SlideShare a Scribd company logo
What is the minimum number of nodes in an AVL tree of height 8? Let N(H) be the minimum
number of nodes in an AVL tree of height h.
What is the minimum number of nodes in an AVL tree of height 8? Let N(H) be the minimum
number of nodes in an AVL tree of height h.
Solution
(* contains(t,x) is whether x is in the tree *) fun contains(t: tree, x: value): bool = case t of Empty
=> false | Node{value, left, right} => (case compare(x, value) of EQUAL => true | LESS =>
contains(left, x) | GREATER => contains(right, x)) (* add(t,x) is a BST with the same values as
t, plus x *) fun add(t: tree, x: value): tree = let fun balance(t: tree): tree = t (* what to write here?
*) in case t of Empty => Node{value=x, left=Empty, right=Empty} | Node {value, left, right} =>
(case compare(x, value) of EQUAL => Node{value=x, left=left, right=right} | LESS =>
Node{value=value, left=add(left, x), right=right} | GREATER => Node{value=value, left=left,
right=add(right,x) } ) end

More Related Content

More from dorisc7

- Answer the following questions about acids 1- What is the phase of a.docx
- Answer the following questions about acids 1- What is the phase of a.docx- Answer the following questions about acids 1- What is the phase of a.docx
- Answer the following questions about acids 1- What is the phase of a.docx
dorisc7
 
- At time 110 four processes (P1 P4) are waiting for a timeout signal.docx
- At time 110 four processes (P1  P4) are waiting for a timeout signal.docx- At time 110 four processes (P1  P4) are waiting for a timeout signal.docx
- At time 110 four processes (P1 P4) are waiting for a timeout signal.docx
dorisc7
 
(70 pts) Nuclear History Identify the event in nuclear history that oc.docx
(70 pts) Nuclear History Identify the event in nuclear history that oc.docx(70 pts) Nuclear History Identify the event in nuclear history that oc.docx
(70 pts) Nuclear History Identify the event in nuclear history that oc.docx
dorisc7
 
(2) The CPU incorporates several major components (as shown in Fig- de.docx
(2) The CPU incorporates several major components (as shown in Fig- de.docx(2) The CPU incorporates several major components (as shown in Fig- de.docx
(2) The CPU incorporates several major components (as shown in Fig- de.docx
dorisc7
 
(Audit evidence) The third GAAS of field work requires that the audito.docx
(Audit evidence) The third GAAS of field work requires that the audito.docx(Audit evidence) The third GAAS of field work requires that the audito.docx
(Audit evidence) The third GAAS of field work requires that the audito.docx
dorisc7
 
What is the Big Bang-SolutionBig Bang is a theory which talks ababo th.docx
What is the Big Bang-SolutionBig Bang is a theory which talks ababo th.docxWhat is the Big Bang-SolutionBig Bang is a theory which talks ababo th.docx
What is the Big Bang-SolutionBig Bang is a theory which talks ababo th.docx
dorisc7
 
What is the concept of sustainable income- Please describe it in your.docx
What is the concept of sustainable income- Please describe it in your.docxWhat is the concept of sustainable income- Please describe it in your.docx
What is the concept of sustainable income- Please describe it in your.docx
dorisc7
 
What is the backbone for the Internet- Briefly describe how the Intern.docx
What is the backbone for the Internet- Briefly describe how the Intern.docxWhat is the backbone for the Internet- Briefly describe how the Intern.docx
What is the backbone for the Internet- Briefly describe how the Intern.docx
dorisc7
 
What is the pH of a 0-1 M aqueous solution of NaH2PO4SolutionNaH2PO4 -.docx
What is the pH of a 0-1 M aqueous solution of NaH2PO4SolutionNaH2PO4 -.docxWhat is the pH of a 0-1 M aqueous solution of NaH2PO4SolutionNaH2PO4 -.docx
What is the pH of a 0-1 M aqueous solution of NaH2PO4SolutionNaH2PO4 -.docx
dorisc7
 
what is the ph of a 0-16M NaF(aq) solution-SolutionNaF(aq) -----------.docx
what is the ph of a 0-16M NaF(aq) solution-SolutionNaF(aq) -----------.docxwhat is the ph of a 0-16M NaF(aq) solution-SolutionNaF(aq) -----------.docx
what is the ph of a 0-16M NaF(aq) solution-SolutionNaF(aq) -----------.docx
dorisc7
 
What is the pH of a 0-114 M solution of the acid HA if its ionization (1).docx
What is the pH of a 0-114 M solution of the acid HA if its ionization (1).docxWhat is the pH of a 0-114 M solution of the acid HA if its ionization (1).docx
What is the pH of a 0-114 M solution of the acid HA if its ionization (1).docx
dorisc7
 
What is the meaning of the keyword this- Explain why it is valid only.docx
What is the meaning of the keyword this- Explain why it is valid only.docxWhat is the meaning of the keyword this- Explain why it is valid only.docx
What is the meaning of the keyword this- Explain why it is valid only.docx
dorisc7
 
what is the foundation for strategy implementation-SolutionA challengi.docx
what is the foundation for strategy implementation-SolutionA challengi.docxwhat is the foundation for strategy implementation-SolutionA challengi.docx
what is the foundation for strategy implementation-SolutionA challengi.docx
dorisc7
 
What is the future of cloud computing--SolutionCloud computing occupie.docx
What is the future of cloud computing--SolutionCloud computing occupie.docxWhat is the future of cloud computing--SolutionCloud computing occupie.docx
What is the future of cloud computing--SolutionCloud computing occupie.docx
dorisc7
 
What is the amount of the capitalization of retained earnings for the.docx
What is the amount of the capitalization of retained earnings for the.docxWhat is the amount of the capitalization of retained earnings for the.docx
What is the amount of the capitalization of retained earnings for the.docx
dorisc7
 
What is the formal definition of a CSIRT- What is the difference in th.docx
What is the formal definition of a CSIRT- What is the difference in th.docxWhat is the formal definition of a CSIRT- What is the difference in th.docx
What is the formal definition of a CSIRT- What is the difference in th.docx
dorisc7
 
What is the difference between the creation and the exploitation of te.docx
What is the difference between the creation and the exploitation of te.docxWhat is the difference between the creation and the exploitation of te.docx
What is the difference between the creation and the exploitation of te.docx
dorisc7
 
What is the difference between routing and forwarding- Do routers hav.docx
What is the difference between routing and forwarding-  Do routers hav.docxWhat is the difference between routing and forwarding-  Do routers hav.docx
What is the difference between routing and forwarding- Do routers hav.docx
dorisc7
 
What is the difference between information found on the internet and o.docx
What is the difference between information found on the internet and o.docxWhat is the difference between information found on the internet and o.docx
What is the difference between information found on the internet and o.docx
dorisc7
 
What is the difference between Information System and Information Tech.docx
What is the difference between Information System and Information Tech.docxWhat is the difference between Information System and Information Tech.docx
What is the difference between Information System and Information Tech.docx
dorisc7
 

More from dorisc7 (20)

- Answer the following questions about acids 1- What is the phase of a.docx
- Answer the following questions about acids 1- What is the phase of a.docx- Answer the following questions about acids 1- What is the phase of a.docx
- Answer the following questions about acids 1- What is the phase of a.docx
 
- At time 110 four processes (P1 P4) are waiting for a timeout signal.docx
- At time 110 four processes (P1  P4) are waiting for a timeout signal.docx- At time 110 four processes (P1  P4) are waiting for a timeout signal.docx
- At time 110 four processes (P1 P4) are waiting for a timeout signal.docx
 
(70 pts) Nuclear History Identify the event in nuclear history that oc.docx
(70 pts) Nuclear History Identify the event in nuclear history that oc.docx(70 pts) Nuclear History Identify the event in nuclear history that oc.docx
(70 pts) Nuclear History Identify the event in nuclear history that oc.docx
 
(2) The CPU incorporates several major components (as shown in Fig- de.docx
(2) The CPU incorporates several major components (as shown in Fig- de.docx(2) The CPU incorporates several major components (as shown in Fig- de.docx
(2) The CPU incorporates several major components (as shown in Fig- de.docx
 
(Audit evidence) The third GAAS of field work requires that the audito.docx
(Audit evidence) The third GAAS of field work requires that the audito.docx(Audit evidence) The third GAAS of field work requires that the audito.docx
(Audit evidence) The third GAAS of field work requires that the audito.docx
 
What is the Big Bang-SolutionBig Bang is a theory which talks ababo th.docx
What is the Big Bang-SolutionBig Bang is a theory which talks ababo th.docxWhat is the Big Bang-SolutionBig Bang is a theory which talks ababo th.docx
What is the Big Bang-SolutionBig Bang is a theory which talks ababo th.docx
 
What is the concept of sustainable income- Please describe it in your.docx
What is the concept of sustainable income- Please describe it in your.docxWhat is the concept of sustainable income- Please describe it in your.docx
What is the concept of sustainable income- Please describe it in your.docx
 
What is the backbone for the Internet- Briefly describe how the Intern.docx
What is the backbone for the Internet- Briefly describe how the Intern.docxWhat is the backbone for the Internet- Briefly describe how the Intern.docx
What is the backbone for the Internet- Briefly describe how the Intern.docx
 
What is the pH of a 0-1 M aqueous solution of NaH2PO4SolutionNaH2PO4 -.docx
What is the pH of a 0-1 M aqueous solution of NaH2PO4SolutionNaH2PO4 -.docxWhat is the pH of a 0-1 M aqueous solution of NaH2PO4SolutionNaH2PO4 -.docx
What is the pH of a 0-1 M aqueous solution of NaH2PO4SolutionNaH2PO4 -.docx
 
what is the ph of a 0-16M NaF(aq) solution-SolutionNaF(aq) -----------.docx
what is the ph of a 0-16M NaF(aq) solution-SolutionNaF(aq) -----------.docxwhat is the ph of a 0-16M NaF(aq) solution-SolutionNaF(aq) -----------.docx
what is the ph of a 0-16M NaF(aq) solution-SolutionNaF(aq) -----------.docx
 
What is the pH of a 0-114 M solution of the acid HA if its ionization (1).docx
What is the pH of a 0-114 M solution of the acid HA if its ionization (1).docxWhat is the pH of a 0-114 M solution of the acid HA if its ionization (1).docx
What is the pH of a 0-114 M solution of the acid HA if its ionization (1).docx
 
What is the meaning of the keyword this- Explain why it is valid only.docx
What is the meaning of the keyword this- Explain why it is valid only.docxWhat is the meaning of the keyword this- Explain why it is valid only.docx
What is the meaning of the keyword this- Explain why it is valid only.docx
 
what is the foundation for strategy implementation-SolutionA challengi.docx
what is the foundation for strategy implementation-SolutionA challengi.docxwhat is the foundation for strategy implementation-SolutionA challengi.docx
what is the foundation for strategy implementation-SolutionA challengi.docx
 
What is the future of cloud computing--SolutionCloud computing occupie.docx
What is the future of cloud computing--SolutionCloud computing occupie.docxWhat is the future of cloud computing--SolutionCloud computing occupie.docx
What is the future of cloud computing--SolutionCloud computing occupie.docx
 
What is the amount of the capitalization of retained earnings for the.docx
What is the amount of the capitalization of retained earnings for the.docxWhat is the amount of the capitalization of retained earnings for the.docx
What is the amount of the capitalization of retained earnings for the.docx
 
What is the formal definition of a CSIRT- What is the difference in th.docx
What is the formal definition of a CSIRT- What is the difference in th.docxWhat is the formal definition of a CSIRT- What is the difference in th.docx
What is the formal definition of a CSIRT- What is the difference in th.docx
 
What is the difference between the creation and the exploitation of te.docx
What is the difference between the creation and the exploitation of te.docxWhat is the difference between the creation and the exploitation of te.docx
What is the difference between the creation and the exploitation of te.docx
 
What is the difference between routing and forwarding- Do routers hav.docx
What is the difference between routing and forwarding-  Do routers hav.docxWhat is the difference between routing and forwarding-  Do routers hav.docx
What is the difference between routing and forwarding- Do routers hav.docx
 
What is the difference between information found on the internet and o.docx
What is the difference between information found on the internet and o.docxWhat is the difference between information found on the internet and o.docx
What is the difference between information found on the internet and o.docx
 
What is the difference between Information System and Information Tech.docx
What is the difference between Information System and Information Tech.docxWhat is the difference between Information System and Information Tech.docx
What is the difference between Information System and Information Tech.docx
 

Recently uploaded

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
 
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
 
Digital Tools and AI for Teaching Learning and Research
Digital Tools and AI for Teaching Learning and ResearchDigital Tools and AI for Teaching Learning and Research
Digital Tools and AI for Teaching Learning and Research
Vikramjit Singh
 
Palestine last event orientationfvgnh .pptx
Palestine last event orientationfvgnh .pptxPalestine last event orientationfvgnh .pptx
Palestine last event orientationfvgnh .pptx
RaedMohamed3
 
CACJapan - GROUP Presentation 1- Wk 4.pdf
CACJapan - GROUP Presentation 1- Wk 4.pdfCACJapan - GROUP Presentation 1- Wk 4.pdf
CACJapan - GROUP Presentation 1- Wk 4.pdf
camakaiclarkmusic
 
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
 
Polish students' mobility in the Czech Republic
Polish students' mobility in the Czech RepublicPolish students' mobility in the Czech Republic
Polish students' mobility in the Czech Republic
Anna Sz.
 
678020731-Sumas-y-Restas-Para-Colorear.pdf
678020731-Sumas-y-Restas-Para-Colorear.pdf678020731-Sumas-y-Restas-Para-Colorear.pdf
678020731-Sumas-y-Restas-Para-Colorear.pdf
CarlosHernanMontoyab2
 
How to Make a Field invisible in Odoo 17
How to Make a Field invisible in Odoo 17How to Make a Field invisible in Odoo 17
How to Make a Field invisible in Odoo 17
Celine George
 
Supporting (UKRI) OA monographs at Salford.pptx
Supporting (UKRI) OA monographs at Salford.pptxSupporting (UKRI) OA monographs at Salford.pptx
Supporting (UKRI) OA monographs at Salford.pptx
Jisc
 
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
 
Home assignment II on Spectroscopy 2024 Answers.pdf
Home assignment II on Spectroscopy 2024 Answers.pdfHome assignment II on Spectroscopy 2024 Answers.pdf
Home assignment II on Spectroscopy 2024 Answers.pdf
Tamralipta Mahavidyalaya
 
The Roman Empire A Historical Colossus.pdf
The Roman Empire A Historical Colossus.pdfThe Roman Empire A Historical Colossus.pdf
The Roman Empire A Historical Colossus.pdf
kaushalkr1407
 
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
 
Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf
Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdfAdversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf
Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf
Po-Chuan Chen
 
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
Levi Shapiro
 
How libraries can support authors with open access requirements for UKRI fund...
How libraries can support authors with open access requirements for UKRI fund...How libraries can support authors with open access requirements for UKRI fund...
How libraries can support authors with open access requirements for UKRI fund...
Jisc
 
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdf
Welcome to TechSoup   New Member Orientation and Q&A (May 2024).pdfWelcome to TechSoup   New Member Orientation and Q&A (May 2024).pdf
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdf
TechSoup
 
Embracing GenAI - A Strategic Imperative
Embracing GenAI - A Strategic ImperativeEmbracing GenAI - A Strategic Imperative
Embracing GenAI - A Strategic Imperative
Peter Windle
 
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
 

Recently uploaded (20)

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
 
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...
 
Digital Tools and AI for Teaching Learning and Research
Digital Tools and AI for Teaching Learning and ResearchDigital Tools and AI for Teaching Learning and Research
Digital Tools and AI for Teaching Learning and Research
 
Palestine last event orientationfvgnh .pptx
Palestine last event orientationfvgnh .pptxPalestine last event orientationfvgnh .pptx
Palestine last event orientationfvgnh .pptx
 
CACJapan - GROUP Presentation 1- Wk 4.pdf
CACJapan - GROUP Presentation 1- Wk 4.pdfCACJapan - GROUP Presentation 1- Wk 4.pdf
CACJapan - GROUP Presentation 1- Wk 4.pdf
 
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
 
Polish students' mobility in the Czech Republic
Polish students' mobility in the Czech RepublicPolish students' mobility in the Czech Republic
Polish students' mobility in the Czech Republic
 
678020731-Sumas-y-Restas-Para-Colorear.pdf
678020731-Sumas-y-Restas-Para-Colorear.pdf678020731-Sumas-y-Restas-Para-Colorear.pdf
678020731-Sumas-y-Restas-Para-Colorear.pdf
 
How to Make a Field invisible in Odoo 17
How to Make a Field invisible in Odoo 17How to Make a Field invisible in Odoo 17
How to Make a Field invisible in Odoo 17
 
Supporting (UKRI) OA monographs at Salford.pptx
Supporting (UKRI) OA monographs at Salford.pptxSupporting (UKRI) OA monographs at Salford.pptx
Supporting (UKRI) OA monographs at Salford.pptx
 
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
 
Home assignment II on Spectroscopy 2024 Answers.pdf
Home assignment II on Spectroscopy 2024 Answers.pdfHome assignment II on Spectroscopy 2024 Answers.pdf
Home assignment II on Spectroscopy 2024 Answers.pdf
 
The Roman Empire A Historical Colossus.pdf
The Roman Empire A Historical Colossus.pdfThe Roman Empire A Historical Colossus.pdf
The Roman Empire A Historical Colossus.pdf
 
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.
 
Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf
Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdfAdversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf
Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf
 
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
 
How libraries can support authors with open access requirements for UKRI fund...
How libraries can support authors with open access requirements for UKRI fund...How libraries can support authors with open access requirements for UKRI fund...
How libraries can support authors with open access requirements for UKRI fund...
 
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdf
Welcome to TechSoup   New Member Orientation and Q&A (May 2024).pdfWelcome to TechSoup   New Member Orientation and Q&A (May 2024).pdf
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdf
 
Embracing GenAI - A Strategic Imperative
Embracing GenAI - A Strategic ImperativeEmbracing GenAI - A Strategic Imperative
Embracing GenAI - A Strategic Imperative
 
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
 

What is the minimum number of nodes in an AVL tree of height 8- Let N(.docx

  • 1. What is the minimum number of nodes in an AVL tree of height 8? Let N(H) be the minimum number of nodes in an AVL tree of height h. What is the minimum number of nodes in an AVL tree of height 8? Let N(H) be the minimum number of nodes in an AVL tree of height h. Solution (* contains(t,x) is whether x is in the tree *) fun contains(t: tree, x: value): bool = case t of Empty => false | Node{value, left, right} => (case compare(x, value) of EQUAL => true | LESS => contains(left, x) | GREATER => contains(right, x)) (* add(t,x) is a BST with the same values as t, plus x *) fun add(t: tree, x: value): tree = let fun balance(t: tree): tree = t (* what to write here? *) in case t of Empty => Node{value=x, left=Empty, right=Empty} | Node {value, left, right} => (case compare(x, value) of EQUAL => Node{value=x, left=left, right=right} | LESS => Node{value=value, left=add(left, x), right=right} | GREATER => Node{value=value, left=left, right=add(right,x) } ) end