Download presentation

Presentation is loading. Please wait.

Published byPhilippa Gilbert Modified over 2 years ago

1
Appendix B Solving Recurrence Equations ： With Applications to Analysis of Recursive Algorithms

2
B.1 Solving Recurrences Using Induction Algorithm B.1 Factorial Problem: Determine n!=n(n-1)(n-2)…(3)(2)(1) when n>=1. 0!=1 Input: a nonnegative integer n. Output: n!. int fact(int n){ if(n==0) return 1; else return n*fact(n-1); }

3
B.1 Solving Recurrences Using Induction

5
Example B.2

6
B.1 Solving Recurrences Using Induction

8
B.2 Solving Recurrences Using The Characteristic Equation B.2.1 Homogeneous Linear Recurrences Definition A recurrence of the form a 0 t n + a 1 t n-1 + ··· + a k t n-k = 0 where k and the a i terms are constants, is called a homogeneous linear recurrence equation with constant coefficients.

9
B.2 Solving Recurrences Using The Characteristic Equation Example B.4 The following are homogeneous linear recurrence equations with constant coefficients: 7t n - 3t n-1 = 0 6t n - 5t n-1 + 8t n-2 = 0 8t n - 4t n-3 = 0

10
B.2 Solving Recurrences Using The Characteristic Equation

21
Example B.10 We solve the recurrence

22
B.2 Solving Recurrences Using The Characteristic Equation

23
Example B.11

24
B.2 Solving Recurrences Using The Characteristic Equation

25
B.2.2 Nonhomogeneous Linear Recurrences Definition: A recurrence of the form a 0 t n + a 1 t n-1 + ··· + a k t n-k = f(n) where k and the a i terms are constants and f(n) is a function other than the zero function, is called a nonhomogeneous linear recurrence equation with constant coefficients.

26
B.2 Solving Recurrences Using The Characteristic Equation Example B.14

27
B.2 Solving Recurrences Using The Characteristic Equation

29
Example B.15

30
B.2 Solving Recurrences Using The Characteristic Equation

31
Example B.16

32
B.2 Solving Recurrences Using The Characteristic Equation

33
Example B.17

34
B.2.3 Change of Variables (Domain Transformations) Example B.18

35
B.2.3 Change of Variables (Domain Transformations)

36
Example B.19

37
B.2.3 Change of Variables (Domain Transformations)

38
Example B.20

39
B.2.3 Change of Variables (Domain Transformations)

40
B.3 Solving Recurrences By Substitution

Similar presentations

OK

Discrete Mathematics Lecture 8 Alexander Bukharovich New York University.

Discrete Mathematics Lecture 8 Alexander Bukharovich New York University.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on type 2 diabetes facts Ppt on south african culture videos Ppt on limitation act pakistan Ppt on domain name system Ppt on peak load pricing economics Ppt on web browser Ppt on first conditional exercises Ppt on share market in india Ppt on condition based maintenance software Ppt on changing face of london