Examples

T(n) = 9 T(n/3) + n

• a = 9, b=3, f(n) = n, . is polynomially bigger.
• So, .

• a = 3, b=7, , . is polynomially bigger.
• So, .

Note: As long as , for , Master Theorem definitely applies!

• a = 1, b=5/4, , . f(n) is not polynomially bigger. But Rule 4 applies (with k=2).
• So, .

• a = 2, b=4, , , so f(n) is not polynomially larger than .
• So Master Theorem does not apply.