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ELLIS HOROWITZ SARTAL SAHNI SANBUTHEVAR RAJASEKARAN COMPUTER ALGORITHMS COMPUTER SCIENCE PRESS A a,c Lavy Poundonone Compe toe Pesce Eon oust Compa toe deta Senet anon Pasa a ALK. Downe. ra of en Cnt ta ane Ratan Fog Send ins atom: 4 Easy ‘aed a, LE ef Teaser Space Penni a Sena rot katte dlls Havowis, Lent of Scat Calin Su Sa. Uris cf Foy Stigues Rasharn, Unvovsy Hens, Goes 17 Rawums ain Ueec ‘hye: Onur ara lic xing COMPUTER ALGORITHMS calcu Bia: tect Heme Poet Pear. Pence Hall Text Designer: The ators {est Morons: The there (Cover Desig: A Grod Thing (Cover Mustsion: Torck Ofinsh Froduston Coonan Sha Sndern Compostion: The Auhere Munutscaring: RR Dorney & Sone Company TH ibeny of Comes Calaoging in Publier Docu ‘Copter algal ly ore, Sat Sani, Sungulhevar Rafe, aes Inches ibang rx al ides, ISDN 0 F167 8816-9 [Coal slave. 2 usar Comat proce gui. 1 Suni Sut UL easehare, Songun, ade Gamay AestO7 10 WSA8be yeroas er 4 1908 iy W. H Fura ond Corgany, All sighie iowa wed No pat tis hook my herguedacad hy ae mchanicl. pteinblc ow loshans press, os EBL OTE uuraulis sending, oe ny i ved 0 aretiwal yatn ranshted oceania pid fi public x sate use, hou! Wot poumsinn foe the puis Pinte nthe Une Stas Ata ies peg, SOF Computer Science Pres Stein uf WH Leeman oa Company 4 Muden Avenue, New York, New York 18010 auntie, basingbe ROT XS, England Fa voy melas frsots, MARYANNE, PIP, CHANUCT, mul LRA — Ellis Hosnil a NESTA, GAM. NENA, tl BARAM = Suraj Sabai te NEERAN, RRLSHVA, PANDY, cad PONNUTHAT Sangrtbexar Rajaselouren Contents PREFACE a ANTRODUCTION Ll WHAT TS AN ALCORITIIG? 12 ALGORITIIN SPECIFICATION 121 Paulo Cousens 122 Reweesive Algesition LA PERFORMANCE NALYSIS LT Synor Complexity 132 Thue Gomateaiag F339 Agpmplatie Nowninn (0, 8 TA raed Comp exitoa LAS Pectormauue Mearustuseat at RANDOMIZED ALGORITIM TAL Basi of Pavbabiioe Thasay 12 Raudeouived Algorthaas: vn bolas] Dawription, TAS Mleatiying the Rept! Blew Ls Publi Teang, Teh Adeantages an Disaenenges 13) REFERENCES AND READINGS: ELEMENTARY DATA STRUCTURES 21 STACKS ANT! QUEUES 22 TREES 22.1 terrninokey 222 Binary heen 2a DICTIONARIES, 231 Binsay Secceh ‘Ter 22 Cost Aumestisaicn, 24 ME ONTTY QUEUES 2a. leap 2A Heap AND DISIOINT SET UNIO 25.1 tuinalyelion 282 Lion cud Find Opeeotions 2.6 GRAPHS 26.1 Inteedyetiaw 2d Welintiann 2.83} | Geaph Repenentarions IELRBNCES ARD READINGS DIVIDE-AND-CONQUER. Id GENERAL MEVTION 2 DINARY SbAKCHt 88 FINDING TIE MAX RAIM AND MINTULM 34 MERCH: SORT 13 QUICKSOLL Bsa Pevfinmanne ut 352. Thuvloubed Sutinge Alpaithaos 40) SFLECTION BG A Warst Cow Optics) Agora 362 Tuuplououlavion of Select STRASSEN'S MATRIX MULTIPLIC. TON 38.1 Sone Greuneluie Priutives 382 The Guicksilt Alqurithon 383 Codusm's Seam B84 An Otnlogse: Divideiad-Ceagues Algoritlnn Mt REFERENCES AND RFADINGS AJ ADDITIONAL EXERCISES THE GREEDY METHOD AL THE GENERAT. WRTHOD 42 KNAPSACK PROBLEM 48 TREK VERTEX SPITTING 42 108 SEQUENCING WITH DEADLINES: 4G MINIMIIM COST SPANNING TREES 2S Fvan"s Algor tw CONTENTS CONTENYS 452 Kewski's Abseiline AES Au Opsined Magia! Alyoritaa (6) 46 OPTIMAL STORAGE ON TAPE: 47 OPUIMAL VERGE PATTERNS 48 SINGLE SOURCE SHORTEST PATHS 49. REFLRENCES AND READINGS I ADDITIONAL EXERCISES DYNAMIC PROGHAM MING 1 TK GENERAL METHOD 52. MULTISTAGE GRAPHS 33 ALL PAIRS SHORTEST PATIIS $4. SINGLE-SOURCE SIONTEST PATHS: GENERAL WEICITS 88 QDTIMAL BIKARY SEANC: TREES :+) 66 STRING EDITING fa Gg 1KRAPSACK Ss RECIADILITY DESIGN A THICTRACELING S4LESPERSON EROMLEM F.ln FLOW SHOP SCHFNUNIAG AA RERERENCES AND READINGS A ADDPITONAL EXERCISES @ RASIC: TRAVERSAL ANI) SRARCH TECHNIQUES fil ‘TECUINIQLES FOR BINARY TREES fz TROMNQCES FOR GRAPHS fi.1- Se. Bitsy Seteh ane Trewern 6.22 Dep Meu Sonveh wl Traweal CONNECTED COMPONENTS AND SPANNING TREES 4 RICONNEGTRD COMPONENTS AND DPS 5. REFDRENCES AND READINGS 1 BACKTRACKING HE GENENAS MELIOD THE §-QUEENS PROBLEM SUM OF SUBSETS BRAPIL COLORING HAMILTONIAN GveLES Bal KRABSACK MOLI * consis 77 REFERENCKY AND READINGS ord 74. ADDITIONAL EXERCIS a 8 BRANCH-AND-BOUND 370 31 THE METHOD. 370 SAL Lave Gist 14 Searels 3e0 $12 The UGesurale: aa Exauple 32 AIA. Contre Atatrneticns LC-Soaeeh 386 S14 Botting 383 AUG FIFQ Branleaul Boil 301 S16 LC Aeancesal-Bound 302 2 ll KNAPSACK PROBLEM ma S21 LC BraasnsL Toate Solution at $2.2 FICO Brauchund-Ttond Selneina nF 83. TRAVELING SALTSPIRSOR & sks 8a EFFICIENCY CONSIDERATIONS eed 88 REFERENCES AND READINGS, a6 9 ALGEBRAIC PROBLEMS ay ba THE CENERAL METION a7 92. EVALTIATION AND INTERPOLATION 220 3 THETAST FOURIER TRANSTORM, 430 Yoko A Tuepleee Version of tom FE a8 832 See Remaining Paints 4 gel MON WNT ARTI EMIT! st B93 GVER FASTER IVALUSTION ARD INTERFOLSTION | 13 Yi REFERENCES AND READINGS 458, 1p LOWE BOUND THEORY S01 COMPARISON THEES 101.1 Ovlered Searching 1012 Somting UAL Selo 102 ORACLES AND ADVERSARY ARGLMENTS WL Merging W022 Lager ane Hecend Laagost 1.233 State Spee Mot byd W2A Selection O44 LOWER HOCIMIDS THROUGH REDUCTIONS 4