Sistemas

Instructor’s Manual
by Thomas H. Cormen
Clara Lee
Erica Lin

to Accompany

Introduction to Algorithms
Second Edition
by Thomas H. Cormen
Charles E. Leiserson
Ronald L. Rivest
Clifford Stein

The MIT Press
Cambridge, Massachusetts

London, England

McGraw-Hill Book Company
Boston
Burr Ridge, IL
New York
San Francisco

Dubuque, IA
St. Louis
Montr´ al
e

Madison, WIToronto

Instructor’s Manual
by Thomas H. Cormen, Clara Lee, and Erica Lin
to Accompany
Introduction to Algorithms, Second Edition
by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein
Published by The MIT Press and McGraw-Hill Higher Education, an imprint of The McGraw-Hill Companies,
Inc., 1221 Avenue of the Americas, New York, NY 10020. Copyright c 2002 byThe Massachusetts Institute of
Technology and The McGraw-Hill Companies, Inc. All rights reserved.
No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database
or retrieval system, without the prior written consent of The MIT Press or The McGraw-Hill Companies, Inc., including, but not limited to, network or other electronic storage ortransmission, or broadcast for distance learning.

Contents

Revision History
Preface

R-1

P-1

Chapter 2: Getting Started
Lecture Notes 2-1
Solutions 2-16
Chapter 3: Growth of Functions
Lecture Notes 3-1
Solutions 3-7
Chapter 4: Recurrences
Lecture Notes 4-1
Solutions 4-8
Chapter 5: Probabilistic Analysis and Randomized Algorithms
Lecture Notes 5-1
Solutions 5-8
Chapter 6:Heapsort
Lecture Notes 6-1
Solutions 6-10
Chapter 7: Quicksort
Lecture Notes 7-1
Solutions 7-9
Chapter 8: Sorting in Linear Time
Lecture Notes 8-1
Solutions 8-9
Chapter 9: Medians and Order Statistics
Lecture Notes 9-1
Solutions 9-9
Chapter 11: Hash Tables
Lecture Notes 11-1
Solutions 11-16
Chapter 12: Binary Search Trees
Lecture Notes 12-1
Solutions 12-12
Chapter 13: Red-Black TreesLecture Notes 13-1
Solutions 13-13
Chapter 14: Augmenting Data Structures
Lecture Notes 14-1
Solutions 14-9

iv

Contents

Chapter 15: Dynamic Programming
Lecture Notes 15-1
Solutions 15-19
Chapter 16: Greedy Algorithms
Lecture Notes 16-1
Solutions 16-9
Chapter 17: Amortized Analysis
Lecture Notes 17-1
Solutions 17-14
Chapter 21: Data Structures for Disjoint Sets
LectureNotes 21-1
Solutions 21-6
Chapter 22: Elementary Graph Algorithms
Lecture Notes 22-1
Solutions 22-12
Chapter 23: Minimum Spanning Trees
Lecture Notes 23-1
Solutions 23-8
Chapter 24: Single-Source Shortest Paths
Lecture Notes 24-1
Solutions 24-13
Chapter 25: All-Pairs Shortest Paths
Lecture Notes 25-1
Solutions 25-8
Chapter 26: Maximum Flow
Lecture Notes 26-1
Solutions 26-15
Chapter27: Sorting Networks
Lecture Notes 27-1
Solutions 27-8
Index

I-1

Revision History

Revisions are listed by date rather than being numbered. Because this revision
history is part of each revision, the affected chapters always include the front matter
in addition to those listed below.
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18 January 2005.Corrected an error in the transpose-symmetry properties.
Affected chapters: Chapter 3.
2 April 2004. Added solutions to Exercises 5.4-6, 11.3-5, 12.4-1, 16.4-2,
16.4-3, 21.3-4, 26.4-2, 26.4-3, and 26.4-6 and to Problems 12-3 and 17-4. Made
minor changes in the solutions to Problems 11-2 and 17-2. Affected chapters:
Chapters 5, 11, 12, 16, 17, 21, and 26; index.
7 January 2004. Corrected twominor typographical errors in the lecture notes
for the expected height of a randomly built binary search tree. Affected chapters: Chapter 12.
23 July 2003. Updated the solution to Exercise 22.3-4(b) to adjust for a correction in the text. Affected chapters: Chapter 22; index.
23 June 2003. Added the link to the website for the clrscode package to the
preface.
2 June 2003. Added the...