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 4SA
When recursion is used to solve a problem, why must the recursive module call itself to solve a smaller version of the original problem?
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When recursion is used to solve a problem, why must the recursive method call itself to solve a smaller version of the original problem?
Why does the recursive function that uses recursion to solve a problem have to call itself in order to resolve a smaller version of the original problem?
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) {
}
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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- How does a recursion function's repeated calls to itself be controlled? Which control structure is employed?arrow_forwardwhat do you understand by recursion?arrow_forwardRecursive Syntax The recursive structure i.e of natural language like English can be expressed in syntax rules written in the format known as BNF (Bachus-Naur Form). While BNF is ordinarily used as a guide for parsing (that is, determining whether and how a given string follows the syntax rules), An example of this can be found in the sample program SimpleRandomSentences. You should write a similar program that implements the following rules:<sentence> ::= <simple_sentence> [ <conjunction> <sentence> ]<simple_sentence> ::= <noun_phrase> <verb_phrase><noun_phrase> ::= <proper_noun> |<determiner> [ <adjective> ]. <common_noun> [ who <verb_phrase> ]<verb_phrase> ::= <intransitive_verb> |<transitive_verb> <noun_phrase> |is <adjective> |believes that <simple_sentence><conjunction> ::= and | or | but | because<proper_noun> ::= Fred | Jane | Richard Nixon | Miss…arrow_forward
- Why, when using recursion to solve a problem, does the recursive function have to call itself in order to solve a smaller version of the original problem?arrow_forwardIn a recursive algorithm, the goal is to solve a problem by breaking it into smaller sub-problems to solve. This is accomplished by constructing an algorithm using two important components. What are these components, what is the purpose of each?arrow_forwardHow is it controlled that a recursion function be called several times? What kind of command and control structure is employed in this case?arrow_forward
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