Starting Out with Programming Logic and Design (5th Edition) (What's New in Computer Science)
5th Edition
ISBN: 9780134801155
Author: Tony Gaddis
Publisher: PEARSON
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Textbook Question
Chapter 13, Problem 2SA
In this chapter, the rules given for calculating the factorial of a number are as follows:
If n = 0 then factorial(n) = 1
If n > 0 then factorial(n) = n × factorial(n – 1)
If you were designing a module from these rules, what would the base case be? What would the recursive case be?
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In this chapter, the rules given for calculating the factorial of a number are as follows:If n = 0 then factorial(n) = 1If n . 0 then factorial(n) = n × factorial(n – 1)If you were designing a function from these rules, what would the base case be? What wouldthe recursive case be?
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) {
}
Task 1
Count the number of vowels in a phrase using recursion only. You can think of this problem as
"I can count the number of vowels in this phrase by counting the number of vowels in the first
character, then counting the number of vowels in the rest of the phrase." We define a vowel as
being A, E, I, O or U.
This is one of those problems that can just as easily be solved with traditional programming
structures such as a loop - but we're asking you to use recursion for the exercise.
Consider: what replaces the loop structure? When will we stop recursion?
Task 2
The constant e (Euler's number) is approximated by the following sequence:
1₁
n!
where the number of terms in the sequence is sufficient to generate the required precision in
decimal places.
1+
2!
+
...
We say that there is some value epsilon (e) such that, when the change in the approximation
from one term to the next is less than said epsilon, we have reached sufficient precision. That
is, when the term you're proposing to…
Chapter 13 Solutions
Starting Out with Programming Logic and Design (5th Edition) (What's New in Computer Science)
Ch. 13.2 - It is said that a recursive algorithm has more...Ch. 13.2 - Prob. 13.2CPCh. 13.2 - What is a recursive case?Ch. 13.2 - What causes a recursive algorithm to stop calling...Ch. 13.2 - What is direct recursion? What is indirect...Ch. 13 - Prob. 1MCCh. 13 - A module is called once from a programs main...Ch. 13 - The part of a problem that can be solved without...Ch. 13 - Prob. 4MCCh. 13 - Prob. 5MC
Ch. 13 - Prob. 6MCCh. 13 - Any problem that can be solved recursively can...Ch. 13 - Actions taken by the computer when a module is...Ch. 13 - A recursive algorithm must _______ in the...Ch. 13 - A recursive algorithm must _____ in the base case....Ch. 13 - An algorithm that uses a loop will usually run...Ch. 13 - Some problems can be solved through recursion...Ch. 13 - It is not necessary to have a base case in all...Ch. 13 - In the base case, a recursive method calls itself...Ch. 13 - In Program 13-2, presented earlier in this...Ch. 13 - In this chapter, the rules given for calculating...Ch. 13 - Is recursion ever required to solve a problem?...Ch. 13 - When recursion is used to solve a problem, why...Ch. 13 - How is a problem usually reduced with a recursive...Ch. 13 - What will the following program display? Module...Ch. 13 - What will the following program display? Module...Ch. 13 - The following module uses a loop. Rewrite it as a...Ch. 13 - Prob. 1PECh. 13 - Prob. 2PECh. 13 - Recursive Array Sum Design a function that accepts...Ch. 13 - Prob. 4PECh. 13 - Prob. 5PECh. 13 - Ackermanns Function 7. Ackermanns Function is a...
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