SlideShare a Scribd company logo
Give asymptotic upper and lower bounds for T(n) in each of the following recurrences. Assume
that each T(n) is a constant for n 2. Make your bounds as tight as possible, and justify your
answers.
I) T(n) = 2T(n/2) + n^4
II) T(n) = 16T(n/4) + n^2
III) T(n) = T(n-2) + n^2
IV) T(n) = 2T(n/4) + n

More Related Content

More from francescaj1

Given the class specification of Unsorted Type as below- class Unsorte.docx
Given the class specification of Unsorted Type as below- class Unsorte.docxGiven the class specification of Unsorted Type as below- class Unsorte.docx
Given the class specification of Unsorted Type as below- class Unsorte.docx
francescaj1
 
Given numRows and numColumns- print a list of all seats in a theater-.docx
Given numRows and numColumns- print a list of all seats in a theater-.docxGiven numRows and numColumns- print a list of all seats in a theater-.docx
Given numRows and numColumns- print a list of all seats in a theater-.docx
francescaj1
 
Given is the IntNode class that represents an element in a linked list.docx
Given is the IntNode class that represents an element in a linked list.docxGiven is the IntNode class that represents an element in a linked list.docx
Given is the IntNode class that represents an element in a linked list.docx
francescaj1
 
Given its reactants- state whether the reaction is an example of a hyd.docx
Given its reactants- state whether the reaction is an example of a hyd.docxGiven its reactants- state whether the reaction is an example of a hyd.docx
Given its reactants- state whether the reaction is an example of a hyd.docx
francescaj1
 
Given is the IntNode class that represents an element in a linked list (3).docx
Given is the IntNode class that represents an element in a linked list (3).docxGiven is the IntNode class that represents an element in a linked list (3).docx
Given is the IntNode class that represents an element in a linked list (3).docx
francescaj1
 
Given is the IntNode class that represents an element in a linked list (1).docx
Given is the IntNode class that represents an element in a linked list (1).docxGiven is the IntNode class that represents an element in a linked list (1).docx
Given is the IntNode class that represents an element in a linked list (1).docx
francescaj1
 
Given is the class IntNode representing a member of a linked list- and.docx
Given is the class IntNode representing a member of a linked list- and.docxGiven is the class IntNode representing a member of a linked list- and.docx
Given is the class IntNode representing a member of a linked list- and.docx
francescaj1
 
Given extremely high rates of obesity- diabetes and cancer- should the.docx
Given extremely high rates of obesity- diabetes and cancer- should the.docxGiven extremely high rates of obesity- diabetes and cancer- should the.docx
Given extremely high rates of obesity- diabetes and cancer- should the.docx
francescaj1
 
Given input And a filter What is the output- (zero padding -0- stride-.docx
Given input And a filter What is the output- (zero padding -0- stride-.docxGiven input And a filter What is the output- (zero padding -0- stride-.docx
Given input And a filter What is the output- (zero padding -0- stride-.docx
francescaj1
 
Give your own person opinion and response to this post- I think that C.docx
Give your own person opinion and response to this post- I think that C.docxGive your own person opinion and response to this post- I think that C.docx
Give your own person opinion and response to this post- I think that C.docx
francescaj1
 
GENERAL ANIMAL ORGANIZATION - What are the three types of germ layers-.docx
GENERAL ANIMAL ORGANIZATION - What are the three types of germ layers-.docxGENERAL ANIMAL ORGANIZATION - What are the three types of germ layers-.docx
GENERAL ANIMAL ORGANIZATION - What are the three types of germ layers-.docx
francescaj1
 
Give an example of homeostasis at each of these levels- cells- tissues.docx
Give an example of homeostasis at each of these levels- cells- tissues.docxGive an example of homeostasis at each of these levels- cells- tissues.docx
Give an example of homeostasis at each of these levels- cells- tissues.docx
francescaj1
 
Genetics- A geneticist is studying two genes- Each gene can be either.docx
Genetics- A geneticist is studying two genes- Each gene can be either.docxGenetics- A geneticist is studying two genes- Each gene can be either.docx
Genetics- A geneticist is studying two genes- Each gene can be either.docx
francescaj1
 
GEOMETRIC- SOCIAL MEDIA PRESENCE According to a recent Pew Research po.docx
GEOMETRIC- SOCIAL MEDIA PRESENCE According to a recent Pew Research po.docxGEOMETRIC- SOCIAL MEDIA PRESENCE According to a recent Pew Research po.docx
GEOMETRIC- SOCIAL MEDIA PRESENCE According to a recent Pew Research po.docx
francescaj1
 
Geologic History of Yellowstone What is the sequence of geologic even.docx
Geologic History of Yellowstone  What is the sequence of geologic even.docxGeologic History of Yellowstone  What is the sequence of geologic even.docx
Geologic History of Yellowstone What is the sequence of geologic even.docx
francescaj1
 
g each label into the proper position to identify the vertebra it desc.docx
g each label into the proper position to identify the vertebra it desc.docxg each label into the proper position to identify the vertebra it desc.docx
g each label into the proper position to identify the vertebra it desc.docx
francescaj1
 
Frustration of purpose requires all of the following to occur except.docx
Frustration of purpose requires all of the following to occur except.docxFrustration of purpose requires all of the following to occur except.docx
Frustration of purpose requires all of the following to occur except.docx
francescaj1
 
Future value of an ordinary annuity- Fill in the missing future values.docx
Future value of an ordinary annuity- Fill in the missing future values.docxFuture value of an ordinary annuity- Fill in the missing future values.docx
Future value of an ordinary annuity- Fill in the missing future values.docx
francescaj1
 
fx(x)-fx(x)- then prove xPr(x-x)E(x)x.docx
fx(x)-fx(x)- then prove xPr(x-x)E(x)x.docxfx(x)-fx(x)- then prove xPr(x-x)E(x)x.docx
fx(x)-fx(x)- then prove xPr(x-x)E(x)x.docx
francescaj1
 
FS 21 Travis McAllister operates a surveying company- For the first fe.docx
FS 21 Travis McAllister operates a surveying company- For the first fe.docxFS 21 Travis McAllister operates a surveying company- For the first fe.docx
FS 21 Travis McAllister operates a surveying company- For the first fe.docx
francescaj1
 

More from francescaj1 (20)

Given the class specification of Unsorted Type as below- class Unsorte.docx
Given the class specification of Unsorted Type as below- class Unsorte.docxGiven the class specification of Unsorted Type as below- class Unsorte.docx
Given the class specification of Unsorted Type as below- class Unsorte.docx
 
Given numRows and numColumns- print a list of all seats in a theater-.docx
Given numRows and numColumns- print a list of all seats in a theater-.docxGiven numRows and numColumns- print a list of all seats in a theater-.docx
Given numRows and numColumns- print a list of all seats in a theater-.docx
 
Given is the IntNode class that represents an element in a linked list.docx
Given is the IntNode class that represents an element in a linked list.docxGiven is the IntNode class that represents an element in a linked list.docx
Given is the IntNode class that represents an element in a linked list.docx
 
Given its reactants- state whether the reaction is an example of a hyd.docx
Given its reactants- state whether the reaction is an example of a hyd.docxGiven its reactants- state whether the reaction is an example of a hyd.docx
Given its reactants- state whether the reaction is an example of a hyd.docx
 
Given is the IntNode class that represents an element in a linked list (3).docx
Given is the IntNode class that represents an element in a linked list (3).docxGiven is the IntNode class that represents an element in a linked list (3).docx
Given is the IntNode class that represents an element in a linked list (3).docx
 
Given is the IntNode class that represents an element in a linked list (1).docx
Given is the IntNode class that represents an element in a linked list (1).docxGiven is the IntNode class that represents an element in a linked list (1).docx
Given is the IntNode class that represents an element in a linked list (1).docx
 
Given is the class IntNode representing a member of a linked list- and.docx
Given is the class IntNode representing a member of a linked list- and.docxGiven is the class IntNode representing a member of a linked list- and.docx
Given is the class IntNode representing a member of a linked list- and.docx
 
Given extremely high rates of obesity- diabetes and cancer- should the.docx
Given extremely high rates of obesity- diabetes and cancer- should the.docxGiven extremely high rates of obesity- diabetes and cancer- should the.docx
Given extremely high rates of obesity- diabetes and cancer- should the.docx
 
Given input And a filter What is the output- (zero padding -0- stride-.docx
Given input And a filter What is the output- (zero padding -0- stride-.docxGiven input And a filter What is the output- (zero padding -0- stride-.docx
Given input And a filter What is the output- (zero padding -0- stride-.docx
 
Give your own person opinion and response to this post- I think that C.docx
Give your own person opinion and response to this post- I think that C.docxGive your own person opinion and response to this post- I think that C.docx
Give your own person opinion and response to this post- I think that C.docx
 
GENERAL ANIMAL ORGANIZATION - What are the three types of germ layers-.docx
GENERAL ANIMAL ORGANIZATION - What are the three types of germ layers-.docxGENERAL ANIMAL ORGANIZATION - What are the three types of germ layers-.docx
GENERAL ANIMAL ORGANIZATION - What are the three types of germ layers-.docx
 
Give an example of homeostasis at each of these levels- cells- tissues.docx
Give an example of homeostasis at each of these levels- cells- tissues.docxGive an example of homeostasis at each of these levels- cells- tissues.docx
Give an example of homeostasis at each of these levels- cells- tissues.docx
 
Genetics- A geneticist is studying two genes- Each gene can be either.docx
Genetics- A geneticist is studying two genes- Each gene can be either.docxGenetics- A geneticist is studying two genes- Each gene can be either.docx
Genetics- A geneticist is studying two genes- Each gene can be either.docx
 
GEOMETRIC- SOCIAL MEDIA PRESENCE According to a recent Pew Research po.docx
GEOMETRIC- SOCIAL MEDIA PRESENCE According to a recent Pew Research po.docxGEOMETRIC- SOCIAL MEDIA PRESENCE According to a recent Pew Research po.docx
GEOMETRIC- SOCIAL MEDIA PRESENCE According to a recent Pew Research po.docx
 
Geologic History of Yellowstone What is the sequence of geologic even.docx
Geologic History of Yellowstone  What is the sequence of geologic even.docxGeologic History of Yellowstone  What is the sequence of geologic even.docx
Geologic History of Yellowstone What is the sequence of geologic even.docx
 
g each label into the proper position to identify the vertebra it desc.docx
g each label into the proper position to identify the vertebra it desc.docxg each label into the proper position to identify the vertebra it desc.docx
g each label into the proper position to identify the vertebra it desc.docx
 
Frustration of purpose requires all of the following to occur except.docx
Frustration of purpose requires all of the following to occur except.docxFrustration of purpose requires all of the following to occur except.docx
Frustration of purpose requires all of the following to occur except.docx
 
Future value of an ordinary annuity- Fill in the missing future values.docx
Future value of an ordinary annuity- Fill in the missing future values.docxFuture value of an ordinary annuity- Fill in the missing future values.docx
Future value of an ordinary annuity- Fill in the missing future values.docx
 
fx(x)-fx(x)- then prove xPr(x-x)E(x)x.docx
fx(x)-fx(x)- then prove xPr(x-x)E(x)x.docxfx(x)-fx(x)- then prove xPr(x-x)E(x)x.docx
fx(x)-fx(x)- then prove xPr(x-x)E(x)x.docx
 
FS 21 Travis McAllister operates a surveying company- For the first fe.docx
FS 21 Travis McAllister operates a surveying company- For the first fe.docxFS 21 Travis McAllister operates a surveying company- For the first fe.docx
FS 21 Travis McAllister operates a surveying company- For the first fe.docx
 

Recently uploaded

Chapter 3 - Islamic Banking Products and Services.pptx
Chapter 3 - Islamic Banking Products and Services.pptxChapter 3 - Islamic Banking Products and Services.pptx
Chapter 3 - Islamic Banking Products and Services.pptx
Mohd Adib Abd Muin, Senior Lecturer at Universiti Utara Malaysia
 
TESDA TM1 REVIEWER FOR NATIONAL ASSESSMENT WRITTEN AND ORAL QUESTIONS WITH A...
TESDA TM1 REVIEWER  FOR NATIONAL ASSESSMENT WRITTEN AND ORAL QUESTIONS WITH A...TESDA TM1 REVIEWER  FOR NATIONAL ASSESSMENT WRITTEN AND ORAL QUESTIONS WITH A...
TESDA TM1 REVIEWER FOR NATIONAL ASSESSMENT WRITTEN AND ORAL QUESTIONS WITH A...
EugeneSaldivar
 
Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46
Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46
Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46
MysoreMuleSoftMeetup
 
A Survey of Techniques for Maximizing LLM Performance.pptx
A Survey of Techniques for Maximizing LLM Performance.pptxA Survey of Techniques for Maximizing LLM Performance.pptx
A Survey of Techniques for Maximizing LLM Performance.pptx
thanhdowork
 
Biological Screening of Herbal Drugs in detailed.
Biological Screening of Herbal Drugs in detailed.Biological Screening of Herbal Drugs in detailed.
Biological Screening of Herbal Drugs in detailed.
Ashokrao Mane college of Pharmacy Peth-Vadgaon
 
"Protectable subject matters, Protection in biotechnology, Protection of othe...
"Protectable subject matters, Protection in biotechnology, Protection of othe..."Protectable subject matters, Protection in biotechnology, Protection of othe...
"Protectable subject matters, Protection in biotechnology, Protection of othe...
SACHIN R KONDAGURI
 
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptxChapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Mohd Adib Abd Muin, Senior Lecturer at Universiti Utara Malaysia
 
special B.ed 2nd year old paper_20240531.pdf
special B.ed 2nd year old paper_20240531.pdfspecial B.ed 2nd year old paper_20240531.pdf
special B.ed 2nd year old paper_20240531.pdf
Special education needs
 
The Accursed House by Émile Gaboriau.pptx
The Accursed House by Émile Gaboriau.pptxThe Accursed House by Émile Gaboriau.pptx
The Accursed House by Émile Gaboriau.pptx
DhatriParmar
 
Unit 8 - Information and Communication Technology (Paper I).pdf
Unit 8 - Information and Communication Technology (Paper I).pdfUnit 8 - Information and Communication Technology (Paper I).pdf
Unit 8 - Information and Communication Technology (Paper I).pdf
Thiyagu K
 
Overview on Edible Vaccine: Pros & Cons with Mechanism
Overview on Edible Vaccine: Pros & Cons with MechanismOverview on Edible Vaccine: Pros & Cons with Mechanism
Overview on Edible Vaccine: Pros & Cons with Mechanism
DeeptiGupta154
 
The Diamond Necklace by Guy De Maupassant.pptx
The Diamond Necklace by Guy De Maupassant.pptxThe Diamond Necklace by Guy De Maupassant.pptx
The Diamond Necklace by Guy De Maupassant.pptx
DhatriParmar
 
Thesis Statement for students diagnonsed withADHD.ppt
Thesis Statement for students diagnonsed withADHD.pptThesis Statement for students diagnonsed withADHD.ppt
Thesis Statement for students diagnonsed withADHD.ppt
EverAndrsGuerraGuerr
 
Lapbook sobre os Regimes Totalitários.pdf
Lapbook sobre os Regimes Totalitários.pdfLapbook sobre os Regimes Totalitários.pdf
Lapbook sobre os Regimes Totalitários.pdf
Jean Carlos Nunes Paixão
 
Digital Artifact 1 - 10VCD Environments Unit
Digital Artifact 1 - 10VCD Environments UnitDigital Artifact 1 - 10VCD Environments Unit
Digital Artifact 1 - 10VCD Environments Unit
chanes7
 
Operation Blue Star - Saka Neela Tara
Operation Blue Star   -  Saka Neela TaraOperation Blue Star   -  Saka Neela Tara
Operation Blue Star - Saka Neela Tara
Balvir Singh
 
1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx
JosvitaDsouza2
 
MASS MEDIA STUDIES-835-CLASS XI Resource Material.pdf
MASS MEDIA STUDIES-835-CLASS XI Resource Material.pdfMASS MEDIA STUDIES-835-CLASS XI Resource Material.pdf
MASS MEDIA STUDIES-835-CLASS XI Resource Material.pdf
goswamiyash170123
 
Synthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptxSynthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptx
Pavel ( NSTU)
 
Introduction to AI for Nonprofits with Tapp Network
Introduction to AI for Nonprofits with Tapp NetworkIntroduction to AI for Nonprofits with Tapp Network
Introduction to AI for Nonprofits with Tapp Network
TechSoup
 

Recently uploaded (20)

Chapter 3 - Islamic Banking Products and Services.pptx
Chapter 3 - Islamic Banking Products and Services.pptxChapter 3 - Islamic Banking Products and Services.pptx
Chapter 3 - Islamic Banking Products and Services.pptx
 
TESDA TM1 REVIEWER FOR NATIONAL ASSESSMENT WRITTEN AND ORAL QUESTIONS WITH A...
TESDA TM1 REVIEWER  FOR NATIONAL ASSESSMENT WRITTEN AND ORAL QUESTIONS WITH A...TESDA TM1 REVIEWER  FOR NATIONAL ASSESSMENT WRITTEN AND ORAL QUESTIONS WITH A...
TESDA TM1 REVIEWER FOR NATIONAL ASSESSMENT WRITTEN AND ORAL QUESTIONS WITH A...
 
Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46
Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46
Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46
 
A Survey of Techniques for Maximizing LLM Performance.pptx
A Survey of Techniques for Maximizing LLM Performance.pptxA Survey of Techniques for Maximizing LLM Performance.pptx
A Survey of Techniques for Maximizing LLM Performance.pptx
 
Biological Screening of Herbal Drugs in detailed.
Biological Screening of Herbal Drugs in detailed.Biological Screening of Herbal Drugs in detailed.
Biological Screening of Herbal Drugs in detailed.
 
"Protectable subject matters, Protection in biotechnology, Protection of othe...
"Protectable subject matters, Protection in biotechnology, Protection of othe..."Protectable subject matters, Protection in biotechnology, Protection of othe...
"Protectable subject matters, Protection in biotechnology, Protection of othe...
 
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptxChapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
 
special B.ed 2nd year old paper_20240531.pdf
special B.ed 2nd year old paper_20240531.pdfspecial B.ed 2nd year old paper_20240531.pdf
special B.ed 2nd year old paper_20240531.pdf
 
The Accursed House by Émile Gaboriau.pptx
The Accursed House by Émile Gaboriau.pptxThe Accursed House by Émile Gaboriau.pptx
The Accursed House by Émile Gaboriau.pptx
 
Unit 8 - Information and Communication Technology (Paper I).pdf
Unit 8 - Information and Communication Technology (Paper I).pdfUnit 8 - Information and Communication Technology (Paper I).pdf
Unit 8 - Information and Communication Technology (Paper I).pdf
 
Overview on Edible Vaccine: Pros & Cons with Mechanism
Overview on Edible Vaccine: Pros & Cons with MechanismOverview on Edible Vaccine: Pros & Cons with Mechanism
Overview on Edible Vaccine: Pros & Cons with Mechanism
 
The Diamond Necklace by Guy De Maupassant.pptx
The Diamond Necklace by Guy De Maupassant.pptxThe Diamond Necklace by Guy De Maupassant.pptx
The Diamond Necklace by Guy De Maupassant.pptx
 
Thesis Statement for students diagnonsed withADHD.ppt
Thesis Statement for students diagnonsed withADHD.pptThesis Statement for students diagnonsed withADHD.ppt
Thesis Statement for students diagnonsed withADHD.ppt
 
Lapbook sobre os Regimes Totalitários.pdf
Lapbook sobre os Regimes Totalitários.pdfLapbook sobre os Regimes Totalitários.pdf
Lapbook sobre os Regimes Totalitários.pdf
 
Digital Artifact 1 - 10VCD Environments Unit
Digital Artifact 1 - 10VCD Environments UnitDigital Artifact 1 - 10VCD Environments Unit
Digital Artifact 1 - 10VCD Environments Unit
 
Operation Blue Star - Saka Neela Tara
Operation Blue Star   -  Saka Neela TaraOperation Blue Star   -  Saka Neela Tara
Operation Blue Star - Saka Neela Tara
 
1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx
 
MASS MEDIA STUDIES-835-CLASS XI Resource Material.pdf
MASS MEDIA STUDIES-835-CLASS XI Resource Material.pdfMASS MEDIA STUDIES-835-CLASS XI Resource Material.pdf
MASS MEDIA STUDIES-835-CLASS XI Resource Material.pdf
 
Synthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptxSynthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptx
 
Introduction to AI for Nonprofits with Tapp Network
Introduction to AI for Nonprofits with Tapp NetworkIntroduction to AI for Nonprofits with Tapp Network
Introduction to AI for Nonprofits with Tapp Network
 

Give asymptotic upper and lower bounds for T(n) in each of the followi.docx

  • 1. Give asymptotic upper and lower bounds for T(n) in each of the following recurrences. Assume that each T(n) is a constant for n 2. Make your bounds as tight as possible, and justify your answers. I) T(n) = 2T(n/2) + n^4 II) T(n) = 16T(n/4) + n^2 III) T(n) = T(n-2) + n^2 IV) T(n) = 2T(n/4) + n