Question

In: Computer Science

Determine if each of the following recursive definition is a valid recursive definition of a function...

  1. Determine if each of the following recursive definition is a valid recursive definition of a function f from a set of non-negative integers. If f is well defined, find a formula for f(n) where n is non-negative and prove that your formula is valid.

    1. f(0) = 1, f(n) = -f(n-1) + 1 for n ≥ 1

    2. f(0) = 0, f(1) = 1, f(n) = 2f(n-1) +1 for n ≥ 1

    3. f(0) =0, f(n) = 2f(n-1) + 2 for n ≥ 1

Solutions

Expert Solution

Here goes the proof for all parts:

venereology answered 1 year ago
Next > < Previous

Related Solutions

Determine whether each of these proposed definitions is a valid recursive definition of a function f...
Determine whether each of these proposed definitions is a valid recursive definition of a function f from the set of nonnegative integers to the set of integers. If f is well defined, find a formula for f (n) when n is a nonnegative integer and prove that your formula is valid. e) f (0) = 2, f (n) = f (n − 1) if n is odd and n ≥ 1 and f (n) = 2f (n − 2) if...
Determine whether each of these proposed definitions is a valid recursive definition of a function f...
Determine whether each of these proposed definitions is a valid recursive definition of a function f from the set of nonnegative integers to the set of integers. If f is well defined, find a formula for f(n) when n is a nonnegative integer and prove that your formula is valid. a) f(0) = 1, f(n) = -f(n-1) for n ≥ 1 b) f(0) = 1, f(1) = 0, f(2) = 2, (n) = f(n-3) for n ≥ 3. c) f(0)...
Part 1: Write a recursive function that will calculate Fibonacci numbers using a recursive definition. Write...
Part 1: Write a recursive function that will calculate Fibonacci numbers using a recursive definition. Write a short program to test it. The input of this program must be a positive integer n; the output is the corresponding Fibonacci number F(n) Part 2: Write an iterative function to calculate Fibonacci numbers. Write a test driver for it. The input of this program must be a positive integer n; the output is the corresponding Fibonacci number F(n). Part 3: Write a...
Given the following definition of the LNode class, implement the non-recursive method saveCountinLastNode and the recursive...
Given the following definition of the LNode class, implement the non-recursive method saveCountinLastNode and the recursive method addOddNodes for the LinkedList class which represents singly linked lists. public class LNode { private int m_info; private LNode m_link; public LNode(int info){ m_info = info; m_link = null; } public void setLink(LNode link){ m_link = link; } public LNode getLink(){   return m_link; } public void setInfo(int info){ m_info = info; } public int getInfo(){   return m_info; } } public class LinkedList {...
Determine each of the following arguments’ forms to be valid or invalid. You may use the...
Determine each of the following arguments’ forms to be valid or invalid. You may use the Venn Diagram proof method, the rules/fallacies method, or any other method, of your choice. 1. Some athletes are not baseball players and some baseball players are not basketball players. Therefore, some athletes are not basketball players.2. All creationists are fundamentalists because all fundamentalists are religious people and all creationists are religious people. 3. As no conservationists are litterers, no environmentalists are litterers, because all...
Consider the following Python function definition and determine what value will be returned by the 24....
Consider the following Python function definition and determine what value will be returned by the 24. function call that follows. def calculate(value, src): result = 0 val_string = str(value) size = len(val_string) mult = src ** (size - 1) for digit in val_string: d = int(digit) result += d * mult mult = mult // src return result calculate(93, 2)
(4) Determine if the following logical statement is valid. First convert each statement to a symbolic...
(4) Determine if the following logical statement is valid. First convert each statement to a symbolic logic, and then create a truth table. Don’t forget you need to state if the statement is valid or not and state why. Prop A. Steve can exclusively either Study or Sleep. Prop B. If Steve studies, then he’ll Pass his Exam. Conclusion: If Steve Sleeps, then he’ll NOT Pass his Exam.
Provide a recursive definition of some sequence of numbers or function (e.g. log, exponent, polynomial). Choose...
Provide a recursive definition of some sequence of numbers or function (e.g. log, exponent, polynomial). Choose one different from that of any posted thus far. Write a recursive method that given n, computes the nth term of that sequence. Also provide an equivalent iterative implementation. How do the two implementations compare?
Fill in the blanks in each of the following statements: 1. Each function definition can specify...
Fill in the blanks in each of the following statements: 1. Each function definition can specify __________________ that represent additional information the function requires to perform its task correctly. 2. Declaring data members with access modifier __________________ is known as information hiding. 3. The initial value of a string is the __________________which does not contain any characters. 4. Variables declared in the body of a particular function are known as __________________and can be used only in that function. 5. Each...
/** * Write a recursive function that accepts a stack of integers and * replaces each...
/** * Write a recursive function that accepts a stack of integers and * replaces each int with two copies of that integer. For example, * calling repeatStack and passing in a stack of { 1, 2, 3} would change * the stack to hold { 1, 1, 2, 2, 3, 3}. Do not use any loops. Do not use * any data structures other than the stack passed in as a parameter. * @param stack */ public static void...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT