Part 1) Write pseudocode for an iterative algorithm which finds the maximum value of a list of integers. Use a loop invariant to prove your algorithm is correct. (Presumably you have already witten a program like this over the course of your studies! The interesting part here is the proof.) Part 2) Prove by induction the recursive program Foo is correct: Foo determines if there are two indices i and j, p

Part 1) Write pseudocode for an iterative algorithm which finds the maximum value of a list of integers. Use a loop invariant to prove your algorithm is correct. (Presumably you have already witten a program like this over the course of your studies! The interesting part here is the proof.) Part 2) Prove by induction the recursive program Foo is correct: Foo determines if there are two indices i and j, p

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Related questions

Q: ACTIVITY 3 RECURSION Instructions: Use any size of bond paper. Write your name, course and year,…

A: Given, g(n+1)=2n-n Putting the value of n=n-1 on both the sides g(n-1+1)=2n-1-(n-1)…

Q: Algortimhs Recursive Thinking) Carefully read the comment of the following function, then complete…

A: Answer: I have done code and also I have attached code as well as output

Q: Write a recursive algorithm with the following prototype: int divide(int x, int y); that returns…

A: Solution :

Q: a) Give a recursive deﬁnition for the set of all strings of a’s and b’s where n a’s followed by n…

A: Given: Give a recursive deﬁnition for the set of all strings of a’s and b’s where n a’s followed by…

Q: Exercise 1: The number of combinations Ch represents the number of subsets of cardi- nal p of a set…

A: ALGORITHM:- 1. Take values of n and p from user. 2. Pass these values to the recursive function. 3.…

Q: se the recursion to solve the following problems 1. Calculate the sum of an array of n integers.…

A: In this question we have to write the code for the recursion to solve the following problems:1.…

Q: Use the recursion to solve the following problems using Java Programming Language 1. Calculate the…

A: In this question we have to write the list of Java Program1. Calculate the sum of an array of n…

Q: T/F 7. The recursive procedure for solving the Towers of Hanoi can only be used if the number of…

A: T/F The recursive procedure for solving the Towers of Hanoi can only be used if the number of discs…

Q: Consider a rectangle whose side lengths are two consecutive Fibonacci numbers. (Of course, neither…

A: The idea is to break the rectangle into a square of size Fib(n - 1) and a rectangle of size Fib(n -…

Q: Consider the following recursive function: { a if b = 0, %3D f(b, a) 1 f(6, 2. (a f(a, b) if b > a >…

A: Answer is given below .

Q: Using Python Recursion is the concept of a function calling itself until the problem is solved when…

A: The Python code is given below with output screenshot

Q: So far, we have learned that we can perform repetitive tasks using loops. However, another way is by…

A: Actually, Java is a general-purpose also class-based, object-oriented programming language designed…

Q: Run a program that tests De Moivre's formula on page 325 by comparing the values obtained from it…

A: program to test the De moivre's formula for fibonacci number followed in next step--

Q: Recursion can be direct or indirect. It is direct when a function calls itself and it is indirect…

A: Recursion can be direct or indirect. It is direct when a function calls itself and it is indirect…

Q: Using the algorithm discussed in class, write an iterative program to solve the Towers of Hanoi…

A: I have written the code in C with a more improved solution in terms of time & space complexity.…

Q: ii. Let K be an integer and suppose F(K) is recursively defined by: F( int k)…

A: Here we have to find the F(7) and the function given is recursive function. The trace of function…

Q: Write a recursive function that outputs the sequence of steps needed to solve the puzzle with n…

A: The current situation is to develop a c++ program that solves the puzzle game Tower of Hanoi using…

Q: For function sumtok, write the missing recursive call. This function returns the sum of the values…

A: Correct Code:- public int sumtok(int k) { if (k<= 0){ return 0; }else{ return k +…

Q: Recursion Find how many possible combinations that a number can be decomposed into the multiple of…

A: Program Approach:- 1. First define the recursive function countCombination() 2. In this function, we…

Q: Write a recursive algorithm with the following prototype: int divide (int x, int y); that returns…

A: Please find the answer below :

Q: For function isReverse, write the two missing base case conditions. Given two strings, this function…

A: The Answer is

Q: T/F 9. As loop variables and recursive solutions are also not used for iterative solutions, the…

A: Given: As loop variables and recursive solutions are also not used for iterative solutions, the…

Q: One-friend recursion vs iteration. 1. Your objective is to receive the tuple a1, a2,..., a and…

A: A friend recursion function is a function that calls itself repeatedly in order to solve a larger…

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

Part 1) Write pseudocode for an iterative algorithm which finds the maximum value of a list
of integers. Use a loop invariant to prove your algorithm is correct. (Presumably you have
already witten a program like this over the course of your studies! The interesting part here
is the proof.)
Part 2) Prove by induction the recursive program Foo is correct:
Foo determines if there are two indices i and j, p<i < j< q, such that a; +a; = x.
(We're looking in a particular range of sorted list A, indices [p, q] (so including index p as
well as index q), for two values a; and a, which sum to r. We don't allow i and j to be equal.)
laj

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

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

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

Ex. 01 : Recursion About So far, we have learned that we can perform repetitive tasks using loops. However, another way is by creating methods that call themselves. This programming technique is called recursion and, a method that calls itself within it's own body is called a recursive method. One use of recursion is to perform repetitive tasks instead of using loops, since some problems seem to be solved more naturally with recursion than with loops. To solve a problem using recursion, it is broken down into sub-problems. Each sub-problem is similar to the original problem, but smaller in size. You can apply the same approach to each sub-problem to solve it recursively. All recursive methods use conditional tests to either 1. stop or 2. continue the recursion. Each recursive method has the following characteristics: 1. end/terminating case: One or more end cases to stop the recursion. 2. recursive case: reduces the problem in to smaller sub-problems, until it reaches (becomes) the end…
One-friend recursion vs iteration. 1. Your objective is to receive the tuple a1, a2,..., a and return the tuple an, an1,..., a1 that has been inverted. You will only take an element off of one end or put an element back on one end because you are being lazy. But you have friends in recursion who can assist you.Please provide the recursive code as well as a paragraph with the friend's description of the algorithm.2. Now imagine that you lack friends but have a stack. Quickly design an iterative programme to address this issue. Include loop invariants and other crucial stages that are necessary to describe an iterative method.3. Trace both of these scripts separately. On a computer, step by step compare and contrast their calculations.
T/F 7. The recursive procedure for solving the Towers of Hanoi can only be used if the number of discs parameter is 7 or less.
The Tower of Hanoi is a puzzle where n disks of different sizes arestacked in ascending order on one rod and there are two other rods with nodisks on them. The objective is to move all disks from the first rod to thethird, such that:- only one disk is moved at a time- a larger disk can never be placed on top of a smaller oneWrite a recursive function that outputs the sequence of steps needed tosolve the puzzle with n disks.Write a test program in C++ that allows the user to input number of disks andthen uses your function to output the steps needed to solve the puzzle.Hint: If you could move up n−1 of the disks from the first post to thethird post using the second post as a spare, the last disk could be moved fromthe first post to the second post. Then by using the same technique you canmove the n−1 disks from the third post to the second post, using the firstdisk as a spare. There! You have the puzzle solved. You only have to decidewhat the nonrecursive case is, what the recursive…
CodeW For fun X C Solved https://codeworkou... 臺亂 CodeWorkout X272: Recursion Programming Exercise: Is Reverse For function isReverse, write the two missing base case conditions. Given two strings, this function returns true if the two strings are identical, but are in reverse order. Otherwise it returns false. For example, if the inputs are "tac" and "cat", then the function should return true. Examples: isReverse("tac", "cat") -> true Your Answer: 1 public boolean isReverse(String s1, String s2) { 2. if > 3. 4. else if > return true; return false; 5. 6. else { String s1first = String s2last return s1first.equals (s2last) && 51. substring(0, 1); s2, substring(s2.length() 1); 7. 8. 6. isReverse(s1.substring(1), s2.substring(0, s2.length() 1)); { 12} 1:11AM 50°F Clear 12/4/2021
F Run a program that tests De Moivre's formula on page 325 by comparing the values obtained from it with those obtained from the recursive definition of the Fibonacci numbers.
Algortimhs Recursive Thinking) Carefully read the comment of the following function, then complete the function so that it correctly solves the problem. Verify your answer by writing down the three questions rule and answer the questions for your completed algorithm. /* Return true if there exist duplicate values in sublist a[first...last], i.e., there are a[i]==a[j] for some i,j where i is not equal to j @param a: the vector/list @param first, last: two integer specifying the starting and ending indices of list@return return true if there are duplicate values in a[first...last], otherwise return false */ bool ContainDuplicate (vector<int> a, int first, int last) { //1. what should be the base case? What should be returned? // general case if (ContainDuplicate (a, first+1, last)==true) _______________; //Finish the rest based upon comment:// if a[first] does not equal to ANY value in a[first+1...last], // then return false;// else return true } (Recursive Thinking) For the…
Use the recursion to solve the following problems 1. Calculate the sum of an array of n integers. 2. Compute Powers, p(x,n)=xn 3. Revers an array of n integers 4. Calculate the length of string (number of characters) 5. Implement the tail recursion for problems 1 and 2. Please test the program by using 2 different input sets!
Only typing answers please.
CS211 Non-recursive solution for Towers of Hanoi Using the algorithm discussed in class, write an iterative program to solve the Towers of Hanoi problem. The problem: You are given three towers a, b, and c. We start with n rings on tower a and we need to transfer them to tower b subject to the following restrictions: 1. We can only move one ring at a time, and 2. We may never put a larger numbered ring on top of a smaller numbered one. There are always 3 towers. Your program will prompt the user for the number of rings. Here is the algorithm. Definition: A ring is "available" if it is on the top of one of the towers. Definition: The "candidate" is the smallest available ring that has not been moved on the most recent move. The first candidate is ring 1. The Algorithm: 1. Find the candidate. 2. Move the candidate (right or left, depending if the number of rings is odd or even) to the closest tower on which it can be placed. Move "around the circle" if necessary. 3. If not done, go back…
please help me answer this question I will give you a good rating
An ascending array is an array such as "124678", “abcfgkl", and “5789", is in an increasing order. The empty array is regarded as an ascending array. Write a function 2. that every character bool isAscending (char* arr, int size) that returns true if this array is ascending. (a) Use iteration (b) Use recursion (c) Convert the function that you wrote in part (b) into a template function. The template function should work for arrays of any type.