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Appendix B
Solving Recurrence Equations:With Applications to Analysis of R
n n>=1. 0!=1Input: a nonnegative integer n.Output: n!. int fact(int n){ if(n==0) return 1; else return n*fact(n-1); }
B.1 Solving Recurrences Using Induction
B.1 Solving Recurrences Using Induction
B.1 Solving Recurrences Using Induction
Example B.2
B.1 Solving Recurrences Using Induction
B.1 Solving Recurrences Using Induction
B.2 Solving Recurrences Using The Characteristic Equation
B.2.1 Homogeneous Linear Recurrences
Definition
A recurrence of the form
a0tn + a1tn-1 + ··· + aktn-k = 0
where k and the ai terms are constants, is called a homogeneous linear recurrence equation with constant coefficients.
B.2 Solving Recurrences Using The Characteristic Equation
Example B.4 The following are homogeneous linear recurrence equations with constant coefficients:
7tn - 3tn-1 = 0
6tn - 5tn-1 + 8tn-2 = 0
8tn - 4tn-3 = 0
B.2 Solving Recurrences Using The Characteristic Equation
B.2 Solving Recurrences Using The Characteristic Equation
B.2 Solving Recurrences Using The Characteristic Equation
B.2 Solving Recurrences Using The Characteristic Equation
B.2 Solving Recurrences Using The Characteristic Equation
B.2 Solving Recurrences Using The Characteristic Equation
B.2 Solving Recurrences Using The Characteristic Equation
B.2 Solving Recurrences Using The Characteristic Equation
B.2 Solving Recurrences Using The Characteristic Equation
B.2 Solving Recurrences Using The Characteristic Equation
B.2 Solving Recurrences Using The Characteristic Equation
B.2 Solving Recurrences Using The Characteristic Equation
Example B.10 We solve the recurrence
B.2 Solving Recurrences Using The Characteristic Equation
B.2 Solving Recurrences Using The Characteristic Equation
Example B.11
B.2 Solving Recurrences Using The Characteristic Equation
B.2 Solving Recurrences Using The Characteristic Equation
B.2.2 Nonhomogeneous Linear Recurrences
Definition: A recurrence of the form
a0tn + a1tn-1 + ··· + aktn-k = f(n)
where k and the ai terms are constants and f(n) is a function other than the zero function, is called a nonhomogeneous linear recurrence equation with constant coefficients.
B.2 Solving Recurrences Using The Characteristic Equation
Example B.14
B.2 Solving Recurrences Using The Characteristic Equation
B.2 Solving Recurrences Using The Characteristic Equation
B.2 Solving Recurrences Using The Characteristic Equation
Example B.15
B.2 Solving Recurrences Using The Characteristic Equation
B.2 Solving Recurrences Using The Characteristic Equation
Example B.16
B.2 Solving Recurrences Using The Characteristic Equation
B.2 Solving Recurrences Using The Characteristic Equation
Example B.17
B.2.3 Change of Variables (Domain Transformations)
Example B.18
B.2.3 Change of Variables (Domain Transformations)
B.2.3 Change of Variables (Domain Transformations)
Example B.19
B.2.3 Change of Variables (Domain Transformations)
B.2.3 Change of Variables (Domain Transformations)
Example B.20
B.2.3 Change of Variables (Domain Transformations)