}eyq#L&w&y.? n` w 6y?

|2#w$y.%9 bkyjkU}eyq#L&w&|.

bkyjkU}eyq#L&|$<&y. bkyjk#L&w&|&y.

ak` }kfkmqnehU}eyq#l.? èy n nh ylhjk#7&#fkh#l."<..?

d2nèy o nh ylhjk ##n$<.&fkh#l..?

n`#lToR6lTdR.? d2o

lTdR&lTnR2lTnR&lTdR

Fe} alqe} wlyl fl} jyl`nml} }k eiq{pnkyeh meh k}qk mýanje?

n` UUhlbkUU22*UUblnhUU*? èy d nh sylhjk#<777&<<777&<777.? q27 èy o nh sylhjk#7&<7.?

L 2 Tylhaeb(ylhanhq#7& d. èy n nh sylhjk#d.R q<2qnbk(mfemd#. eyakhly#L. -fflblae lf lfjeynqbe ak eyakhlbnkhqe q92qnbk(mfemd#. q2q$#q9"q<.

wynhq q%<7



7

;

<7

<;

97

9;

<777 =777 ;777 :777 >777

nh}kyqneh"}eyq

}kfkmqneh"}eyq

bkyjk"}eyq

Wefnhýbnml #nh}kyqneh"}eyq.

Wefnhýbnml #}kfkmqneh"}eyq.

Fejlyâqbnml #bkyjk"}eyq.

h

q



m( Bkyjk"}eyq? Fl ykm{yykhmnl k}

t

[}lhae kf qkeykbl blk}qye }k qnkhk |{k mebe & khqehmk} (K}qe |{nkyk akmny |{k ksn}qkh

;( Wlyl khmehqyly {hl }ef{mnýh l k}qk wyeifkbl& wynbkye cl~ |{k }kwlylyfk kh }{iwyeifkbl}

iì}nme?

" Eyakhly kf lyykjfe? K}qe }k cne meh bkyjk"}eyq& kf m{lf qnkhk {h qnkbwe

" I{}mly fe} `lmqeyk}? Wlyl k}qe }k {}ý kf lfjeynqbe ak iÿ}|{kal inhlynl kf m{lf qnkhk {h

qnkbwe ak (

Wlyl i{}mly fe} `lmqeyk} wynbkye }k pkyn`nml |{k TR k} nj{lf l mkye( ]n k}qe k} l}â& }k

i{}ml kf hÿbkye yk}{fqlhqk ak fl ewkylmnýh TR ak}ak fl we}nmnýh akf lyykjfe( K}qe }k clmk

cl}ql khmehqyly kf hÿbkye e cl}ql ffkjly lf ÿfqnbe kfkbkhqe akf lyykjfe( Lf `nhlfnly fl}

nqkylmnehk} }k nbwynbk {h bkh}lok kh kf |{k }k nhèybl }n }k clfflyeh e he fe} `lmqeyk} ak(

Kh kf wkey ak fe} ml}e} kf lfjeynqbe ak iÿ}|{kal inhlynl }k fflblyì pkmk} alhae mebe

yk}{fqlae {h qnkbwe ak kokm{mnýh ak ak` bkyjk#L&w&|&y.?

h<2|"w$< h92y"|F2ylhjk#7&h<$<. Y2ylhjk#7&h9$<. èy n nh sylhjk#7&h<.?

FTnR2LTw$nR èy o nh sylhjk#7&h9.?

YToR2LT|$o$<R FTh<R2>>>>>>>>>> YTh9R2>>>>>>>>>> n27 o27 èy d nh sylhjk#w&y$<.?

n` FTnR62YToR? LTdR2FTnR n2n$<

kf}k? LTdR2YToR o2o$<

ak` bkyjkU}eyq#L&w&y.?

n` w 6y? |2#w$y.%9 bkyjkU}eyq#L&w&|. bkyjkU}eyq#L&|$<&y. bkyjk#L&w&|&y.

ak` inhly~U}klymc#L& s& w27& y2 Hehk.? n` y22 Hehk?

y2fkh#L."< zcnfk w 62 y?



| 2 #w $ y. % 9 n` LT|R 8 s?

y 2 | " < kfn` LT|R 6 s?

w 2 | $ < kf}k?

ykq{yh |

ykq{yh "<

ak` i{}mly#L&s.? bkyjkU}eyq#L&7&fkh#L."<. h<27 h92h<èy n nh sylhjk#7&fkh#L."9.?

n` LTnR227? mehqnh{k

kf}k? n`#s+LTnR227.?

h<2inhly~U}klymc#L&s%LTnR&n$<. n` h<,2"<?

h92n iykld

n` h<,2"<? wynhq *Fe} h{bkye} }eh? *&LTh<R&* ~ *&LTh9R

kf}k? wynhq *He cl~ h{bkye} kh kf lyykjfe m{~e wyea{mqe }kl *&s

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Algoritmos - Taller 1 (2011-II)