Can I use the Master Theorem here? (Algorithm Complexity)

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SUMMARY

The discussion centers on the application of the Master Theorem to analyze the recurrence relation T(n) = (9/4)T((2/3)n) + n². The user identifies parameters a = 9/4 and f(n) = n², questioning the correct value of b. The conclusion drawn is that T(n) is Θ(n²) since f(n) dominates n^(log_b_a), confirming the use of the Master Theorem in this context.

PREREQUISITES
  • Understanding of recurrence relations in algorithm analysis
  • Familiarity with the Master Theorem for solving recurrences
  • Knowledge of asymptotic notation (Θ, O, Ω)
  • Basic algebra for manipulating logarithmic expressions
NEXT STEPS
  • Study the Master Theorem in detail, focusing on its conditions and applications
  • Learn how to compute log_b_a for various values of a and b
  • Explore examples of different types of recurrences and their solutions
  • Investigate alternative methods for solving recurrences, such as the Iteration Method
USEFUL FOR

Students in computer science courses, particularly those studying algorithms and data structures, as well as anyone looking to deepen their understanding of algorithm complexity analysis.

frank1
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Homework Statement


What is the complexity of the following recurrence: T(n) = (9/4)T((2/3)n) + n²

Homework Equations


My question is: can I use the Master Theorem here?

The Attempt at a Solution


My attemp:
a=9/4
b=3/(1/2) (this is where I think I may be wrong)
f(n) = n²

so, in this case T(n) would be theta(n²) because it would be greater than n^(log_b_a)

Anyway, the point is if I can use Master Theorem and what would be the value of b.

PS: English is not my native english. Sorry for the grammar.
 
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frank1 said:

Homework Statement


What is the complexity of the following recurrence: T(n) = (9/4)T((2/3)n) + n²

Homework Equations


My question is: can I use the Master Theorem here?

The Attempt at a Solution


My attemp:
a=9/4
b=3/(1/2) (this is where I think I may be wrong)
f(n) = n²

so, in this case T(n) would be theta(n²) because it would be greater than n^(log_b_a)

Anyway, the point is if I can use Master Theorem and what would be the value of b.

PS: English is not my native english. Sorry for the grammar.
You are right. Are you in cmps101 at ucsc?
 

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