Starting Out with Python (4th Edition)
4th Edition
ISBN: 9780134444321
Author: Tony Gaddis
Publisher: PEARSON
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Textbook Question
Chapter 12, Problem 3SA
Is recursion ever required to solve a problem? What other approach can you use to solve a problem that is repetitive in nature?
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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?
Recursion is the best and the fastest way to solve any problem.True or False
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 12 Solutions
Starting Out with Python (4th Edition)
Ch. 12.2 - It is said that a recursive algorithm has more...Ch. 12.2 - Prob. 2CPCh. 12.2 - What is a recursive case?Ch. 12.2 - What causes a recursive algorithm to stop calling...Ch. 12.2 - What is direct recursion? What is indirect...Ch. 12 - Prob. 1MCCh. 12 - A function is called once from a program's main...Ch. 12 - Prob. 3MCCh. 12 - Prob. 4MCCh. 12 - Prob. 5MC
Ch. 12 - Prob. 6MCCh. 12 - Any problem that can be solved recursively can...Ch. 12 - Actions taken by the computer when a function is...Ch. 12 - A recursive algorithm must _______ in the...Ch. 12 - A recursive algorithm must ______ in the base...Ch. 12 - An algorithm that uses a loop will usually run...Ch. 12 - Some problems can be solved through recursion...Ch. 12 - It is not necessary to have a base case in all...Ch. 12 - In the base case, a recursive method calls itself...Ch. 12 - In Program 12-2 , presented earlier in this...Ch. 12 - In this chapter, the rules given for calculating...Ch. 12 - Is recursion ever required to solve a problem?...Ch. 12 - When recursion is used to solve a problem, why...Ch. 12 - How is a problem usually reduced with a recursive...Ch. 12 - What will the following program display? def...Ch. 12 - Prob. 2AWCh. 12 - The following function uses a loop. Rewrite it as...Ch. 12 - Prob. 1PECh. 12 - Prob. 2PECh. 12 - Prob. 3PECh. 12 - Largest List Item Design a function that accepts a...Ch. 12 - Recursive List Sum Design a function that accepts...Ch. 12 - Prob. 6PECh. 12 - Prob. 7PECh. 12 - Ackermann's Function Ackermann's Function is a...
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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…arrow_forwardThe part of a problem that is solved with recursion is the case.a. baseb. iterativec. unknownd. recursivearrow_forwardIndirect recursion is when function A calls function B, which in turn calls function A. is it true or false.arrow_forward
- what is a recursive solution to a problem?arrow_forwardHelp me in recursion. Your task is to print I am coder using recursion for 7 times In elixir programming languagearrow_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_forward
- Any problem that can be solved recursively can also be solved with a .arrow_forwardWhy 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?arrow_forwardWhy, 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_forward
- 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.arrow_forwardWhen recursion is used to solve a problem, why must the recursive function call itself to solve asmaller version of the original problem?arrow_forwardIn order to accomplish the task of terminating recursion, you must first describe three distinct types of recursion, a high-level description of each kind, and a specific technique that fits into each category.arrow_forward
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