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Problem 1: Give an asymptotic estimate, using the e-notation, of the number of letters printed by the algorithms given below. Give a complete justification for your answer, by providing an appropriate recurrence equation and its solution. (a) algorithm PrintAs(n) if n < 7 then print("A") else for j+1 to n² for do print ("A") 1 to 25 do PrintAs([n/5]) (b) algorithm PrintBs(n) if n ≥ 7 then for j+1 to 7n do print ("B") PrintBs([n/7]) Print Bs([n/7]) Print Bs([n/7]) Print Bs([n/7]) Print Bs([n/7])

Problem 1: Give an asymptotic estimate, using the e-notation, of the number of letters printed by the algorithms given below. Give a complete justification for your answer, by providing an appropriate recurrence equation and its solution. (a) algorithm PrintAs(n) if n < 7 then print("A") else for j+1 to n² for do print ("A") 1 to 25 do PrintAs([n/5]) (b) algorithm PrintBs(n) if n ≥ 7 then for j+1 to 7n do print ("B") PrintBs([n/7]) Print Bs([n/7]) Print Bs([n/7]) Print Bs([n/7]) Print Bs([n/7])

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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**Problem 1:** Give an asymptotic estimate, using the Θ-notation, of the number of letters printed by the algorithms given below. Give a complete justification for your answer, by providing an appropriate recurrence equation and its solution. (a) **Algorithm PrintAs(n)** &nbsp;&nbsp;&nbsp;&nbsp;if \( n < 7 \) then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;print(”A”) &nbsp;&nbsp;&nbsp;&nbsp;else &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;for \( j \leftarrow 1 \) to \( n^2 \) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;do print(”A”) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;for \( i \leftarrow 1 \) to 25 do &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;PrintAs( \( \lfloor n/5 \rfloor \) ) (b) **Algorithm PrintBs(n)** &nbsp;&nbsp;&nbsp;&nbsp;if \( n \geq 7 \) then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;for \( j \leftarrow 1 \) to \( 7n \) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;do print(”B”) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;PrintBs( \( \lfloor n/7 \rfloor \) ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;PrintBs( \( \lfloor n/7 \rfloor \) ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;PrintBs( \( \lfloor n/7 \rfloor \) ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;PrintBs( \( \lfloor n/7 \rfloor \) )
Transcribed Image Text:**Problem 1:** Give an asymptotic estimate, using the Θ-notation, of the number of letters printed by the algorithms given below. Give a complete justification for your answer, by providing an appropriate recurrence equation and its solution. (a) **Algorithm PrintAs(n)** &nbsp;&nbsp;&nbsp;&nbsp;if \( n < 7 \) then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;print(”A”) &nbsp;&nbsp;&nbsp;&nbsp;else &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;for \( j \leftarrow 1 \) to \( n^2 \) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;do print(”A”) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;for \( i \leftarrow 1 \) to 25 do &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;PrintAs( \( \lfloor n/5 \rfloor \) ) (b) **Algorithm PrintBs(n)** &nbsp;&nbsp;&nbsp;&nbsp;if \( n \geq 7 \) then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;for \( j \leftarrow 1 \) to \( 7n \) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;do print(”B”) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;PrintBs( \( \lfloor n/7 \rfloor \) ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;PrintBs( \( \lfloor n/7 \rfloor \) ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;PrintBs( \( \lfloor n/7 \rfloor \) ) &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;PrintBs( \( \lfloor n/7 \rfloor \) )
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