Problems for Homework 1 - Algorithms | CMSC 351, Assignments of Algorithms and Programming

Material Type: Assignment; Professor: Kruskal; Class: Algorithms; Subject: Computer Science; University: University of Maryland; Term: Unknown 2007;

Typology: Assignments

Pre 2010

Uploaded on 07/30/2009

koofers-user-qlx
koofers-user-qlx ๐Ÿ‡บ๐Ÿ‡ธ

10 documents

1 / 1

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
๎˜€๎˜‚๎˜๎˜„๎˜ƒ๎˜…๎˜ƒ๎˜‡๎˜†๎˜‰๎˜ˆ๎˜‹๎˜Š๎˜๎˜Œ๎˜Ž๎˜Œ๎˜๎˜ ๎˜‘๎˜“๎˜’๎˜•๎˜”๎˜–๎˜‘๎˜˜๎˜—๎˜š๎˜™๎˜œ๎˜›๎˜ž๎˜ ๎˜Ÿ"!$#&%(')!๎˜ž*,+-๎˜› .0/21๎˜‚34๎˜†656๎˜ˆ7๎˜๎˜„8:9,;๎˜Ž/
<
๎˜4๎˜† ;๎˜=>=:?๎˜„๎˜† 8@=:;๎˜๎˜ˆ:=>A๎˜ŽBDC๎˜‰/E;๎˜Ž8:8๎˜‹F4๎˜ˆ7GE3๎˜„;H1๎˜ŽI๎˜šJK๎˜๎˜žL4๎˜† MNI๎˜š๎˜Š๎˜๎˜Œ๎˜Ž๎˜Œ๎˜๎˜(O
P
*,!๎˜žQDRS%N# ๎˜›๎˜„TU.VAKL๎˜ž8:GE34๎˜†๎˜‰๎˜ˆ๎˜‹;๎˜…=@๎˜ˆ:๎˜†๎˜‰๎˜† WX?4๎˜†๎˜‰๎˜ˆ:๎˜† ๎˜†๎˜‰Y๎˜Ž๎˜†๎˜‰๎˜ˆ71ZL4AN3๎˜„๎˜† ?๎˜„;๎˜Ž8X๎˜†\[๎˜‚;๎˜ŽC\=:/21"]๎˜‰๎˜†๎˜‰๎˜ˆ:A๎˜…A๎˜Ž๎˜ˆ^=_WVA`Ca?๎˜„GE/E3๎˜„๎˜ˆ:๎˜†bL๎˜œO0cd๎˜†๎˜‰=fehgi๎˜†
=:?๎˜„๎˜† L(๎˜๎˜ž๎˜ƒ gi๎˜†๎˜‰๎˜ˆjA๎˜ŽBDGEL๎˜=@๎˜†๎˜‰๎˜ˆaL๎˜„;๎˜Ž/dL4A๎˜‚34๎˜†b8lkmL4AKL๎˜„/E๎˜†b;bY๎˜Ž๎˜†b8an>;๎˜ŽL๎˜„3Zopgi๎˜†6=:?4๎˜†lLN๎˜๎˜„๎˜ƒUgi๎˜†๎˜‰๎˜ˆjA๎˜ŽBD/E๎˜†b;bY๎˜Ž๎˜†b8๎˜‰O
km;๎˜nZq6G2Y๎˜Ž๎˜†๎˜‹;๎˜ŽL๎˜„3๎˜‡๎˜†brN๎˜๎˜„;๎˜=:G2AKLs๎˜ˆ:๎˜†b/E;๎˜=:GEL4tleU;๎˜ŽL๎˜„3so๎˜‹OjkSuvOw๎˜†๎˜ŽO2I๎˜‚?4AHWx3๎˜„A(๎˜†b8y=:?๎˜„๎˜†๎˜‹L(๎˜๎˜ž๎˜ƒ gi๎˜†๎˜‰๎˜ˆyA๎˜ŽB๎˜œGEL(=@๎˜†๎˜‰๎˜ˆ7L๎˜„;๎˜Ž/4L4A๎˜‚34๎˜†b8
C\AK๎˜ƒsz๎˜ž;๎˜๎˜ˆ:๎˜†lW๎˜‹GE=:?{=:?4๎˜† LN๎˜๎˜„๎˜ƒ gi๎˜†๎˜‰๎˜ˆjA๎˜ŽBD/2๎˜†b;bY๎˜Ž๎˜†b8v|}n
kSg$n`~๎™ฟ๎˜ˆ:AHY๎˜Ž๎˜†U1๎˜ŽAK๎˜4๎˜ˆ๎˜‹;๎˜ŽL๎˜„8:W๎š€๎˜†๎˜‰๎˜ˆ๎˜‹๎˜๎˜ž8:GEL4t๎˜‡๎˜ƒs;๎˜=:?4๎˜†b๎˜ƒ๎˜…;๎˜=:GEC๎˜‰;๎˜Ž/๎šGEL๎˜ž3๎˜„๎˜๎˜„C\=:G2AKL๎˜œO
P
*,!๎˜žQDRS%N#๎šƒ๎š‚iTU.VAKL๎˜ž8:GE34๎˜†๎˜‰๎˜ˆ๎˜œ=:?4๎˜†๎š€z๎˜„๎˜ˆ:A๎˜Žg๎˜ž/E๎˜†b๎˜ƒ๎š„A๎˜ŽB๎˜„L4A๎˜Ž=dAKL๎˜„/E1^๎š…๎˜šL๎˜„3๎˜„GEL4t0=:?4๎˜†๎š€Y,;๎˜Ž/๎š†๎˜4๎˜†๎š‡A๎˜ŽB4=:?4๎˜†๎™ฟ๎˜ƒ๎˜…;,[๎˜‚GE๎˜ƒ๎˜“๎˜๎˜„๎˜ƒ๎šˆC\AKL๎˜=:G2tK๎˜๎˜„AK๎˜๎˜„8
87๎˜๎˜„๎˜ƒ๎š‰GEL๎˜‡;๎˜ŽL๎˜‡;๎˜๎˜ˆ:๎˜ˆ7;H1๎˜ŽI(g๎˜š๎˜4=y;๎˜Ž/E8@A634๎˜†๎˜‰=@๎˜†๎˜‰๎˜ˆ7๎˜ƒsG๎š†L๎˜„GEL4t^=:?4๎˜†j=_WVA ๎˜†bL๎˜ž34ziAKGEL๎˜=:8bODqfG2Y๎˜Ž๎˜†>;6/๎š†GEL4๎˜†b;๎˜๎˜ˆD=:GE๎˜ƒ๎˜‡๎˜†>;๎˜Ž/2t๎˜ŽA๎˜Ž๎˜ˆaG2=:?๎˜„๎˜ƒ
BSA๎˜Ž๎˜ˆ๎˜‹8@AK/EYNGEL๎˜„t๎˜“=:?๎˜žGE8jz๎˜„๎˜ˆ:A๎˜Žg๎˜š/2๎˜†b๎˜ƒ๎šŠO>๎š‹ ๎šŒ-?๎˜ž;๎˜=๎˜‹?๎˜„;๎˜z๎˜„zi๎˜†bL๎˜„8jG2B๎˜–;๎˜Ž/E/i๎˜†bL(=@๎˜ˆ7G2๎˜†b8๎˜‹;๎˜๎˜ˆ7๎˜†lL4๎˜†๎˜‰tK;๎˜=:G2Y๎˜Ž๎˜†}|๎˜‰๎š
P
*,!๎˜žQDRS%N#๎šŽ๎˜—๎˜œT6๎šŒ๎š๎˜†0C๎˜‰;๎˜ŽL t๎˜Ž๎˜†bL๎˜„๎˜†๎˜‰๎˜ˆ7;๎˜Ž/EG2]๎˜‰๎˜†V=:?4๎˜†U๎š@๎˜ƒ๎˜…;,[๎˜‚GE๎˜ƒ๎˜“๎˜๎˜„๎˜ƒ๎š‘C\AKL๎˜=:GEtK๎˜4AK๎˜๎˜„8๎˜–8:๎˜๎˜„๎˜ƒ๎š’z๎˜ž๎˜ˆ:A๎˜Žg๎˜ž/2๎˜†b๎˜ƒs๎š“>=@AX=๎š”W๎š€A63๎˜„GE๎˜ƒs๎˜†bL๎˜„8:G2AKL๎˜„8
=@A๎š•8@AK/2Y๎˜Ž๎˜†"=:?4๎˜†๎š–๎š@๎˜ƒs;,[4GE๎˜ƒ๎˜“๎˜๎˜„๎˜ƒ๎š—C\AKL(=:G2tK๎˜4AK๎˜๎˜ž8๎˜…๎˜ˆ:๎˜†bC\=:;๎˜ŽL๎˜„tK/2๎˜†"z๎˜„๎˜ˆ7A๎˜Žg๎˜ž/2๎˜†b๎˜ƒs๎š“๎˜‚O๎š’qfG2Y๎˜Ž๎˜†bL๎š–;๎˜ŽLx๎š˜๎šš๎š™๎šœ๎š›๎šˆ;๎˜๎˜ˆ:๎˜ˆ7;b1๎šA๎˜ŽB
kSziAK8:GE=:G2Y๎˜Ž๎˜†๎šž;๎˜ŽL๎˜ž3๎š„L4๎˜†๎˜‰tK;๎˜=:G2Y๎˜Ž๎˜†}n`LN๎˜๎˜„๎˜ƒ gi๎˜†๎˜‰๎˜ˆ78bI>๎š…๎˜žL๎˜„3๎š–=:?4๎˜†๎š/E;๎˜๎˜ˆ:t๎˜Ž๎˜†b8@=๎šŠ8:๎˜๎˜ž๎˜ƒ๎šŸA๎˜ŽBUY,;๎˜Ž/๎š†๎˜4๎˜†b8{GEL๎š ;๎š kmC\AKL(=:G2tK๎˜4AK๎˜๎˜ž8an
๎˜ˆ7๎˜†bC\=:;๎˜ŽL4tK/2๎˜†๎˜ŽO
km;๎˜n`๎šŒ๎š๎˜ˆaG2=@๎˜† 34A}W๎˜‹L๎šŠ;๎˜ŽLZยก๎™ฟL๎˜„tK/EGE8:?`34๎˜†b8:C\๎˜ˆ7GEz๎˜„=:G2AKL`A๎˜ŽBยข=:?๎˜„๎˜†"๎šยฃg๎˜„๎˜ˆ7๎˜4=@๎˜†fBSA๎˜Ž๎˜ˆ7C\๎˜†b๎š“s;๎˜Ž/2t๎˜ŽA๎˜Ž๎˜ˆaG2=:?๎˜„๎˜ƒยคBSA๎˜Ž๎˜ˆ>=:?4๎˜†Z๎š@๎˜ƒs;,[Nยฅ
G๎š†๎˜ƒU๎˜๎˜„๎˜ƒยฆC\AKL(=:G2tK๎˜4AK๎˜๎˜ž8>๎˜ˆ:๎˜†bC\=:;๎˜ŽL4tK/E๎˜†lz๎˜„๎˜ˆ:A๎˜Žg๎˜ž/E๎˜†b๎˜ƒs๎š“๎˜‚O๎š€ยงfL4๎˜†6A๎˜Ž๎˜ˆ>=๎š”W๎š€A`8@๎˜†bL(=@๎˜†bL๎˜„C\๎˜†b8๎˜‹8:?๎˜„AK๎˜๎˜„/E3{8:๎˜4ยจ๎˜…C\๎˜†๎˜ŽO
kSg$nh๎šŒ๎š๎˜ˆaG2=@๎˜† 34A}W๎˜‹L๎šŠ=:?4๎˜†"๎šยฃg๎˜ž๎˜ˆ7๎˜4=@๎˜†6BSA๎˜Ž๎˜ˆ7C\๎˜†b๎š“s;๎˜Ž/2t๎˜ŽA๎˜Ž๎˜ˆ7GE=:?๎˜„๎˜ƒยฆGEL๎šŠz๎˜ž87๎˜4๎˜†b34A๎˜‚C\AN34๎˜†๎˜ŽO
kmCHn{ยฉXAHW๎š‘๎˜ƒs;๎˜ŽL(1`=:G๎š†๎˜ƒ๎˜‡๎˜†b8>GE80=:?4๎˜†UGEL๎˜„L4๎˜†๎˜‰๎˜ˆj/2ANA๎˜ŽzZ๎˜†\[๎˜‚๎˜†bC๎˜‰๎˜4=@๎˜†b3๎˜š|"๎šŒ๎š๎˜ˆ7G2=@๎˜† GE=>๎˜๎˜„8:GEL4t๎˜‡8:๎˜๎˜ž๎˜ƒs๎˜ƒs;๎˜=:G2AKL๎˜„8bO
km3๎˜šn๎šŠ๎˜€4GE๎˜ƒ๎˜‡z๎˜ž/EGEBยช1๎šœ1๎˜ŽAK๎˜4๎˜ˆ๎šŠ;๎˜ŽL๎˜„8@WV๎˜†๎˜‰๎˜ˆbO๎š‘J๎˜๎˜๎˜„8@=:G2BS1๎š•1๎˜ŽAK๎˜4๎˜ˆhWVA๎˜Ž๎˜ˆ:9$Oยค๎š‹ uยซB61๎˜ŽAK๎˜๎š 34Aยฌ=:?๎˜„GE8s๎˜ˆaG2tK?๎˜=๎˜‰I๎˜‹=:?4๎˜†๎šญ8@AK/๎š†๎˜4=:G2AKL
G๎š†L๎˜Y๎˜ŽAK/2Y๎˜Ž๎˜†b8๎˜‹Y๎˜Ž๎˜†๎˜‰๎˜ˆ:1{/EG2=@=:/2๎˜†lC๎˜‰;๎˜Ž/EC๎˜‰๎˜๎˜ž/E;๎˜=:G2AKL๎˜œO ๎š
kS๎˜†}n๎šญ๎˜‘)ยฎ๎šยฏ๎˜žRmRS%๎˜‚ยฐ๎šยฑ๎˜š%
P
*}!๎˜šQ๎˜–RS%๎˜‚#pT๎š’FDGEL๎˜„3๎š;ยฒg$๎˜†๎˜‰=@=@๎˜†๎˜‰๎˜ˆh;๎˜Ž/2t๎˜ŽA๎˜Ž๎˜ˆ7G2=:?๎˜„๎˜ƒยณBยชA๎˜Ž๎˜ˆs=:?๎˜„๎˜†Z๎˜ƒs;,[๎˜‚G๎š†๎˜ƒU๎˜๎˜„๎˜ƒ๎š—C\AKL๎˜=:G2tK๎˜๎˜„AK๎˜๎˜„8
๎˜ˆ7๎˜†bC\=:;๎˜ŽL4tK/2๎˜†lz๎˜„๎˜ˆ7A๎˜Žg๎˜ž/2๎˜†b๎˜ƒ๎šŠO๎š‡ยฉXAHW๎šˆW๎š€๎˜†b/E/๎˜œC๎˜‰;๎˜ŽL"1๎˜ŽAK๎˜Z34A(|
P
*,!๎˜žQDRS%N#ยตยดdTUqfGEY๎˜Ž๎˜†lC\A๎˜Ž๎˜ˆ:๎˜ˆ:๎˜†bC\=๎˜‹z๎˜š8@๎˜†b๎˜๎˜„34A๎˜ยฅ_C\A๎˜‚34๎˜†6BSA๎˜Ž๎˜ˆ>=:?4๎˜† ๎˜ƒ๎˜‡A๎˜‚3๎˜„G2๎š…๎˜ž๎˜†b3hg๎˜š๎˜4g๎˜„g๎˜ž/2๎˜†f8@A๎˜Ž๎˜ˆ:=X;๎˜Ž/2t๎˜ŽA๎˜Ž๎˜ˆ7G2=:?๎˜„๎˜ƒZO๎™ฟยถ";๎˜9๎˜Ž๎˜†U1๎˜ŽAK๎˜4๎˜ˆ
;๎˜Ž/Et๎˜ŽA๎˜Ž๎˜ˆ7G2=:?๎˜„๎˜ƒยท;๎˜Ž8๎˜…๎šยฃ๎˜†b/2๎˜†๎˜‰tK;๎˜ŽL๎˜=:๎š“`;๎˜Ž8jziAK8:8:GEg๎˜ž/2๎˜†๎˜ŽO
ยธ

Partial preview of the text

Download Problems for Homework 1 - Algorithms | CMSC 351 and more Assignments Algorithms and Programming in PDF only on Docsity!

< 4^ ;=>=:?^8 @=:;^ :=>ABDC^ /E;8:8^ F47GE3;H1IJKL4^ MNI^  (O

P *,!QDRS%N# TU.VAKL8:GE34  ;=@:  WX?4 : Y 71ZL4AN3 ?;8X[;C=:/21"] :AA^=_WVA`Ca?GE/E3:bLO0cd =fehgi =:? L( gi jABDGEL=@ aL;/dL4A34b8lkmL4AKL/Eb;bYb8an>;L3Zopgi6=:?4lLNUgi jABD/Eb;bYb8 O

km;nZq6G2Y ;L3brN; =:G2AKLs:b/E; =:GEL4tleU;L3so OjkSuvOwO2I?4AHWx3A(b8y=:? L( gi yABGEL(=@ 7L;/4L4A34b C\AKsz; :lW GE=:?{=:?4 LN gi jABD/2b;bYb8v|}n kSg$n`~:AHYU1AK4 ;L8:Wย€  8:GEL4ts; =:?4b; =:GEC ;/ยGEL3C=:G2AKLO

P *,!QDRS%N#ยƒย‚iTU.VAKL8:GE34 =:?4ย€z:Ag/Ebย„ABL4A=dAKL/E1^ L3GEL4t0=:?4ย€Y,;/ย†4ย‡AB4=:?4;,[GEยˆC\AKL=:G2tKAK 8 7ย‰GEL;L; :7;H1I(g4=y;/E8@A634 =@ 7sGย†LGEL4t^=:?4j=_WVA bL34ziAKGEL=:8bODqfG2Y>;6/ย†GEL4b; D=:GE>;/2tAaG2=:? BSA 8 @AK/EYNGELt=:?GE8jz:Ag/2bยŠO>ย‹ ยŒ-?; = ?; zzibL8jG2B;/E/ibL(=@7G2b8 ; 7lL4 tK; =:G2Y}| ย

P *,!QDRS%N#ยŽT6ยŒย0C^ ;L^ tbL^ 7;/EG2]^ V=:?4Uย@;,[GEย‘C\AKL=:GEtK4AK88:ย’z:Ag/2bsย“>=@AX=ย”Wย€A63GEsbL8:G2AKL =@Aย•8@AK/2Y"=:?4ย–ย@s;,[4GEย—C\AKL(=:G2tK4AK8:bC=:;LtK/2"z7Ag/2bsย“Oย’qfG2YbLย–;Lxย˜ยšย™ยœย›ยˆ; :7;b1ยAB kSziAK8:GE=:G2Yยž;L3ย„L4 tK; =:G2Y}n`LN gi 78bI> L3ย–=:?4ย/E; :tb8@=ยŠ8:ยŸABUY,;/ย†4b8{GEL ; kmC\AKL(=:G2tK4AK8an 7bC=:;L4tK/2O

km;nยŒยaG2=@ 3 4A}W LยŠ;LZยกLtK/EGE8:?34b8:C\7GEz=:G2AKLABยข=:?"ยยฃg74=@fBSA7C\bย“s;/2tAaG2=:?ยคBSA>=:?4Zย@s;,[Nยฅ Gย†UยฆC\AKL(=:G2tK4AK8>:bC\=:;L4tK/Elz:Ag/Ebsย“Oย€ยงfL46A>=ย”Wย€A8@bL(=@bLC\b8 8 :?AK/E3{8:4ยจC\O kSg$nhยŒยaG2=@ 3 4A}W LยŠ=:?4"ยยฃg74=@6BSA7C\bย“s;/2tA7GE=:?ยฆGELยŠz874b34AC\AN34O kmCHn{ยฉXAHWย‘s;L(1`=:Gย†b8>GE80=:?4UGELL4 j/2ANAzZ[bC 4=@b3|"ยŒย7G2=@ GE=>8:GEL4t8:ss; =:G2AKL8bO km3nยŠ4GEz/EGEBยช1ยœ1AK4ยŠ;L8@WV bOย‘J8@=:G2BS1ย•1AK4hWVA:9$Oยคย‹ uยซB61AK 3 4Aยฌ=:?GE8saG2tK?= I =:?48@AK/ย†4=:G2AKL Gย†LYAK/2Yb8 Y :1{/EG2=@=:/2lC ;/EC /E; =:G2AKLO ย kS}n)ยฎยยฏRmRS%ยฐยยฑ% P *}!QRS%#pTย’FDGEL3ย;ยฒg$ =@=@ h;/2tA7G2=:?ยณBยชAs=:?Zs;,[Gย†Uย—C\AKL=:G2tKAK 7bC=:;L4tK/2lz7Ag/2bยŠOย‡ยฉXAHWยˆWย€b/E/C ;L"1AKZ34A(|

P *,!QDRS%N#ฮผยดdTUqfGEYlC\A::bC= z8@b34A ยฅ_C\A346BSA>=:?4 A3G2 b3hg4gg/2f8@A:=X;/2tA7G2=:?ZOยถ"; 9 U1AK4 ;/EtA7G2=:?ยท;8ยยฃb/2 tK;L=:ย“`;8jziAK8:8:GEg/2O