Problem Solving with C++ (10th Edition)
10th Edition
ISBN: 9780134448282
Author: Walter Savitch, Kenrick Mock
Publisher: PEARSON
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Textbook Question
Chapter 14.1, Problem 11STE
Trace the recursive solution you made to Self-Test Exercise 5.
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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…
1. 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.
Is the recursive solution to the triangle number the best way to obtain the triangle number?
A.
Yes, because recursive solutions are always efficient.
B.
Yes, because the shape of the triangle number diagram lends itself to a recursive solution.
C.
No, the triangle number can be found in a more efficient manner.
D.
None of the above are true.
Chapter 14 Solutions
Problem Solving with C++ (10th Edition)
Ch. 14.1 - Prob. 1STECh. 14.1 - Prob. 2STECh. 14.1 - Prob. 3STECh. 14.1 - Prob. 4STECh. 14.1 - Prob. 5STECh. 14.1 - If your program produces an error message that...Ch. 14.1 - Write an iterative version of the function cheers...Ch. 14.1 - Write an iterative version of the function defined...Ch. 14.1 - Prob. 9STECh. 14.1 - Trace the recursive solution you made to Self-Test...
Ch. 14.1 - Trace the recursive solution you made to Self-Test...Ch. 14.2 - What is the output of the following program?...Ch. 14.2 - Prob. 13STECh. 14.2 - Redefine the function power so that it also works...Ch. 14.3 - Prob. 15STECh. 14.3 - Write an iterative version of the one-argument...Ch. 14 - Prob. 1PCh. 14 - Prob. 2PCh. 14 - Write a recursive version of the search function...Ch. 14 - Prob. 4PCh. 14 - Prob. 5PCh. 14 - The formula for computing the number of ways of...Ch. 14 - Write a recursive function that has an argument...Ch. 14 - Prob. 3PPCh. 14 - Prob. 4PPCh. 14 - Prob. 5PPCh. 14 - The game of Jump It consists of a board with n...Ch. 14 - Prob. 7PPCh. 14 - Prob. 8PP
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- Indirect recursion is when function A calls function B, which in turn calls function A. is it true or false.arrow_forwardCheck recursively if the following objects are palindromes: a word a sentence (ignoring blanks, lower- and uppercase differences, and punctuation marks so that “Madam, I’m Adam” is accepted as a palindrome)arrow_forwardWrite a recursive function for int powerOfTwo (int k). The function determines the value of 2k. (Note: k is a positive integer). Example, when k=0 the function returns 1 and when k-3 the function returns 8. To show that your code is correct, give the recursive trace for powerOfTwo (2) that returns 4.arrow_forward
- Help me in recursion. Your task is to print I am coder using recursion for 7 times In elixir programming languagearrow_forwardIn what instances do you think it’s impractical to use recursion over loops?arrow_forwardOne-friend recursion vs iteration. 1. Your objective is to receive the tuple a1, a2,..., a and return the tuple an, an1,..., a1 that has been inverted. You will only take an element off of one end or put an element back on one end because you are being lazy. But you have friends in recursion who can assist you.Please provide the recursive code as well as a paragraph with the friend's description of the algorithm.2. Now imagine that you lack friends but have a stack. Quickly design an iterative programme to address this issue. Include loop invariants and other crucial stages that are necessary to describe an iterative method.3. Trace both of these scripts separately. On a computer, step by step compare and contrast their calculations.arrow_forward
- Which of the following is/are true regarding the characteristics of recursion? a.Every recursive call reduces the original problem, bringing it increasingly closer to a base case until it becomes that case. b.Recursive method requires less memory than an iterative method. c. It is possible to convert every recursive method to an iterative method. d.The method is implemented using an if-else or a switch statement that leads to different cases. e.One or more base cases are used to stop recursion.arrow_forwardExplain the meaning of the recursion with a simple examplearrow_forwardWrite a recursive version of the function reverse(s), which reverses thestring s in place.arrow_forward
- Pascal's triangle is a useful recursive definition that tells us the coefficients in the expansion of the polynomial (x + a)^n. Each element in the triangle has a coordinate, given by the row it is on and its position in the row (which you could call a column). Every number in Pascals triangle is defined as the sum of the item above it and the item above it and to the left. If there is a position that does not have an entry, we treat it as if we had a 0 there. *picture of the pascals triangle* Given the following recursive function signature, write the recursive function that takes a row and a column and finds the value at that position in the triangle. Assume that the triangle starts at row 0 and column 0. Examples: pascal(2, 1) -> 2, pascal(1, 2) -> 0 public int pascal(int row, int column) { }arrow_forwardWhen recursion is used to solve a problem, why must the recursive method call itself to solve a smaller version of the original problem?arrow_forward1. Let product(n,m) be a recursive method that computes the product of two positive integers, using only addition and subtraction. To make this method a recursive one, you are to make a) a base case when m = 1, b) a general case when m ≠ 1. For a general case, the return value should be n plus the result of a recursive call to the method product() with parameters n and m - 1. Write a short Java code for this method, along with a test program.arrow_forward
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