Question 2 only please. 2. Given the following recursive algorithm:procedure sum(x, y)Input: x: nonnegative integer, y: nonnegative integerOutput: x+y: nonnegative integerif y==0 then return xelse return sum(x, y-1) + 1Prove that sum(x, y) returns x+y for any nonnegative integers x and y. Part I: InductionProve each of the following statements using induction, strong induction,or structural induction. For each statement, answer the following questions.а.Complete the basis step of the proof.b.What is the inductive hypothesis?C.What do you need to show in the inductive step of the proof?d.Complete the inductive step of the proof.1. Let S be the set of perfect binary trees, defined as:• Basic step: a single vertex with no edges is a perfect binary tree T,.• Recursive step: if T1 and T2 are perfect binary trees of the same height, then a newperfect binary tree T' can be constructed by taking T1 and T2, adding a new vertexv, and adding edges between v and the roots of T, and T2.Prove that h(T) = log2(n(T) + 1) – 1 for any perfect binary tree T, where n(T) is the numberof vertices of T and h(T) is the height of T.Hint: Remember that h(T,) = h(T2) and n(T,) = n(T,). Also remember that h(T') = h(T,) + 1 andn(T') = n(T,) + n(T2) + 1.

As only question 2 is asked . So i am solving for question 2 . procedure sum(x,y) Hence the method…

2. Given the following recursive algorithm: procedure sum(x, y) Input: x: nonnegative integer, y: nonnegative integer Output: x+y: nonnegative integer if y--0 then return x else return sum(x, y-1) + 1 Prove that sum(x, y) returns x+y for any nonnegative integers x and y.

2. Given the following recursive algorithm: procedure sum(x, y) Input: x: nonnegative integer, y: nonnegative integer Output: x+y: nonnegative integer if y--0 then return x else return sum(x, y-1) + 1 Prove that sum(x, y) returns x+y for any nonnegative integers x and y.

C++ for Engineers and Scientists

4th Edition

ISBN:9781133187844

Author:Bronson, Gary J.

Publisher:Bronson, Gary J.

Chapter2: Problem Solving Using C++using

Section2.4: Arithmetic Operations

Problem 6E

See similar textbooks

Related questions

Q: Create a program named ConsoleAppException that divide 2 numbers and display the result. Ensure that…

A: No language is mentioned in question statement so providing solution in Java language. Code: public…

Q: Q-1. what is actput of this logic gati? A F=?

Q: Compare and contrast different types of networks?

A: The Network: A network is made up of two or more computers that are linked together to share…

Q: How many host addresses are available in a /17 network?

A: The Answer is in step2

Q: What happens if the operating system doesn't correctly distribute the available main memory across…

A: Introduction: Pointers that are dangling and premature frees are two examples of this. The memory of…

Q: O Discuss 19T Piotocal archilecbure design goal S veauied -to tart a horizantal Syskm of al-world…

A: here we have given solution for the questions asked in step 2.

Q: What are the principles behind cyclic redundancy checks?

A: CRC is an error-detection technique commonly used in digital networks and storage devices to detect…

Q: What exactly are memory leaks?

A: Justification: Memory leaks are a form of resource leak that happens when a computer software poorly…

Q: What are the three primary cloud computing platforms?

A: When it comes to cloud computing, rather than having a program operating on local computing devices…

Q: What variables influence the topology of a network's selection?

A: A variety of variables influence network topology selection, the most significant of which are as…

Q: c) int sum(int n) { if (0 == n) { return 0; } else { return n + sum(n); } } d) void product(void) {…

A: Given: We have to Find the error (s) in each of the following program segments.

Q: Assume your boss has tasked you with selecting a database management system for the organization.…

A: Introduction:A collection of questionnaires that can meet all of the criteria for choosing a…

Q: What is EBCDIC, and what does it have to do with BCD

A: EBCDIC EBCDIC is a development of previous codes. It is an eight-bit code that encodes 256 symbols.…

Q: Display all power of 2 that are less than 20000. Display list 5 in each line Pascal code please

A: HI THERE I AM ADDING PASCAL CODE AS PER REQUIREMENT BELOWPLEASE GO THROUGH IT THANK YOU

Q: • Define a void function called myFunc that takes a 2-by-3 integer array as an argument and performs…

A: Note :- You have not mention the language of the program, so i'm answering your question in C++.…

Q: Discuss the FVE (5) most critical aspects to consider when choosing a database management system…

A: When choosing a database management system there are several aspects should be consider because…

Q: Write a function called checkArray that takes an array of 20 integer elements as its argument and…

A: Please refer below code and output: Language used is C++: #include <iostream> using…

Q: What are some of the benefits and drawbacks of service-oriented computing?

A: Introduction: Service-Oriented Computing (SOC) is a novel computing paradigm that uses services as…

Q: If you have many processes that are running concurrently, some code is a critical section if one of…

A: Here we have given the option which refers to the critical section. You can find the solution in…

Q: What exactly is failure? What are the many forms of software failures?

A: Justification: If a user feels that the programme no longer delivers the intended output in relation…

Q: Discuss the derived and built-in data types listed here. Each example should be coded in C++. Type…

A: List, Stack, Arrays and Queue are the data structure and built-in data types in C++ STL (Standard…

Q: The HR Manager has requested that you present the advantages of a SQL Server database. The database…

A: Introduction: The SQL database has one or more data files (.mdf /.ndf) as well as one log file…

Q: What are the possible benefits of optical processors?

A: Benefits of optical processors: A visual processor enables us to deconstruct a picture and merge it…

Q: C++ . Using an array. The program should accept multiple entries and iteratively perform the…

A: We have first taken an array named a , which can store as much items prices as the user wants . It…

Q: means the data is same across all the instances at any given point of time. There are many instances…

A: Database Management System

Q: The first element in each array is accessed with index number 0. (e.g., array[0]). Select one: True…

A: Multiple variables with the same name are referred to as an array. It's a user-defined data type…

Q: Answer below question with code and output please There are total three numbers entered by user to…

A: Step-1: Start Step-2: Declare three variable a, b, c and take input from user Step-3: If a is equal…

Q: What's the difference between type casting and automatic type conversion? In Java expressions, what…

A: Type casting and the Type conversion are used in a program to convert one data type to another data…

Q: Explain the concept of a transaction and why database management systems need it.

A: Cannot complete a transaction successfully unless all SQL statements are executed interdependently.…

Q: By using HTML and CSS, create a web page that has a navigation bar on completion. The page will look…

A: Here I have created the style tag inside the head tag. In the style tag, I have defined various CSS…

Q: Explain concurrency and go over four design and management challenges that concurrent raises.

A: Concurrency as a Concept: The architecture of an operating system is concerned with the management…

Q: FUNCTION AND ARRAY ( C++ LANGUAGE) Create a sequence program that will input names to the arrayName…

A: PROGRAM INTRODUCTION: Include the required header files. Declare the required global variable.…

Q: Differentiate between point-to-point, ring, and mesh network topologies by explaining their benefits…

A: Introduction: The differences between point-to-point, ring, and mesh topologies are as follows:…

Q: What is the difference betweenWhat is the difference between DDL and DML commands? DDL and DML…

A: DDL commands : Data Definition Language (DDL) is an abbreviated abbreviation of Data Definition…

Q: Describe the three main circumstances in which concurrency can occur and provide examples of each.

A: Concurrency: In a multiprogramming environment, it is the process of performing many transactions at…

Q: 2. If L is a regular language over E, what can be said about the languages L1 = E* - and L2 =…

A: As per our guidelines, only 3 mcqs will be answered. So, please repost the remaining questions…

Q: how does one go about proving that there has been a breach in security?

A: Although the words "security breach" and "data breach" are sometimes used interchangeably, they…

Q: A program and its data are both stored in memory in the von Neumann architecture. It is thus…

A: Start: This is the design on which many general purpose computers are built, and it is known as Von…

Q: Describe six access technologies briefly. Classify them as home, business, or wide-area wireless…

A: The six modes of access are as follows: - Dial-up modem over telephone lines: HOME. Dial-up is…

Q: What is a translation software, and why do you need one? Describe the numerous sorts of it.

A: Translation software: Any programme that aids human translators in the process of translating text…

Q: Why must the inclusion guard symboVname on a library interface file be unique? (Hint: use proof by…

A: Introduction: Because repeated inclusion is prohibited by using "include guard," also known as…

Q: gm in a f

A: A hybrid cloud is a registering environment which consolidates a public cloud and a private cloud…

Q: How do you prepare for an inspection and perform manual testing?

A: INSPECTION In most cases, the moderator conducts the inspection.A moderator is someone who is…

Q: What is normally included in your own exception class if you create one?

A: Introduction: If you want to create your exception class, you can do so. It must be a Throwable…

Q: Explain two major technological breakthroughs in the history of computing in a few words.

A: Introduction: Computing began on a mechanical level, progressed to an information level (software),…

Q: Please help me with my c++ homework. My question is about this part of the code given by the…

A: Find the answer with explanation given as below :

Q: What dos porallel compuling imply?!

A: According to the question the parallel is generally implemented in the operational that require…

Q: What is the difference between DDL and DML commands?

A: DDL commands DDL full form is data definition language. As the name suggests, DDL commands are used…

Q: Expand to an unsimplified Boolean Function: Use CAPITAL LETTERS for the variables and APOSTROPHE (')…

A: We need to expand the given expression to an un-simplified Boolean Function.

Q: What is the relationship between the number of redundant bits required for code and the number of…

A: Redundant bits Some kind of redundancy is introduced in the system in order to get better…

Concept explainers

Computational Systems

The computation systems can be defined as the systems that are capable of solving a problem that includes calculations either mathematical or logical, and are able to produce the result as an output. For example, a simple calculator that is given a set of numbers and operators as input and produces the result as an output can be defined as a computational system. The above example is a simple illustration only, the computational systems range from simple devices to complex devices such as the systems that control the SpaceX companies, Starlink satellites which are being quite recently seen in the skies at many places globally.

Question

Question 2 only please.

2. Given the following recursive algorithm:
procedure sum(x, y)
Input: x: nonnegative integer, y: nonnegative integer
Output: x+y: nonnegative integer
if y==0 then return x
else return sum(x, y-1) + 1
Prove that sum(x, y) returns x+y for any nonnegative integers x and y.

Part I: Induction
Prove each of the following statements using induction, strong induction,
or structural induction. For each statement, answer the following questions.
а.
Complete the basis step of the proof.
b.
What is the inductive hypothesis?
C.
What do you need to show in the inductive step of the proof?
d.
Complete the inductive step of the proof.
1. Let S be the set of perfect binary trees, defined as:
• Basic step: a single vertex with no edges is a perfect binary tree T,.
• Recursive step: if T1 and T2 are perfect binary trees of the same height, then a new
perfect binary tree T' can be constructed by taking T1 and T2, adding a new vertex
v, and adding edges between v and the roots of T, and T2.
Prove that h(T) = log2(n(T) + 1) – 1 for any perfect binary tree T, where n(T) is the number
of vertices of T and h(T) is the height of T.
Hint: Remember that h(T,) = h(T2) and n(T,) = n(T,). Also remember that h(T') = h(T,) + 1 and
n(T') = n(T,) + n(T2) + 1.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Explaination

VIEW

code and output

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.

Similar questions

Check these two codes and then answer these questions please: 1) Empirically, show the performance curve of the algorithm using time measurements 2) Using the basics of the theoretical analysis, write the complexity of its worst-casetime. 1. Approach: Non recursive: //include necessary header files#include <iostream>using namespace std;//main functionint main(){ int days,buy_on_this_day ,sell_on_this_day; //get number of days as input from user cout<<"Enter number of days: "; cin>>days; int stock_price[days]; for(int i=0;i<days;i++) { cout<<"Enter stock_price"; cin>>stock_price[i]; } int i=0; for(int i=0;i<days-1;i++) { //comparing current price with next day price and finding the minima while(i<days-1 && stock_price[i+1]<=stock_price[i]) i++; if(i==days-1) break; buy_on_this_day =i++; while(i<days && stock_price[i]>=…
a) Consider a recursive function to return the Number of Binary Digits in the Binary Representation of a Positive Decimal Integer (n) using a recursive algorithm. int Process (int n) { if (n == 1) return 1; else return (Extra() + Process (n/4) + Process (n/4)); } Given that Extra(n) is a function of O(n)1) Find T(n) = number of arithmetic operations. 2) Calculate the complexity of this algorithm using Back Substitution.
-check this code then, In python 3 make a code that shows the performance curve of the algorithm using time measurements 1. Approach: Non recursive: //include necessary header files#include <iostream>using namespace std;//main functionint main(){ int days,buy_on_this_day ,sell_on_this_day; //get number of days as input from user cout<<"Enter number of days: "; cin>>days; int stock_price[days]; for(int i=0;i<days;i++) { cout<<"Enter stock_price"; cin>>stock_price[i]; } int i=0; for(int i=0;i<days-1;i++) { //comparing current price with next day price and finding the minima while(i<days-1 && stock_price[i+1]<=stock_price[i]) i++; if(i==days-1) break; buy_on_this_day =i++; while(i<days && stock_price[i]>= stock_price[i-1]) i++; sell_on_this_day =i-1; cout<<buy_on_this_day <<" : index of the change…
Program using Python (see pic) Given code: def print_multiples(a,b,x): #Base Case/s #Add conditions here for base case/s if True : return 0 #Recursive Case/s #Add conditions here for recursive case/s else: return print_multiples(a, b, x) a = int(input("Please enter a: "))print(a)b = int(input("Please enter b: "))x = int(input("Please enter x: ")) print_multiples(a,b,x)
Consider the following algorithm: int f(n) /* n is a positive integer */ if (n <=3) return n int sum = f(n-1) if (n is even) return sum + f(n-2) else return sum + f(n-3) Develop a dynamic programming algorithm that calculates and returns the same value of f(n) for any given integer n>=1. That is, develop a dynamic programming algorithm equivalent to the recursive algorithm f(n). Describe your algorithm using C++ syntax.
Answer the question please?What is the return value of the following recursive algorithm when the input arguments are A=[0,0,1,0,0,1,0,1] and pos=7? function F(A,pos)if(pos<0) return 0 if(pos==length(A)-1 or pos==0 or A[pos-1]==1 or A[pos+1]==1) return 0 + F(A,pos-1) if(A[pos-1]==0 and A[pos+1]==0) return 1+ F(A,pos-1) One of these options below are correct, which one? 7 2 8 5 none of the others
Write a recursive algorithm with the following prototype: int divide(int x, int y); that returns x/y (integer division). You need not test for divide by 0. THE FUNCTION MUST BE RECURSIVE. (hint: base case should be when x<y)
Develop two algorithms, one based on a loop structure and the other on a recursive structure, to print the daily salary of a worker who each day is paid 2.5 times the previous day’s salary (starting with one penny for the first day’s work) for a 30-day period. What problems relating to number storage are you likely to encounter if you implement your solutions on an actual machine?
Exercise 2. Give a recursive definition for the factorial operation k! n! for n ≥ 1. (remember that 1! = 0! = 1) Provide an algorithm in pseudo code to evaluate k! n! as one function Provide an algorithm in pseudo code to evaluate k! n! as three functions Evaluate the complexity of the algorithm at point 2 Evaluate the complexity of the algorithm at point 3
Induction and RecursionA number sequence, t(n), where n ≥ 1, is given by the following recursive algorithm, value a = 1, b = 2 Function t(n):1. If n = 1 then1.1. t ← 3b+5else1.2. t ← -n + a∙t(n-1) a) Calculate the first 3 numbers in the number sequence ( t(1), t(2), ...t(3) ). b) For the fifth number t(5) , a call to the function with n=5, make a trace table for the algorithm, thatis calculate and write down a table with the contents of the different variables for every copy of therecursive algorithm, as the computer would go through the algorithm step by step.
In C program We want to emulate that, too! Using a recursive function, make it so that we print the number we are currently in on a new line. When we encounter a number n divisible by 5, we print "YEHEY" and jump 7 steps forward. However when we encounter a number divisible by 8, we print "OHNO" and go back 6 steps. If it is divisible by both, we print "LUCKY" and jump 11 steps. Otherwise just move 1 step. Start at n=1 and continue doing this until you reach a number greater than or equal to the number entered by the user. Instructions: In the code editor, you are provided with a main() function that must ask the user for a number and calls the snake_ladder() function. This snake_ladder() function is a recursive function which should perform the functionality explained in the problem description above. This function is declared but is initially empty. Input 1. Stopping number Description Input the number to which the recursive function must stop Constraints The input is a…
In C program We want to emulate that, too! Using a recursive function, make it so that we print the number we are currently in on a new line. When we encounter a number n divisible by 5, we print "YEHEY" and jump 7 steps forward. However when we encounter a number divisible by 8, we print "OHNO" and go back 6 steps. If it is divisible by both, we print "LUCKY" and jump 11 steps. Otherwise just move 1 step. Start at n=1 and continue doing this until you reach a number greater than or equal to the number entered by the user. Instructions: In the code editor, you are provided with a main() function that must ask the user for a number and calls the snake_ladder() function.This snake_ladder() function is a recursive function which should perform the functionality explained in the problem description above.This function is declared but is initially empty.Input 1. Stopping number Description Input the number to which the recursive function must stop Constraints The input is a positive integer…