SlideShare a Scribd company logo
Consider the two functions below which both compute the value of f(n). The function f1 was
replaced with f2 because integer multiplications () were found to take 4 times longer than integer
additions (+).
int f1(n : integer)
if (n == 1) then return(1)
else return(2 f1(n 1));
int f2(n : integer)
if (n == 1) then return(1)
else return(f2(n 1) + f2(n 1));
i. Give a recurrence relation for f1, which satisfies the number of multiplications (*) executed as
a function of n.
ii. Solve the recurrence relation from Part i.
iii. Give a recurrence relation for f2, which satisfies the number of additions (+) executed as a
function of n.
iv. Solve the recurrence relation from Part iii. v. Both functions compute the same function f.
Was it a good idea to replace f1 with f2?

More Related Content

More from americancolor

Consider the following scenarioIn the last few weeks, residents h.pdf
Consider the following scenarioIn the last few weeks, residents h.pdfConsider the following scenarioIn the last few weeks, residents h.pdf
Consider the following scenarioIn the last few weeks, residents h.pdf
americancolor
 
Consider the following wage regression in which you have data on gen.pdf
Consider the following wage regression in which you have data on gen.pdfConsider the following wage regression in which you have data on gen.pdf
Consider the following wage regression in which you have data on gen.pdf
americancolor
 
core issue in frank by ocbc singapore case studyIn 2010, Jin Kang .pdf
core issue in frank by ocbc singapore case studyIn 2010, Jin Kang .pdfcore issue in frank by ocbc singapore case studyIn 2010, Jin Kang .pdf
core issue in frank by ocbc singapore case studyIn 2010, Jin Kang .pdf
americancolor
 
Coronado Corporation tuvo una utilidad neta de $240 000 y pag� divid.pdf
Coronado Corporation tuvo una utilidad neta de $240 000 y pag� divid.pdfCoronado Corporation tuvo una utilidad neta de $240 000 y pag� divid.pdf
Coronado Corporation tuvo una utilidad neta de $240 000 y pag� divid.pdf
americancolor
 
convert this python code to java script. Make sure it works on Eclip.pdf
convert this python code to java script. Make sure it works on Eclip.pdfconvert this python code to java script. Make sure it works on Eclip.pdf
convert this python code to java script. Make sure it works on Eclip.pdf
americancolor
 
Convert M9 to a regular expression. Consider the following generalis.pdf
Convert M9 to a regular expression. Consider the following generalis.pdfConvert M9 to a regular expression. Consider the following generalis.pdf
Convert M9 to a regular expression. Consider the following generalis.pdf
americancolor
 
Control en Netflix Los gerentes no solo controlan los procesos d.pdf
Control en Netflix Los gerentes no solo controlan los procesos d.pdfControl en Netflix Los gerentes no solo controlan los procesos d.pdf
Control en Netflix Los gerentes no solo controlan los procesos d.pdf
americancolor
 
CONTRATO DE ARRENDAMIENTO COMERCIAL Este Contrato de Arrendamiento C.pdf
CONTRATO DE ARRENDAMIENTO COMERCIAL Este Contrato de Arrendamiento C.pdfCONTRATO DE ARRENDAMIENTO COMERCIAL Este Contrato de Arrendamiento C.pdf
CONTRATO DE ARRENDAMIENTO COMERCIAL Este Contrato de Arrendamiento C.pdf
americancolor
 
Contrast the oral and poster method of presenting research at a conf.pdf
Contrast the oral and poster method of presenting research at a conf.pdfContrast the oral and poster method of presenting research at a conf.pdf
Contrast the oral and poster method of presenting research at a conf.pdf
americancolor
 
Contribution Margin Molly Company sells 40,000 units at $14 per unit.pdf
Contribution Margin Molly Company sells 40,000 units at $14 per unit.pdfContribution Margin Molly Company sells 40,000 units at $14 per unit.pdf
Contribution Margin Molly Company sells 40,000 units at $14 per unit.pdf
americancolor
 
ContextualizeWhat are YOUR learning goals What are the course .pdf
ContextualizeWhat are YOUR learning goals What are the course .pdfContextualizeWhat are YOUR learning goals What are the course .pdf
ContextualizeWhat are YOUR learning goals What are the course .pdf
americancolor
 
Contesta las preguntas del siguiente p�rrafo �Deber�a respons.pdf
Contesta las preguntas del siguiente p�rrafo �Deber�a respons.pdfContesta las preguntas del siguiente p�rrafo �Deber�a respons.pdf
Contesta las preguntas del siguiente p�rrafo �Deber�a respons.pdf
americancolor
 
CONTABILIDAD GERENCIAL - DECLARACIONES VERDADERAS O FALSAS.(SALTE .pdf
CONTABILIDAD GERENCIAL - DECLARACIONES VERDADERAS O FALSAS.(SALTE .pdfCONTABILIDAD GERENCIAL - DECLARACIONES VERDADERAS O FALSAS.(SALTE .pdf
CONTABILIDAD GERENCIAL - DECLARACIONES VERDADERAS O FALSAS.(SALTE .pdf
americancolor
 
Continental Airlines vuela alto con su almac�n de datos en tiempo re.pdf
Continental Airlines vuela alto con su almac�n de datos en tiempo re.pdfContinental Airlines vuela alto con su almac�n de datos en tiempo re.pdf
Continental Airlines vuela alto con su almac�n de datos en tiempo re.pdf
americancolor
 
Consider this scenario. Miguel is an experienced forensic evidence a.pdf
Consider this scenario. Miguel is an experienced forensic evidence a.pdfConsider this scenario. Miguel is an experienced forensic evidence a.pdf
Consider this scenario. Miguel is an experienced forensic evidence a.pdf
americancolor
 
Considere una econom�a donde la industria dominante es la producci�n.pdf
Considere una econom�a donde la industria dominante es la producci�n.pdfConsidere una econom�a donde la industria dominante es la producci�n.pdf
Considere una econom�a donde la industria dominante es la producci�n.pdf
americancolor
 
Considere una econom�a descrita por las siguientes ecuacionesY .pdf
Considere una econom�a descrita por las siguientes ecuacionesY .pdfConsidere una econom�a descrita por las siguientes ecuacionesY .pdf
Considere una econom�a descrita por las siguientes ecuacionesY .pdf
americancolor
 
Considere un pa�s con un producto interno bruto (PIB) nominal de $ 1.pdf
Considere un pa�s con un producto interno bruto (PIB) nominal de $ 1.pdfConsidere un pa�s con un producto interno bruto (PIB) nominal de $ 1.pdf
Considere un pa�s con un producto interno bruto (PIB) nominal de $ 1.pdf
americancolor
 
Considere todo lo que ha aprendido en este curso sobre problemas soc.pdf
Considere todo lo que ha aprendido en este curso sobre problemas soc.pdfConsidere todo lo que ha aprendido en este curso sobre problemas soc.pdf
Considere todo lo que ha aprendido en este curso sobre problemas soc.pdf
americancolor
 
Considere los virus en soluci�n como una suspensi�n. �C�mo esperar�a.pdf
Considere los virus en soluci�n como una suspensi�n. �C�mo esperar�a.pdfConsidere los virus en soluci�n como una suspensi�n. �C�mo esperar�a.pdf
Considere los virus en soluci�n como una suspensi�n. �C�mo esperar�a.pdf
americancolor
 

More from americancolor (20)

Consider the following scenarioIn the last few weeks, residents h.pdf
Consider the following scenarioIn the last few weeks, residents h.pdfConsider the following scenarioIn the last few weeks, residents h.pdf
Consider the following scenarioIn the last few weeks, residents h.pdf
 
Consider the following wage regression in which you have data on gen.pdf
Consider the following wage regression in which you have data on gen.pdfConsider the following wage regression in which you have data on gen.pdf
Consider the following wage regression in which you have data on gen.pdf
 
core issue in frank by ocbc singapore case studyIn 2010, Jin Kang .pdf
core issue in frank by ocbc singapore case studyIn 2010, Jin Kang .pdfcore issue in frank by ocbc singapore case studyIn 2010, Jin Kang .pdf
core issue in frank by ocbc singapore case studyIn 2010, Jin Kang .pdf
 
Coronado Corporation tuvo una utilidad neta de $240 000 y pag� divid.pdf
Coronado Corporation tuvo una utilidad neta de $240 000 y pag� divid.pdfCoronado Corporation tuvo una utilidad neta de $240 000 y pag� divid.pdf
Coronado Corporation tuvo una utilidad neta de $240 000 y pag� divid.pdf
 
convert this python code to java script. Make sure it works on Eclip.pdf
convert this python code to java script. Make sure it works on Eclip.pdfconvert this python code to java script. Make sure it works on Eclip.pdf
convert this python code to java script. Make sure it works on Eclip.pdf
 
Convert M9 to a regular expression. Consider the following generalis.pdf
Convert M9 to a regular expression. Consider the following generalis.pdfConvert M9 to a regular expression. Consider the following generalis.pdf
Convert M9 to a regular expression. Consider the following generalis.pdf
 
Control en Netflix Los gerentes no solo controlan los procesos d.pdf
Control en Netflix Los gerentes no solo controlan los procesos d.pdfControl en Netflix Los gerentes no solo controlan los procesos d.pdf
Control en Netflix Los gerentes no solo controlan los procesos d.pdf
 
CONTRATO DE ARRENDAMIENTO COMERCIAL Este Contrato de Arrendamiento C.pdf
CONTRATO DE ARRENDAMIENTO COMERCIAL Este Contrato de Arrendamiento C.pdfCONTRATO DE ARRENDAMIENTO COMERCIAL Este Contrato de Arrendamiento C.pdf
CONTRATO DE ARRENDAMIENTO COMERCIAL Este Contrato de Arrendamiento C.pdf
 
Contrast the oral and poster method of presenting research at a conf.pdf
Contrast the oral and poster method of presenting research at a conf.pdfContrast the oral and poster method of presenting research at a conf.pdf
Contrast the oral and poster method of presenting research at a conf.pdf
 
Contribution Margin Molly Company sells 40,000 units at $14 per unit.pdf
Contribution Margin Molly Company sells 40,000 units at $14 per unit.pdfContribution Margin Molly Company sells 40,000 units at $14 per unit.pdf
Contribution Margin Molly Company sells 40,000 units at $14 per unit.pdf
 
ContextualizeWhat are YOUR learning goals What are the course .pdf
ContextualizeWhat are YOUR learning goals What are the course .pdfContextualizeWhat are YOUR learning goals What are the course .pdf
ContextualizeWhat are YOUR learning goals What are the course .pdf
 
Contesta las preguntas del siguiente p�rrafo �Deber�a respons.pdf
Contesta las preguntas del siguiente p�rrafo �Deber�a respons.pdfContesta las preguntas del siguiente p�rrafo �Deber�a respons.pdf
Contesta las preguntas del siguiente p�rrafo �Deber�a respons.pdf
 
CONTABILIDAD GERENCIAL - DECLARACIONES VERDADERAS O FALSAS.(SALTE .pdf
CONTABILIDAD GERENCIAL - DECLARACIONES VERDADERAS O FALSAS.(SALTE .pdfCONTABILIDAD GERENCIAL - DECLARACIONES VERDADERAS O FALSAS.(SALTE .pdf
CONTABILIDAD GERENCIAL - DECLARACIONES VERDADERAS O FALSAS.(SALTE .pdf
 
Continental Airlines vuela alto con su almac�n de datos en tiempo re.pdf
Continental Airlines vuela alto con su almac�n de datos en tiempo re.pdfContinental Airlines vuela alto con su almac�n de datos en tiempo re.pdf
Continental Airlines vuela alto con su almac�n de datos en tiempo re.pdf
 
Consider this scenario. Miguel is an experienced forensic evidence a.pdf
Consider this scenario. Miguel is an experienced forensic evidence a.pdfConsider this scenario. Miguel is an experienced forensic evidence a.pdf
Consider this scenario. Miguel is an experienced forensic evidence a.pdf
 
Considere una econom�a donde la industria dominante es la producci�n.pdf
Considere una econom�a donde la industria dominante es la producci�n.pdfConsidere una econom�a donde la industria dominante es la producci�n.pdf
Considere una econom�a donde la industria dominante es la producci�n.pdf
 
Considere una econom�a descrita por las siguientes ecuacionesY .pdf
Considere una econom�a descrita por las siguientes ecuacionesY .pdfConsidere una econom�a descrita por las siguientes ecuacionesY .pdf
Considere una econom�a descrita por las siguientes ecuacionesY .pdf
 
Considere un pa�s con un producto interno bruto (PIB) nominal de $ 1.pdf
Considere un pa�s con un producto interno bruto (PIB) nominal de $ 1.pdfConsidere un pa�s con un producto interno bruto (PIB) nominal de $ 1.pdf
Considere un pa�s con un producto interno bruto (PIB) nominal de $ 1.pdf
 
Considere todo lo que ha aprendido en este curso sobre problemas soc.pdf
Considere todo lo que ha aprendido en este curso sobre problemas soc.pdfConsidere todo lo que ha aprendido en este curso sobre problemas soc.pdf
Considere todo lo que ha aprendido en este curso sobre problemas soc.pdf
 
Considere los virus en soluci�n como una suspensi�n. �C�mo esperar�a.pdf
Considere los virus en soluci�n como una suspensi�n. �C�mo esperar�a.pdfConsidere los virus en soluci�n como una suspensi�n. �C�mo esperar�a.pdf
Considere los virus en soluci�n como una suspensi�n. �C�mo esperar�a.pdf
 

Recently uploaded

ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
PECB
 
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptxPengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Fajar Baskoro
 
How to Manage Your Lost Opportunities in Odoo 17 CRM
How to Manage Your Lost Opportunities in Odoo 17 CRMHow to Manage Your Lost Opportunities in Odoo 17 CRM
How to Manage Your Lost Opportunities in Odoo 17 CRM
Celine George
 
UGC NET Exam Paper 1- Unit 1:Teaching Aptitude
UGC NET Exam Paper 1- Unit 1:Teaching AptitudeUGC NET Exam Paper 1- Unit 1:Teaching Aptitude
UGC NET Exam Paper 1- Unit 1:Teaching Aptitude
S. Raj Kumar
 
PCOS corelations and management through Ayurveda.
PCOS corelations and management through Ayurveda.PCOS corelations and management through Ayurveda.
PCOS corelations and management through Ayurveda.
Dr. Shivangi Singh Parihar
 
Cognitive Development Adolescence Psychology
Cognitive Development Adolescence PsychologyCognitive Development Adolescence Psychology
Cognitive Development Adolescence Psychology
paigestewart1632
 
The History of Stoke Newington Street Names
The History of Stoke Newington Street NamesThe History of Stoke Newington Street Names
The History of Stoke Newington Street Names
History of Stoke Newington
 
BBR 2024 Summer Sessions Interview Training
BBR  2024 Summer Sessions Interview TrainingBBR  2024 Summer Sessions Interview Training
BBR 2024 Summer Sessions Interview Training
Katrina Pritchard
 
Walmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdfWalmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdf
TechSoup
 
How to Fix the Import Error in the Odoo 17
How to Fix the Import Error in the Odoo 17How to Fix the Import Error in the Odoo 17
How to Fix the Import Error in the Odoo 17
Celine George
 
How to Create a More Engaging and Human Online Learning Experience
How to Create a More Engaging and Human Online Learning Experience How to Create a More Engaging and Human Online Learning Experience
How to Create a More Engaging and Human Online Learning Experience
Wahiba Chair Training & Consulting
 
Présentationvvvvvvvvvvvvvvvvvvvvvvvvvvvv2.pptx
Présentationvvvvvvvvvvvvvvvvvvvvvvvvvvvv2.pptxPrésentationvvvvvvvvvvvvvvvvvvvvvvvvvvvv2.pptx
Présentationvvvvvvvvvvvvvvvvvvvvvvvvvvvv2.pptx
siemaillard
 
C1 Rubenstein AP HuG xxxxxxxxxxxxxx.pptx
C1 Rubenstein AP HuG xxxxxxxxxxxxxx.pptxC1 Rubenstein AP HuG xxxxxxxxxxxxxx.pptx
C1 Rubenstein AP HuG xxxxxxxxxxxxxx.pptx
mulvey2
 
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptxNEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
iammrhaywood
 
clinical examination of hip joint (1).pdf
clinical examination of hip joint (1).pdfclinical examination of hip joint (1).pdf
clinical examination of hip joint (1).pdf
Priyankaranawat4
 
Main Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docxMain Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docx
adhitya5119
 
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...
Diana Rendina
 
Hindi varnamala | hindi alphabet PPT.pdf
Hindi varnamala | hindi alphabet PPT.pdfHindi varnamala | hindi alphabet PPT.pdf
Hindi varnamala | hindi alphabet PPT.pdf
Dr. Mulla Adam Ali
 
Film vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movieFilm vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movie
Nicholas Montgomery
 
PIMS Job Advertisement 2024.pdf Islamabad
PIMS Job Advertisement 2024.pdf IslamabadPIMS Job Advertisement 2024.pdf Islamabad
PIMS Job Advertisement 2024.pdf Islamabad
AyyanKhan40
 

Recently uploaded (20)

ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
 
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptxPengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
 
How to Manage Your Lost Opportunities in Odoo 17 CRM
How to Manage Your Lost Opportunities in Odoo 17 CRMHow to Manage Your Lost Opportunities in Odoo 17 CRM
How to Manage Your Lost Opportunities in Odoo 17 CRM
 
UGC NET Exam Paper 1- Unit 1:Teaching Aptitude
UGC NET Exam Paper 1- Unit 1:Teaching AptitudeUGC NET Exam Paper 1- Unit 1:Teaching Aptitude
UGC NET Exam Paper 1- Unit 1:Teaching Aptitude
 
PCOS corelations and management through Ayurveda.
PCOS corelations and management through Ayurveda.PCOS corelations and management through Ayurveda.
PCOS corelations and management through Ayurveda.
 
Cognitive Development Adolescence Psychology
Cognitive Development Adolescence PsychologyCognitive Development Adolescence Psychology
Cognitive Development Adolescence Psychology
 
The History of Stoke Newington Street Names
The History of Stoke Newington Street NamesThe History of Stoke Newington Street Names
The History of Stoke Newington Street Names
 
BBR 2024 Summer Sessions Interview Training
BBR  2024 Summer Sessions Interview TrainingBBR  2024 Summer Sessions Interview Training
BBR 2024 Summer Sessions Interview Training
 
Walmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdfWalmart Business+ and Spark Good for Nonprofits.pdf
Walmart Business+ and Spark Good for Nonprofits.pdf
 
How to Fix the Import Error in the Odoo 17
How to Fix the Import Error in the Odoo 17How to Fix the Import Error in the Odoo 17
How to Fix the Import Error in the Odoo 17
 
How to Create a More Engaging and Human Online Learning Experience
How to Create a More Engaging and Human Online Learning Experience How to Create a More Engaging and Human Online Learning Experience
How to Create a More Engaging and Human Online Learning Experience
 
Présentationvvvvvvvvvvvvvvvvvvvvvvvvvvvv2.pptx
Présentationvvvvvvvvvvvvvvvvvvvvvvvvvvvv2.pptxPrésentationvvvvvvvvvvvvvvvvvvvvvvvvvvvv2.pptx
Présentationvvvvvvvvvvvvvvvvvvvvvvvvvvvv2.pptx
 
C1 Rubenstein AP HuG xxxxxxxxxxxxxx.pptx
C1 Rubenstein AP HuG xxxxxxxxxxxxxx.pptxC1 Rubenstein AP HuG xxxxxxxxxxxxxx.pptx
C1 Rubenstein AP HuG xxxxxxxxxxxxxx.pptx
 
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptxNEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
 
clinical examination of hip joint (1).pdf
clinical examination of hip joint (1).pdfclinical examination of hip joint (1).pdf
clinical examination of hip joint (1).pdf
 
Main Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docxMain Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docx
 
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...
 
Hindi varnamala | hindi alphabet PPT.pdf
Hindi varnamala | hindi alphabet PPT.pdfHindi varnamala | hindi alphabet PPT.pdf
Hindi varnamala | hindi alphabet PPT.pdf
 
Film vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movieFilm vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movie
 
PIMS Job Advertisement 2024.pdf Islamabad
PIMS Job Advertisement 2024.pdf IslamabadPIMS Job Advertisement 2024.pdf Islamabad
PIMS Job Advertisement 2024.pdf Islamabad
 

Consider the two functions below which both compute the value of f(n.pdf

  • 1. Consider the two functions below which both compute the value of f(n). The function f1 was replaced with f2 because integer multiplications () were found to take 4 times longer than integer additions (+). int f1(n : integer) if (n == 1) then return(1) else return(2 f1(n 1)); int f2(n : integer) if (n == 1) then return(1) else return(f2(n 1) + f2(n 1)); i. Give a recurrence relation for f1, which satisfies the number of multiplications (*) executed as a function of n. ii. Solve the recurrence relation from Part i. iii. Give a recurrence relation for f2, which satisfies the number of additions (+) executed as a function of n. iv. Solve the recurrence relation from Part iii. v. Both functions compute the same function f. Was it a good idea to replace f1 with f2?