Starting Out with Java: From Control Structures through Data Structures (4th Edition) (What's New in Computer Science)
4th Edition
ISBN: 9780134787961
Author: Tony Gaddis, Godfrey Muganda
Publisher: PEARSON
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Chapter 15, Problem 7SA
How is a problem usually reduced with a recursive method?
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what is a recursive solution to a 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) {
}
Java language
Write a recursive method to add all of the odd numbers between two numbers (start and end) and return the result. The method receives these numbers as parameters.
Chapter 15 Solutions
Starting Out with Java: From Control Structures through Data Structures (4th Edition) (What's New in Computer Science)
Ch. 15.2 - It is said that a recursive algorithm has more...Ch. 15.2 - Prob. 15.2CPCh. 15.2 - What is a recursive case?Ch. 15.2 - What causes a recursive algorithm to stop calling...Ch. 15.2 - What is direct recursion? What is indirect...Ch. 15 - Prob. 1MCCh. 15 - This is the part of a problem that can be solved...Ch. 15 - This is the part of a problem that is solved with...Ch. 15 - This is when a method explicitly calls itself. a....Ch. 15 - Prob. 5MC
Ch. 15 - Prob. 6MCCh. 15 - True or False: An iterative algorithm will usually...Ch. 15 - True or False: Some problems can be solved through...Ch. 15 - True or False: It is not necessary to have a base...Ch. 15 - True or False: In the base case, a recursive...Ch. 15 - Find the error in the following program: public...Ch. 15 - Prob. 1AWCh. 15 - Prob. 2AWCh. 15 - What will the following program display? public...Ch. 15 - Prob. 4AWCh. 15 - What will the following program display? public...Ch. 15 - Convert the following iterative method to one that...Ch. 15 - Write an iterative version (using a loop instead...Ch. 15 - What is the difference between an iterative...Ch. 15 - What is a recursive algorithms base case? What is...Ch. 15 - What is the base case of each of the recursive...Ch. 15 - What type of recursive method do you think would...Ch. 15 - Which repetition approach is less efficient: a...Ch. 15 - When recursion is used to solve a problem, why...Ch. 15 - How is a problem usually reduced with a recursive...Ch. 15 - Prob. 1PCCh. 15 - isMember Method Write a recursive boolean method...Ch. 15 - String Reverser Write a recursive method that...Ch. 15 - maxElement Method Write a method named maxElement,...Ch. 15 - Palindrome Detector A palindrome is any word,...Ch. 15 - Character Counter Write a method that uses...Ch. 15 - Recursive Power Method Write a method that uses...Ch. 15 - Sum of Numbers Write a method that accepts an...Ch. 15 - Ackermarms Function Ackermanns function is a...Ch. 15 - Recursive Population Class In Programming...
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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_forwardJava programming language Write a recursion method to sum the odd numbers a) from 100 to 0 b) from 0 to 100 and then test it.arrow_forwardThe part of a problem that is solved with recursion is the case.a. baseb. iterativec. unknownd. recursivearrow_forward
- Recursion is the best and the fastest way to solve any problem.True or Falsearrow_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_forwardWhat is the difference between direct and indirect recursion?arrow_forward
- What are the conditions under which a recursive algorithm will stop calling itself?arrow_forward1. What is the difference between an iterative algorithm and a recursive algorithm? 2. What is a recursive algorithm’s base case? What is the recursive case? 3. What is the base case of each of the recursive methods listed in Algorithm Workbench 3, 4, and 5? 4. What type of recursive method do you think would be more difficult to debug: one that uses direct recursion or one that uses indirect recursion? Why? 5. Which repetition approach is less efficient: a loop or a recursive method? Why? 6. When recursion is used to solve a problem, why must the recursive method call itself to solve a smaller version of the original problem? 7. How is a problem usually reduced with a recursive method?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_forward
- Recursion in programming is described as when a function/method makes a direct or indirect call to itself. Which of the features is not valid for a recursive function. Select one: a. The Recursive calls can be more then one b. The Recursive Call – the function calls itself with an input which is a step closer to the stop condition c. The Stoping Conditions can be more than one d. The Recursive call is optional. e. A Stop Condition – the function returns a value when a certain condition is satisfied, without a further recursive callarrow_forwardRecursive functions are ones that repeat themselves repeatedly.arrow_forwardHow does the concept of recursion work in computer programming?arrow_forward
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