algoritmos - taller 1 (2011-ii)
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5/11/2018 Algoritmos - Taller 1 (2011-II) - slidepdf.com
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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 ⌏
⌄
5/11/2018 Algoritmos - Taller 1 (2011-II) - slidepdf.com
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∜
[}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 yk`eylyfl?
L}{bnkhae meh ~
⌏⌄
⌏⌄ ⌏
⌄ ⌏⌄ ⌏
⌄
5/11/2018 Algoritmos - Taller 1 (2011-II) - slidepdf.com
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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}&
5/11/2018 Algoritmos - Taller 1 (2011-II) - slidepdf.com
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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$< bn}qkyne#h%9.
`ey o nh ylhjk#<&h.? `ey d nh ylhjk#n&o.?
wynhq *hlal*
l. Wflhqkk {hl km{lmnýh ak ykm{yykhmnl wlyl Q#h.& kf qnkbwe |{k qebl fl `{hmnýh bn}qkyne#h.?
i. Akqkybnhk kf mebweyqlbnkhqe l}nhqýqnme ak Q#h. o{}qn`nmlhae ak blhkyl akqlfflal?
K}ql `{hmnýh ak ykm{yykhmnl k}ql kswyk}lal kh qîybnhe} kh fe} m{lfk} w{kak }ky lwfnmlae kf
Qkeykbl Blk}qye& khqehmk} qkhkbe} |{k?
]kjÿh kf qkeykbl blk}qye weakbe} akmny |{k? ]n # . & khqehmk}&
& kh k}qk ml}e (
Wey qlhqe?
5/11/2018 Algoritmos - Taller 1 (2011-II) - slidepdf.com
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# .
=. Kf lfjeynqbe wlyl kf ]kfkmqneh ]eyq k} kf }nj{nkhqk?
ak` }kfkmqnehU}eyq#L.? < `ey n nh ylhjk#7&#fkh#L."<..? 9 d2n= `ey o nh ylhjk ##n$<.&fkh#L..? 1 n`#LToR6LTdR.? ; d2o0 LTdR<nR2LTnR<dR
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$<†hR ~
}k mefeml kh fl we}nmnýh n(
@nhlfnzlmnýh? n }k khm{khqyl meh plfey h& wey qlhqe kf lyykjfe LT7†nR ~l }k cl eyakhlae
qeqlfbkhqk wey bkane akf lfjeynqbe (
i. Akqkybnhk m{ìf }kyâl {h i{kh ilyýbkqye wlyl kf lfjeynqbe(
[h i{kh ilyýbkqye wlyl kf lfjeynqbe }kynl fl fâhkl ;?
n` LToR6LTdR& ~l |{k k}ql fâhkl }k kokm{ql qlhql} pkmk} mebe m{lf|{nky eqyl akf lfjeynqbe
m. Cljl {h lhìfn}n} ak fl mebwfkonala akf qnkbwe akf lfjeynqbe Q#h. wlyl kf wkey ml}e(
Qnkbwe ak L}njhlmnýh& Qnkbwe ak Mebwlylmnýh& Qnkbwe ak Ewkylmnýh
lynqbîqnml& h2 Qlblüe akf lyykjfe
Fâhkl Mebwfkonala akf qnkbwe
<
9
=
1
;
0
a. Jyl`n|{k kf mebweyqlbnkhqe akf lfjeynqbe Q#h. kh kf wkey ml}e p} kf mebweyqlbnkhqe akf
lfjeynqbe Q#h. kh kf bkoey ml}e(
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k.
Akqkybnhk kf mebweyqlbnkhqe l}nhqýqnme ak Q#h. o{}qn`nmìhaefe ak blhkyl akqlfflal(- Fâhkl Me}qe ak Kokm{mnýh
< h$<
9 h
= $<
1
;
0 h
1. l.
ak` nh}kyqnehU}eyq#L.?
***Nh}kyqneh }eyq*** `ey o nh sylhjk#<&fkh#L..?
dk~2LToR n2o"< zcnfk n8"< lha LTnR8 dk~?
LTn$<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
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`ey n nh sylhjk#7&h<.? FTnR2LTw$nR
`ey o nh sylhjk#7&h9.? YToR2LT|$o$<R
FTh<R2>>>>>>>>>> YTh9R2>>>>>>>>>> n27 o27 `ey d nh sylhjk#w&y$<.?
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.? `ey n nh ylhjk#7&#fkh#l."<..?
d2n`ey o nh ylhjk ##n$<.&fkh#l..?
n`#lToR6lTdR.? d2o
lTdR&lTnR2lTnR&lTdR
Fe} alqe} wlyl fl} jyl`nml} }k eiq{pnkyeh meh k}qk mýanje?
n` UUhlbkUU22*UUblnhUU*? `ey d nh sylhjk#<777&<<777&<777.? q27 `ey o nh sylhjk#7&<7.?
L 2 Tylhaeb(ylhanhq#7& d. `ey n nh sylhjk#d.R q<2qnbk(mfemd#. eyakhly#L. -fflblae lf lfjeynqbe ak eyakhlbnkhqe q92qnbk(mfemd#. q2q$#q9"q<.
wynhq q%<7
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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
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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 nh`eybl }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$<. `ey n nh sylhjk#7&h<.?
FTnR2LTw$nR `ey o nh sylhjk#7&h9.?
YToR2LT|$o$<R FTh<R2>>>>>>>>>> YTh9R2>>>>>>>>>> n27 o27 `ey 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?
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| 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<`ey 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? *<h<R&* ~ *<h9R
kf}k? wynhq *He cl~ h{bkye} kh kf lyykjfe m{~e wyea{mqe }kl *&s
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