Algorithms and Complexity - Algorithms and Complexity...

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Algorithms and Complexity Herbert S. Wilf University of Pennsylvania Philadelphia, PA 19104-6395 Copyright Notice Copyright 1994 by Herbert S. Wilf. This material may be reproduced for any educational purpose, multiple copies may be made for classes, etc. Charges, if any, for reproduced copies must be just enough to recover reasonable costs of reproduction. Reproduction for commercial purposes is prohibited. This cover page must be included in all distributed copies. Internet Edition, Summer, 1994 This edition of Algorithms and Complexity is available at the web site <http://www/cis.upenn.edu/ wilf> . It may be taken at no charge by all interested persons. Comments and corrections are welcome, and should be sent to wilf@math.upenn.edu
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CONTENTS Chapter 0: What This Book Is About 0 . 1B a c k g r o u n d ...................................... 1 0 . 2H a r dv s .e a s yp r o b l em s ................................. 2 0 . 3Ap r e v i ew . ...................................... 4 Chapter 1: Mathematical Preliminaries 1 . 1O r d e r so fm a g n i t u d e .................................. 5 1 . 2P o s i t i o n a ln um b e rs y s t s............................... 1 1 1 . 3M a n i p u l a t i o n sw i t hs e r i e s ............................... 1 4 1 . 4R e c u r r e n c e r e l a t i o n s .................................. 1 6 1 . 5C o u n t i n g ...................................... 2 1 1 . 6G r a p h s ....................................... 2 4 Chapter 2: Recursive Algorithms 2 . 1I n t r o d u c t i o n..................................... 3 0 2 . 2Q u i c k s o r t ...................................... 3 1 2.3 Recursive graph algorithms ............................... 3 8 2 . 4F a s tm a t r i xm u l t i p l i c a t i o n............................... 4 7 2 . 5T h ed i s c r e t eF o u r i e r t r a n s f o rm . ............................ 5 0 2 . 6A p p l i c a t i o n ft h F T................................ 5 6 2 . 7Ar e v i ew. 6 0 Chapter 3: The Network Flow Problem 3 . n t r o d u c t i o 6 3 3.2 Algorithms for the network flow problem ......................... 6 4 3.3 The algorithm of Ford and Fulkerson . 6 5 3 . 4T h a x - o wm i n - c u tt h e o r em. 6 9 3.5 The complexity of the Ford-Fulkerson algorithm . .................... 7 0 3 . 6L a y e r e dn e t w o r k s................................... 7 2 3.7 The MPM Algorithm . ................................ 7 6 3 . 8A p p l i c a t i o n fn e t w o r kfl o w.............................. 7 7 Chapter 4: Algorithms in the Theory of Numbers 4 .
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Algorithms and Complexity - Algorithms and Complexity...

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