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´eal Madison, WI Toronto
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, c 2002 by The Massachusetts Institute of Inc., 1221 Avenue of the Americas, New York, NY 10020. Copyright 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 or transmission, 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 Trees Lecture 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 Lecture Notes 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 Chapter 27: Sorting Networks Lecture Notes 27-1 Solutions 27-8 Index I-1