Question: Consider the following algorithm, where f ( n ) : n 2 3 n + 2 . Input: n in Z . ( 1 )

Consider the following algorithm, where f (n) : n23n +2.
Input: n in Z.
(1) If f (n)=0, output n and stop. Otherwise, go to step (2).
(2) Replace n by f (n)%5 and go back to step (1).
Prove that this algorithm terminates for every choice of input.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

Q:

6. (2 points) Consider the following algorithm. ALGORITHM Enigma(A[0.. n - 1, 0.. n - 1]) //Input: A matrix A[0..n - 1, 0..n - 1] of real numbers for i0 ton - 2 do for ji+1 ton - 1 do if A[i, j] A[j,...

Q:

WRITE A C PROGRAM FOR THE FOLLOWING: Problems in Computer Science are often classified as belonging to a certain class of problems (e.g., NP, Unsolvable, Recursive). In this problem you will be...

Q:

Use Pseudo Code for #2 and Master Theroem for #5!! Questions 1. Let T(n) be a running time function defined recursively as 0, T(n) -1, n=0 n-1 3T (n 1)- 2T(n-2), n> 1 a. Find a non-recursive formula...

Q:

resolve the following problem and show the work step by step Consider the following algorithm Procedure quizzy (n : integer) t:= 0 for i : = 1 to n - 2 j := n while j # 1 t : = tti+j j := [3] return...

Q:

Consider the following Algorithm: ALGORITHM P (n) //Input a positive integer n i1j0fork1tondoji+jijireturnj 1. a) What does this algorithm return when n=1,n=2,n=5 ? 2. b) What is its basic operation?...

Q:

3. (15 marks) Consider the following algorithm: Algorithm FactorSum(A, n): 2 Input: Array A of n real numbers. SEO for it 0 to n - 1 for j - i to n - 1 P+1 for kt i to j P + P x A[k] S+S+P return S...

Q:

1) Consider the following algorithm. // Assume that n is a positive integer (= i.e. n > 1), and A[1..n] is a global array . // Note that the index of array A starts from one, not zero. // And also,...

Q:

12. (10 points) Consider the following algorithm. // Assume that n is a positive integer (=i.e. n > 1), and A[1..n] is a global array. // Note that the index of array A starts from one, not zero. //...

Q:

8. Consider the following algorithm and answer the questions. (10%) ALGORITHM Yn) // Input: n is a positive integer if n=1 return 1 else return Y (n 1)+n*n 1. What does this algorithm compute? 2....

Q:

APStatistics 4.01 Transforming Data Directions: Complete the assignment. Clearly label each answer. The last page contains a table of common transformations. (27 points) 1. Consider the following set...

Q:

? Given the input matrix and the final-demand vector [0.2 0.3 0.21 0.4 0.1 0.2 d L0.1 0.3 0.21 A = 0.4 i) ii) iii) iv) v) vi) = [10] 5 6 Explain the economic meaning of the elements 0.4 and 10....

Q:

Find all solutions of the following differential equations: (d) 3y'+y=2e ** eix (e) y+3y=

Q:

does sarasota use an actual costing system or a normal costing system

Q:

CT Corp Comprehensive Question Canadian Tire Corporation, Limited ( Canadian Tire ) is a family of companies that includes a retail segment and a financial services division, among others. The retail...

Q:

Technology. Use the spell-check feature of your word processing program to check for errors in the following paragraph. Compare the results with errors you find as you proofread the text. (Objective...

Q:

In conjunction with the launch of a new program of study, your school will host an open house on the second Tuesday of next month. You have been asked to announce the event to the students in your...

Q:

Teamwork. Technology. Form a four-person group consisting of two subgroups. Each subgroup will find an appropriate substitute for the words in the following list. One subgroup will use a traditional...