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Determine the asymptotic complexity of the function defined by the recurrence relation. Justify your solution using expansion/substitution. You may not use the Master Theorem as justification of your answer. Simplify and express your answer as (n) or (nk log₂ n) whenever possible. If the recurrence is exponential just give exponential lower bounds. a) T(n) = T(n-4) + cn4, T(0) = c' b) T(n) = T(n-3) + T(n-4) + c log₂ n, T(0) = c'

Determine the asymptotic complexity of the function defined by the recurrence relation. Justify your solution using expansion/substitution. You may not use the Master Theorem as justification of your answer. Simplify and express your answer as (n) or (nk log₂ n) whenever possible. If the recurrence is exponential just give exponential lower bounds. a) T(n) = T(n-4) + cn4, T(0) = c' b) T(n) = T(n-3) + T(n-4) + c log₂ n, T(0) = c'

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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1. Determine the asymptotic complexity of the function defined by the recurrence relation. Justify your solution using expansion/substitution. You may not use the Master Theorem as justification of your answer. Simplify and express your answer as (nk) or (nk log₂ n) whenever possible. If the recurrence is exponential just give exponential lower bounds. a) T(n) = T(n-4) + cn¹, T(0) = c' b) T(n) = T(n-3) + T(n-4) + c log₂ n, T(0) = c'
Transcribed Image Text:1. Determine the asymptotic complexity of the function defined by the recurrence relation. Justify your solution using expansion/substitution. You may not use the Master Theorem as justification of your answer. Simplify and express your answer as (nk) or (nk log₂ n) whenever possible. If the recurrence is exponential just give exponential lower bounds. a) T(n) = T(n-4) + cn¹, T(0) = c' b) T(n) = T(n-3) + T(n-4) + c log₂ n, T(0) = c'
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