Download pdf - Cormen Contents 1stEdition

8/13/2019 Cormen Contents 1stEdition

1/5

Introduction to Algorithms,First Edition(1990)

Thomas H. CormenCharles E. Leiserson

Ronald L. RivestTable of Contents

Preface 1 Introduction 1.1 Algorithms1.2 Analyzing algorithms1.3 Designing algorithms1.4 Summary

I Mathematical Foundations

Introduction 2 ro!th of "unctions 2.1 Asymptotic notation2.2 Standard notations and common functions# $ummations 3.1 Summation formulas and properties3.2 Bounding summations% Recurrences 4.1 The substitution method4.2 The iteration method4.3 The master method4.4 roof of the master theorem& $ets, Etc.

!.1 Sets!.2 "elations!.3 #unctions!.4 $raphs!.! Trees' Counting and Pro(a(ilit) %.1 &ounting%.2 robability%.3 Discrete random 'ariables%.4 The geometric and binomial distribution%.! The tails of the binomial distribution%.% robabilistic analysis

II Sorting and Order Statistics Introduction * Hea+sort (.1 )eaps(.2 *aintaining the heap property(.3 Building a heap(.4 The heapsort algorithm(.! riority +ueues -uic sort


2/5


3/5

1(.! A tas- scheduling problem1 Amorti6ed Anal)sis 1,.1 The aggregate method1,.2 The accounting method1,.3 The potential method1,.4 Dynamic tables

V Advanced Data Structures Introduction1/ 45Trees1/.1 3efinition of 45trees1/.2 4asic o+erations on 45trees1/.# 3eleting a e) from a 45tree20 4inomial Hea+s20.1 4inomial trees and (inomial hea+s20.2 +erations on (inomial hea+s21 "i(onacci Hea+s21.1 $tructure of "i(onacci hea+s21.2 ergea(le5hea+ o+erations21.# 3ecreasing a e) and deleting a node21.% 4ounding the ma7imum degree22 3ata $tructures for 3is8oint $ets22.1 3is8oint5set o+erations22.2 Lin ed5list re+resentation of dis8oint sets22.# 3is8oint5set forests22.% Anal)sis of union () ran !ith +ath com+ression

VI #ra$h Algorithms Introduction2# Elementar) ra+h Algorithms2#.1 Re+resentations of gra+hs2#.2 4readth5first search2#.# 3e+th5first search2#.% To+ological sort2#.& $trongl) connected com+onents2% inimum $+anning Trees2%.1 ro!ing a minimum s+anning tree2%.2 The algorithms of 9rus al and Prim2& $ingle5$ource $hortest Paths2&.1 $hortest +aths and rela7ation2&.2 3i8 stra:s algorithm2&.# The 4ellman5"ord algorithm2&.% $ingle5source shortest +aths in directed ac)clic gra+hs2&.& 3ifference constraints and shortest +aths

2' All5Pairs $hortest Paths2'.1 $hortest +aths and matri7 multi+lication2'.2 The "lo)d5;arshall algorithm2'.#


4/5

2*.% Preflo!5+ush algorithms2*.& The lift5to5front algorithm

VII Selected !o$ic Introduction

2 $orting =et!or s2 .1 Com+arison net!or s2 .2 The 6ero5one +rinci+le2 .# A (itonic sorting net!or2 .% A merging net!or2 .& A sorting net!or2/ Arithmetic Circuits2/.1 Com(inational circuits2/.2 Addition circuits2/.# ulti+lication circuits2/.% Cloc ed circuits#0 Algorithms for Parallel Com+uters#0.1 Pointer 8um+ing#0.2 CRC; algorithms versus ERE; algorithms#0.# 4rent:s theorem and !or efficienc)#0.% ;or 5efficient +arallel +refi7 com+utation#0.& 3eterministic s)mmetr) (rea ing#1 atri7 +erations#1.1 Pro+erties of matrices#1.2 $trassen:s algorithm for matri7 multi+lication#1.# Alge(raic num(er s)stems and (oolean matri7 multi+lication#1.% $olving s)stems of linear e>uations#1.& Inverting matrices#1.' $)mmetric +ositive5definite matrices and least5s>uares a++ro7imation#2 Pol)nomials and the ""T#2.1 Re+resentation of +ol)nomials#2.2 The 3"T and ""T#2.# Efficient ""T im+lementation## =um(er5Theoretic Algorithms##.1 Elementar) num(er5theoretic notions##.2 reatest common divisor##.# odular arithmetic##.% $olving modular linear e>uations##.& The Chinese remainder theorem##.' Po!ers of an element##.* The R$A +u(lic5 e) cr)+tos)stem##. Primalit) testing##./ Integer factori6ation

#% $tring atching

#%.1 The naive string5matching algorithm#%.2 The Ra(in59ar+ algorithm#%.# $tring matching !ith finite automata#%.% The 9nuth5 orris5Pratt algorithm#%.& The 4o)er5 oore algorithm#& Com+utational eometr)#&.1 Line5segment +ro+erties#&.2 3etermining !hether an) +air of segments intersects#&.# "inding the conve7 hull#&.% "inding the closest +air of +oints


5/5

#' =P5Com+leteness#'.1 Pol)nomial time#'.2 Pol)nomial5time verification#'.# =P5com+leteness and reduci(ilit)#'.% =P5com+leteness +roofs#'.& =P5com+lete +ro(lems#* A++ro7imation Algorithms#*.1 The verte75cover +ro(lem#*.2 The traveling5salesman +ro(lem#*.# The set5covering +ro(lem#*.% The su(set5sum +ro(lem

4i(liogra+h)Inde7