CS 310 Unit 2a Master Method Recurrences - ε>0 and if a...

CS 310 Unit 2a
Master Method Recurrences
Furman Haddix Ph.D.
Assistant Professor
Minnesota State University,
Mankato

CS 310 Unit 2a Master Method
Recurrences Objectives
•
Master Method
•
Master Method Examples
•
Text, Chapter 4

Master Method – Another Recurrence
Tool
•
Works for recurrences of the form:
T(n) = a T(n/b) + f(n), where a ≥ 1, b >
1, and f(n) is asymptotically positive
 positive for n ≥ n
0
•
Master Method:
1. If f(n) = O(n
log
b
a- ε
) for some constant ε >0, then
T(n) = Θ (n
log
b
a
)
2. If f(n) = Θ (n
log
b
a
), then T(n) = Θ (n
log
b
a
lg n)
3. If f(n) = Ω (n
log
b
a+ ε
) for some constant ε >0, and if
a f(n/b) ≤ cf(n) for some constant c > 1