Java: An Introduction to Problem Solving and Programming (8th Edition)
8th Edition
ISBN: 9780134462035
Author: Walter Savitch
Publisher: PEARSON
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Chapter 11, Problem 3P
One of the most common examples of recursion is an
0! is equal to 1
1! is equal to 1
21 is equal to 2 × 1 = 2
3! is equal to 3 × 2 × 1 = 6
4! is equal to 4 × 3 × 2 × 1 = 24
…
n! is equal to n × (n - 1) × (n- 2) × … × 3 × 2 × 1
An alternative way to describe the calculation of n! is the recursive formula n × (n−1)!, plus a base case of 0!, which is 1. Write a static method that implements this recursive formula for factorials. Place the method in a test
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One of the most common examples of recursion is an algorithm to calculate the factorial of an integer. The notation n! is used for the factorial ofthe integer n and is defined as follows:0! is equal to 11! is equal to 12! is equal to 2 × 1 = 23! is equal to 3 × 2 × 1 = 6
JAVA LANGUAGE
The first examples of recursion are the mathematical functions factorial and fibonacci. These functions are defined for non-negative integers using the following recursive formulas:factorial(0) = 1factorial(N) = N*factorial(N-1) for N > 0fibonacci(0) = 1fibonacci(1) = 1fibonacci(N) = fibonacci(N-1) + fibonacci(N-2) for N > 1Write recursive functions to compute factorial(N) and fibonacci(N) for a given non-negative integer N, and write a main() routine to test your functions.(In fact, factorial and fibonacci are really not very good examples of recursion, since the most natural way to compute them is to use simple for loops. Furthermore, fibonacci is a particularly bad example, since the natural recursive approach to computing this function is extremely inefficient.) JAVA LANGUAGE
Recursion is an approach in which the solution to a particular problem depends on solutions
to same size instances of the same problem.
Select one:
O True
O False
Chapter 11 Solutions
Java: An Introduction to Problem Solving and Programming (8th Edition)
Ch. 11.1 - What output will be produced by the following...Ch. 11.1 - What is the output produced by the following code?Ch. 11.1 - Write a recursive definition for the following...Ch. 11.1 - What is the output of the following code? public...Ch. 11.1 - Prob. 5STQCh. 11.1 - Complete the definition of the following method....Ch. 11.2 - Revise the method getCount in Listing 11.5 so that...Ch. 11.2 - Prob. 8STQCh. 11.2 - Prob. 9STQCh. 11.2 - Suppose you want me class ArraySearcher to work...
Ch. 11.2 - What Java statement will sort the following array,...Ch. 11.2 - How would you change the class MergeSort so that...Ch. 11.2 - How would you change the class MergeSort so that...Ch. 11.2 - If a value in an array of base type int occurs...Ch. 11.3 - Convert the following event handler to use the...Ch. 11 - What output will be produced by the following...Ch. 11 - What output will be produced by the following...Ch. 11 - Write a recursive method that will compute the...Ch. 11 - Write a recursive method that will compute the sum...Ch. 11 - Complete a recursive definition of the following...Ch. 11 - Write a recursive method that will compute the sum...Ch. 11 - Write a recursive method that will find and return...Ch. 11 - Prob. 8ECh. 11 - Write a recursive method that will compute...Ch. 11 - Suppose we want to compute the amount of money in...Ch. 11 - Prob. 11ECh. 11 - Write a recursive method that will count the...Ch. 11 - Write a recursive method that will remove all the...Ch. 11 - Write a recursive method that will duplicate each...Ch. 11 - Write a recursive method that will reverse the...Ch. 11 - Write a static recursive method that returns the...Ch. 11 - Write a static recursive method that returns the...Ch. 11 - One of the most common examples of recursion is an...Ch. 11 - A common example of a recursive formula is one to...Ch. 11 - A palindrome is a string that reads the same...Ch. 11 - A geometric progression is defined as the product...Ch. 11 - The Fibonacci sequence occurs frequently in nature...Ch. 11 - Prob. 4PPCh. 11 - Once upon a time in a kingdom far away, the king...Ch. 11 - There are n people in a room, where n is an...Ch. 11 - Prob. 7PPCh. 11 - Prob. 10PPCh. 11 - Prob. 12PP
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- The “odd/even factorial” of a positive integer n is represented as n!! and is defined recursively as: a. (n)*(n-2)*(n-4)………*(2) if n is even. For example, 6!! = 6*4*2 = 48 b. (n)*(n-2)*(n-4)*…….*(5)*(3)*(1) if n is odd. For example, 7!! = 7*5*3*1 = 105. Come up with a recursive definition for n!! and use it to guide you to write a method definition for a method called “oddevenfact” that recursively calculates the odd/even factorial value of its single int parameter. The value returned by “oddevenfact” is a long.arrow_forwardPython implements Newton's algorithm for finding the square root of a number using recursion NOTE: n = 17 # we want the square root of 17 for exampleg = 4 # our guess is 4 initiallyerror = 0.0000000001 # we want to stop when we are this closewhile abs(n - (g**2)) > error: g = g - ((g**2 - n)/(2 * g))# g holds the square root of n at this point Implement this algorithm in a function sqRoot(n), that returns the square root using recursion your code to return the square root of n to an accuracy within the error e,using Newton's algorithm with an initial guess of g def sqRoot(n, g, e):arrow_forwardComplete the following recursive method for computing the factorial of an integer. Assume that n is greater than or equal to 0. a. result = n * factorial(n - 1)b. result = n * factorial(n)c. result = factorial(n - 1)d. result = (n - 1) * factorial(n)e. result = (n - 1) * factorial(n - 1)arrow_forward
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- The first examples of recursion are the mathematical functions factorial and fibonacci. These functions are defined for non-negative integers using the following recursive formulas:factorial(0) = 1factorial(N) = N*factorial(N-1) for N > 0fibonacci(0) = 1fibonacci(1) = 1fibonacci(N) = fibonacci(N-1) + fibonacci(N-2) for N > 1Write recursive functions to compute factorial(N) and fibonacci(N) for a given non-negative integer N, and write a main() routine to test your functions.(In fact, factorial and fibonacci are really not very good examples of recursion, since the most natural way to compute them is to use simple for loops. Furthermore, fibonacci is a particularly bad example, since the natural recursive approach to computing this function is extremely inefficient.)arrow_forwardUsing recursion, write a program that tells whether a number is palindrome or notarrow_forwardPython Using recursion only No loops Note that in a correct solution the isdigit method or in operator will never be applied to the entire string s. The function must return and not print the resulting string. def getDigits(s):arrow_forward
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