concrete mathematics a foundation for computer science phần 6 doc

... Horses 17 5 Hackers 17 6 Can Computers Kill? 17 7 Summary 17 8 Review Questions 17 9 APPENDIX Answers to Review Questions 18 0 Index 217 CONTENTS vii SCHAUM’S OUTLINE OF Principles of COMPUTER SCIENCE ... most modern computers. 4 INTRODUCTION TO COMPUTER SCIENCE [CHAP. 1 SCHAUM’S OUTLINE OF Principles of COMPUTER SCIENCE CARL REYNOLDS Department of...

Ngày tải lên: 12/08/2014, 21:22

... lists of length one is equal to the logarithm to the base 2 of the number of elements in the list. In the case of our 4-element example, the logarithm to the base 2 of 4 is 2, because 2 2 = 4. ... is the order of growth of your mean algorithm? 2. 4 Write pseudocode for finding the median of a set of numbers. 2. 5 What is the order of growth of your algorithm to...

Ngày tải lên: 12/08/2014, 21:22

... recurrence makes it possible to build a table of small values very quickly. Perhaps we’ll be able to spot a pattern and guess the answer. n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 J(n) 1 1 3 1 3 5 7 1 3 ... index. ISBN o-2 01- 14236-8 1. Mathematics 19 61- 2. Electronic data processing Mathematics. I. Knuth, Donald Ervin, 19 38- . II. Patashnik, Oren, 19 54- . I...

Ngày tải lên: 14/08/2014, 04:21

... as a binary operation, just as addition and subtraction are binary operations. Mathematicians have used mod this way informally for a long time, taking various quantities mod 10, mod 27 7, and ... name and conquer. a = ~ap’J , a- ’ = a+ a’; The change of vari- able from k to j is b = [va-‘l , va-’ = b -v’. Thus a = {a ‘} is the fractional part of a- ‘, and v’ is the mumble-fra...

Ngày tải lên: 14/08/2014, 04:21

... 87 106 1 93 299 492 685 878 1071 1264 1'1'1'2&apos ;3& apos; 4' 7'11'18'25&apos ;32 ' 39 ' 71'110'181'252&apos ;32 3' 39 4' 465"" are ... lo 1'10'9'8'7'b'5'4&apos ;3& apos;5'2&apos ;3& apos;1'2'1'2'1'2'1'1'~'1'1'1&a...

Ngày tải lên: 14/08/2014, 04:21

... n fans. How many ways h(n, k) are there for exactly k fans to get their own hats back? For example, if n = 4 and if the hats and fans are named A, B, C, D, the 4! = 24 possible ways for hats ... land generate the following numbers of rightful owners: ABCD 4 BACD 2 CABD 1 DABC 0 ABDC 2 BADC 0 CADB 0 DACB 1 ACBD 2 BCAD 1 CBAD 2 DBAC 1 ACDB 1 BCDA 0 CBDA 1 DBCA 2 ADBC 1 BDAC 0 CDA...

Ngày tải lên: 14/08/2014, 04:21

... same pattern holds for continued fractions of any depth. It is easily proved by induction; we have, for example, K(ao,al,az ,a3 +l /a4 ) := K(ao,al ,a2 ,a3 ,a4 ) K(al, az, a3 + l /a4 1 K(al,az,as,ad) ... arise naturally. Let’s consider the pedigree of a male bee. Each male (also known as a drone) is produced asexually from a female (also known as a queen); each female, how...

Ngày tải lên: 14/08/2014, 04:21

... because 2 - & z 0. 268 . This needs to be taken into account if we try to use formula (7.38) in numerical calculations. For example, a fairly expensive name-brand hand Icalculator comes ... 0;) as n -+ 00, un:less z = 0. This shows that formal power series can be manipulated algebraically without worrying about convergence. Example 6: A recurrence that goes ail the way...

Ngày tải lên: 14/08/2014, 04:21

... month each person is reassigned to an adjacent state, each adjacent state being equally likely. (Here’s a diagram of the adjacencies: The initial states are circled.) For example, Alice is restationed ... (8.82) that A would probably beat B, that B would probably beat C, and that C would probably beat A; but all three patterns are simultaneously in the game.) What are each player’s cha...

Ngày tải lên: 14/08/2014, 04:21

... “Eulerian” (eighteenth-century) mathematics. 9.3 0 MANIPULATION 447 This may look worse than the sum we began with, but it’s actually a step for- ward, because we have very good approximations for ... actually 15 485 863. Exercise 21 shows that a still more accurate approximation to P, results if we begin with a still more accurate approximation to n(n) in place of (9.46). 9.6...

Ngày tải lên: 14/08/2014, 04:21

... results about Fermat’s Last Theorem; see Ribenboim j249j.j A ANSWERS TO EXERCISES 527 If the harmonic aa and a bb. Thus each bb behaves like a drone in the bee tree and each aa behaves like a ... thereby eliminating an upper parameter and a lower parameter. Thus, for example, we get closed forms for F( a, b; a - 1; z), F( a, b; a - 2; z), etc. Gauss [116, $71...

Ngày tải lên: 14/08/2014, 04:21

... V. Waugh and Margaret W. Maxfield, “Side-and-diagonal num- bers,” Mathematics Magazine 40 (1967), 74-83. 298 Warren Weaver, “Lewis Carroll and a geometrical paradox,” American Mathematical Monthly ... Mark Haiman Andrei Broder, Jim McGrath Oren Patashnik Joan Feigenbaum, Dave Helmbold Anna Karlin Oren Patashnik, Alex Schaffer Pang Chen, Stefan Sharkansky Arif Merchant, Stefan Sharkansky...

Ngày tải lên: 14/08/2014, 04:21