Answered: We have an algorithm that is defined as…

We have an algorithm that is defined as follows: Input: neZ: n< 222 Mysterious-Function(n): if n> 222 then return n – 14 else return Mysterious-Function(Mysterious-Function (n + 15)) endif

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter15: Recursion

Section: Chapter Questions

Problem 6PE

See similar textbooks

*)Algorithm Implementation

*)Growth Curve

We have an algorithm that is defined as follows:
Input:
neZ:
n< 222
Mysterious-Function(n):
if n > 222 then
return n – 14
else
return Mysterious-Function(Mysterious-Function (n + 15))
endif

Process or set of rules that allow for the solving of specific, well-defined computational problems through a specific series of commands. This topic is fundamental in computer science, especially with regard to artificial intelligence, databases, graphics, networking, operating systems, and security.

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Algorithm:

Implementation:

Screenshot:

Output:

Step by step

Solved in 4 steps with 1 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

Factorial of a number is defined as: n! = n(n-1)(n-2)(n-3)...(2)(1) For example, 4! = 4*3*2*1 The n! can be written in terms of (n-1)! as: n! = n* (n-1)! (n-1)! = (n-1)*(n-2) ! and so forth. Thus, in order to compute n!, we need (n-1)!, to have (n-1)!, we need (n-2)! and so forth. As you may immediately notice, the base case for factorial is 1 because 1! = 1. Write a program that uses a recursive function called factorial that takes an integer n as its argument and returns n! to the main. C++ PLEASE
Please see attached
Assume that you were given N cents (N is an integer) and you were asked to break up the N cents into coins consisting of 1 cent, 2 cents and 5 cents. Write a dynamic programming-based recursive algorithm, which returns the smallest (optimal) number of coins needed to solve this problem. For example, if your algorithm is called A, and N = 13, then A(N) = A(13) returns 4, since 5+5+2+1 = 13 used the smallest (optimal) number of coins. In contrast, 5+5+1+1+1 is not an optimal answer. Draw the recursion tree for the algorithm where N = 7. Derive the complexity bound of the algorithm. Do not need to prove the complexity bound formally, just derive it by analyzing each component in your algorithm.
calculate number of operations in this algorithm void my_dgemv(int n, double* A, double* x, double* y) { double alpha=1.0, beta=1.0; int lda=n, incx=1, incy=1; cblas_dgemv(CblasRowMajor, CblasNoTrans, n, n, alpha, A, lda, x, incx, beta, y, incy); }
Artificial Intelligence (Part - 2) ==================== The Towers of Hanoi is a famous problem for studying recursion incomputer science and searching in artificial intelligence. We start with N discs of varying sizes on a peg (stacked in order according to size), and two empty pegs. We are allowed to move a disc from one peg to another, but we are never allowed to move a larger disc on top of a smaller disc. The goal is to move all the discs to the rightmost peg (see figure). To solve the problem by using search methods, we need first formulate the problem. Supposing there are K pegs and N disk. (2) What is the size of the state space?
Algorithm Binary Search Input: L = a1, a2, ... , an list of distinct integers; x integer Output: p integer i = 1; j = n; found = F; p = 0; while i ≤ j and found = F m = ⌊i+j2⌋; if am = x then found = T and p = m else if am < x then i = m + 1 else j = m - 1; return p; When performing Algorithm Binary Search with input L = 1,3,5,7,9,11,13 and x = 9, how many times is x compared to an element ai of the list L?
The algorithm of Euclid computes the greatest common divisor (GCD) of two integer numbers a and b. The following pseudo-code is the original version of this algorithm. Algorithm 1 Euclid1(a,b)Require: a, b > 0Ensure: a = GCD(a, b) while a ̸= b do if a > b then a ← a − b else b ← b − a end if end whilereturn a We want to prove the correctness of this algorithm using the loop invariant technique. Answer the following questions: a. Show the property is maintained during the execuation of the While loop (i.e., maintenance property). b. Prove the termination property and conclude. c. What would happen if a > 0 and b = 0 and thus the pre-condition is not satisfied?
The algorithm of Euclid computes the greatest common divisor (GCD) of two integer numbers a and b. The following pseudo-code is the original version of this algorithm. Algorithm 1 Euclid1(a,b)Require: a, b > 0Ensure: a = GCD(a, b) while a ̸= b do if a > b then a ← a − b else b ← b − a end if end whilereturn a We want to prove the correctness of this algorithm using the loop invariant technique. a. In a first attempt to prove the correctness of this algorithm, we propose the following loop invariant property: “GCD(a, b) is a factor of a and b”. Explain why this property willnot help you as is. b. Use your previous observation to propose another loop invariant property that willhelp you to prove the correctness of the version of Euclid’s algorithm presented above. c. Show that your loop invariant property is true before executing the While loop forthe first time (i.e., initialization property)
Q2. The following algorithm returns the product of two numbers, a and b. The parameters x and y are natural numbers. First, prove the correctness of the algorithm. Then, analyze the time complexity of the algorithm in the worst case scenario. function mult (a, b) if b = 0: return 0 else if b is odd: return (mult (2a, b/2 ) +a) else: return (mult (2a, b/2 ) )
Substitution Method
This function uses a curious mix of iteration and recursion: function F(n) if n < 1 t <- O return 1 for i <- 0 to n for j <- i to n t<- t+j return t + F(n-1) The number of basic operations (additions and subtractions) performed is: ○ O(n) Ⓒ (n²) (n² log n) Ⓒ (n³) Ө Ⓒ (n4)
Write the algorithm for the problem that works in constant space and time complexity. Input: N OUTPUT: 1 if Tom wins, 0 if Jerry wins.