Data Structures and Algorithms in Java
6th Edition
ISBN: 9781118771334
Author: Michael T. Goodrich
Publisher: WILEY
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Chapter 5, Problem 16C
In the Towers of Hanoi puzzle, we are given a platform with three pegs, a, b, and c, sticking out of it. On peg a is a stack of n disks, each larger than the next, so that the smallest is on the top and the largest is on the bottom. The puzzle is to move all the disks from peg a to peg c, moving one disk at a time, so that we never place a larger disk on top of a smaller one. See Figure 5.15 for an example of the case n =4. Describe a recursive
Figure 5.15: An illustration of the Towers of Hanoi puzzle.
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In computer science and mathematics, the Josephus Problem (or Josephus permutation) is a theoretical problem. Following is the problem statement: There are n people standing in a circle waiting to be executed. The counting out begins at some point (rear) in the circle and proceeds around the circle in a fixed direction. In each step, a certain number (k) of people are skipped and the next person is executed. The elimination proceeds around the circle (which is becoming smaller and smaller as the executed people are removed), until only the last person remains, who is given freedom. Given the total number of persons n and a number k which indicates that k-1 persons are skipped and kth person is killed in circle. The task is to choose the place in the initial circle so that you are the last one remaining and so survive. For example, if n = 5 and k = 2, then the safe position is 3. Firstly, the person at position 2 is killed, then person at position 4 is killed, then person at position 1…
Consider a maze represented by a matrix of m rows and n
columns with obstacles (see the figure below). A cell with a
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Chapter 5 Solutions
Data Structures and Algorithms in Java
Ch. 5 - Prob. 1RCh. 5 - Prob. 2RCh. 5 - Prob. 3RCh. 5 - Prob. 4RCh. 5 - Prob. 5RCh. 5 - Draw the recursion trace for the execution of...Ch. 5 - Prob. 7RCh. 5 - Describe a recursive algorithm for converting a...Ch. 5 - Prob. 9RCh. 5 - Prob. 10R
Ch. 5 - Prob. 11CCh. 5 - Prob. 12CCh. 5 - Give a recursive algorithm to compute the product...Ch. 5 - In Section 5.2 we prove by induction that the...Ch. 5 - Write a recursive method that will output all the...Ch. 5 - In the Towers of Hanoi puzzle, we are given a...Ch. 5 - Write a short recursive Java method that takes a...Ch. 5 - Write a short recursive Java method that...Ch. 5 - Use recursion to write a Java method for...Ch. 5 - Write a short recursive Java method that...Ch. 5 - Prob. 21CCh. 5 - Prob. 22CCh. 5 - Prob. 23CCh. 5 - Isabel has an interesting way of summing up the...Ch. 5 - Prob. 25CCh. 5 - Prob. 26CCh. 5 - Prob. 27PCh. 5 - Write a program for solving summation puzzles by...Ch. 5 - Prob. 29PCh. 5 - Write a program that can solve instances of the...
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