Starting Out with Java: From Control Structures through Objects (6th Edition)
6th Edition
ISBN: 9780133957051
Author: Tony Gaddis
Publisher: PEARSON
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Textbook Question
Chapter 16, Problem 7AW
Write an iterative version (using a loop instead of recursion) of the factorial method shown in this chapter.
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Write a recursive method that returns the value of N! (N factorial) using the definition given in this chapter. Explain why you would not normally use recursion to solve this problem.
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…
This program has a bug that leads to infinite recursion. Modify fn(int x, int y) method to fix the problem.
Manually trace the recursive call, fn(2,3) and show the output (step by step).
Can you identify the Base Case in recursive method fn(int x, int y)?
Chapter 16 Solutions
Starting Out with Java: From Control Structures through Objects (6th Edition)
Ch. 16.2 - It is said that a recursive algorithm has more...Ch. 16.2 - Prob. 16.2CPCh. 16.2 - What is a recursive case?Ch. 16.2 - What causes a recursive algorithm to stop calling...Ch. 16.2 - What is direct recursion? What is indirect...Ch. 16 - Prob. 1MCCh. 16 - This is the part of a problem that can be solved...Ch. 16 - This is the part of a problem that is solved with...Ch. 16 - This is when a method explicitly calls itself. a....Ch. 16 - Prob. 5MC
Ch. 16 - Prob. 6MCCh. 16 - True or False: An iterative algorithm will usually...Ch. 16 - True or False: Some problems can be solved through...Ch. 16 - True or False: It is not necessary to have a base...Ch. 16 - True or False: In the base case, a recursive...Ch. 16 - Find the error in the following program: public...Ch. 16 - Prob. 1AWCh. 16 - Prob. 2AWCh. 16 - What will the following program display? public...Ch. 16 - Prob. 4AWCh. 16 - What will the following program display? public...Ch. 16 - Convert the following iterative method to one that...Ch. 16 - Write an iterative version (using a loop instead...Ch. 16 - What is the difference between an iterative...Ch. 16 - What is a recursive algorithms base case? What is...Ch. 16 - What is the base case of each of the recursive...Ch. 16 - What type of recursive method do you think would...Ch. 16 - Which repetition approach is less efficient: a...Ch. 16 - When recursion is used to solve a problem, why...Ch. 16 - How is a problem usually reduced with a recursive...Ch. 16 - Prob. 1PCCh. 16 - isMember Method Write a recursive boolean method...Ch. 16 - String Reverser Write a recursive method that...Ch. 16 - maxElement Method Write a method named maxElement,...Ch. 16 - Palindrome Detector A palindrome is any word,...Ch. 16 - Character Counter Write a method that uses...Ch. 16 - Recursive Power Method Write a method that uses...Ch. 16 - Sum of Numbers Write a method that accepts an...Ch. 16 - Ackermarms Function Ackermanns function is a...Ch. 16 - Recursive Population Class In Programming...
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- Write a recursive method to reverse a string. Explain why you would not normally use recursion to solve this problem.arrow_forwardFlip a fair coin repeatedly until you get two heads in a row (HH). What is the probability of getting HH in at-most N (N > 1) tosses? Can you write a recursive function and implementation to calculate the probability?arrow_forwardJAVA: Rewrite the following recursive method using an iterative approach with a while loop.arrow_forward
- Write a recursive method that will compute the number of even digits in anumber.arrow_forwardplease code in python Here is another recursion example, but with less guidance. Write a function log2(x), which gives an integer approximation of the log base 2 of a positive number x, but it does so using recursion. Use a base case where you return 0 if x is 1 or less. In the general case, add 1 to the answer and divide x by 2. (This is purposely vague so you can figure it out yourself.)arrow_forwardImplement the The triangle.cpp Program.This program uses recursion to calculate triangular numbers. Enter a value for the term number, n, and the program will display the value of the corresponding triangular number.arrow_forward
- Given the sequence, S2 = 1, 2, 4, 5, 7, 8, 10, 11, 13, 14, … Write a RECURSIVE method called “sequence2” that takes a single int parameter (n) and returns the int value of the nth element of the sequence S2. You will need to determine any base cases and a recursive case that describes the listed sequence. Use the following code to test your answers to questions 3 and 4the output should print the two sequences given (S & S2): public class TestSequences { public static void main(String[] args) { for(int i = 0; i < 10; i++) { System.out.print(sequence(i) + " "); // 2, 4, 6, 12, 22, 40, 74, 136, 250, 460 } System.out.println(); for(int i = 0; i < 10; i++) { System.out.print(sequence2(i) + " "); // 1, 2, 4, 5, 7, 8, 10, 11, 13, 14 } } // *** Your method for sequence here *** // *** Your method for sequences2 here *** } // end of TestSequences classarrow_forwardHelp me in recursion. Your task is to print I am coder using recursion for 7 times In elixir programming languagearrow_forwardWrite a recursive solution to the problem below. You MUST use only one method, and that method must have the provided method header. You are allowed to use loops, but you must also use recursion. Given a word of length n, print every possible word of length n that can be made with those characters. Note: The order of the output does not matter, only that all possibilities are listed. Example: Input: rot Output: rot, rto, otr, ort, tro, tor Input: frog Output: frog, frgo, fogr, forg, fgro, fgor, rogf, rofg, rgfo, rgof, rfog, rfgo, ogfr, ogrf, ofrg, ofgr, orgf, orfg, gfro, gfor, grof, grfo, gofr, gorf public void printAllPossibilities (String prefix, String suffix){ }arrow_forward
- Write a recursive implementation of Euclid’s algorithm for finding the greatest common divisor (GCD) of two integers. Descriptions of this algorithm are available in algebra books and on the Web. Write a test program that calls your GCD procedure five times, using the following pairs of integers: (5,20), (24,18), (11,7), (432,226), (26,13). After each procedure call, display the GCD.arrow_forward1. Let product(n,m) be a recursive addition-subtraction method for multiplying two positive integers. Recursive cases for m = 1 and m < 1 make this method. The return value should be n plus a recursive product() call with n and m - 1. Test a Java method.arrow_forwardApply Recursion Method and show the full calculationarrow_forward
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