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Consider the following recursion (suppose n is a power of 2): √4T(n/2) +n².5 if n > 1 if n = 1 T(n): = a) Use the alternation method to guess the asymptotic value of T(n) (using – notation). b) Use induction to prove the correctness of your guess in part (a) (it suffices to prove the value of T(n) using O notation).

Consider the following recursion (suppose n is a power of 2): √4T(n/2) +n².5 if n > 1 if n = 1 T(n): = a) Use the alternation method to guess the asymptotic value of T(n) (using – notation). b) Use induction to prove the correctness of your guess in part (a) (it suffices to prove the value of T(n) using O notation).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the following recursion (suppose n is a power of 2): [4T(n/2) +n².5 if n>1 if n = 1 T(n) = = a) Use the alternation method to guess the asymptotic value of T(n) (using notation). b) Use induction to prove the correctness of your guess in part (a) (it suffices to prove the value of T(n) using O notation). c) Draw the recursion tree for T(n); specify the height of the tree, the number of leaves, and total work done in all levels of the tree. From your work, indicate the asymptotic value of T(n).
Transcribed Image Text:Consider the following recursion (suppose n is a power of 2): [4T(n/2) +n².5 if n>1 if n = 1 T(n) = = a) Use the alternation method to guess the asymptotic value of T(n) (using notation). b) Use induction to prove the correctness of your guess in part (a) (it suffices to prove the value of T(n) using O notation). c) Draw the recursion tree for T(n); specify the height of the tree, the number of leaves, and total work done in all levels of the tree. From your work, indicate the asymptotic value of T(n).
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