Tower of Hanoi Problem and Iterative Solution
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Questions and Answers

What is the main objective of the iterative Tower of Hanoi algorithm?

  • To maximize the number of moves required to sort the disks
  • To minimize the number of moves required to sort the disks
  • To sort the disks in descending order
  • To sort the disks in ascending order (correct)

    • What is the purpose of the auxiliary peg in the Tower of Hanoi algorithm?

  • To act as the destination peg for the disks
  • To hold the disks temporarily during the sorting process (correct)
  • To count the number of moves required to sort the disks
  • To act as the source peg for the disks

    • How are the disks initialized on the source rod in the Tower of Hanoi algorithm?

  • In random order
  • In descending order from top to bottom (correct)
  • In alternating order
  • In ascending order from top to bottom

    • What is the formula used to calculate the total number of moves required to sort the disks?

    <p>$2^n - 1$</p> Signup and view all the answers

    What happens when the number of disks is even in the Tower of Hanoi algorithm?

    <p>The auxiliary and destination pegs are swapped</p> Signup and view all the answers

    What is the purpose of the Stack data structure in the Tower of Hanoi algorithm?

    <p>To represent the three rods in the Tower of Hanoi</p> Signup and view all the answers

    What is the primary objective of the Tower of Hanoi puzzle?

    <p>To move the entire stack of disks from one rod to another, subject to certain rules</p> Signup and view all the answers

    What is the rule that states a disk can only be placed on top of a larger disk or an empty rod?

    <p>No specific rule number is mentioned in the text</p> Signup and view all the answers

    What is the name of the data structure used in the iterative approach to solving the Tower of Hanoi problem?

    <p>Stack</p> Signup and view all the answers

    What is the initial state of the three rods in the Tower of Hanoi puzzle?

    <p>One rod has all the disks stacked in decreasing order of size, and the other two rods are empty</p> Signup and view all the answers

    How many times is the legal move between source and auxiliary pegs made in the iterative approach for an even number of disks?

    <p>Once</p> Signup and view all the answers

    What is the purpose of the auxiliary rod in the Tower of Hanoi puzzle?

    <p>To act as an intermediate step in moving the disks from the source rod to the destination rod</p> Signup and view all the answers

    Study Notes

    Tower of Hanoi Problem

    • The Tower of Hanoi is a classic mathematical puzzle that involves three rods and a set of disks of different sizes.
    • The objective is to move the entire stack of disks from one rod to another, subject to certain rules.

    Rules of the Puzzle

    • Only one disk can be moved at a time.
    • A disk can only be placed on top of a larger disk or an empty rod.
    • No disk can be placed on top of a smaller disk.

    Initial Setup

    • The puzzle starts with all the disks stacked in decreasing order of size on one rod (the source rod).
    • The other two rods (auxiliary and destination rods) are empty.

    Challenge

    • The challenge is to move the entire stack of disks to the destination rod using the auxiliary rod as an intermediate step.

    Iterative Approach

    • The iterative approach involves using a stack data structure to keep track of the movements of the disks.
    • We maintain three pegs (A, B, and C), and we start with all the disks on peg A.
    • The goal is to move all the disks to peg C following the rules of the problem.

    Iterative Algorithm for Even Number of Disks

    • Make the legal move between source and auxiliary pegs.
    • Make the legal move between source and destination pegs.
    • Make the legal move between auxiliary and destination pegs.
    • Repeat steps 1-3 until the disks are sorted.

    Iterative Algorithm for Odd Number of Disks

    • Make the legal move between source and destination pegs.
    • Make the legal move between source and auxiliary pegs.
    • Make the legal move between auxiliary and destination pegs.
    • Repeat steps 1-3 until the disks are sorted.

    Java Implementation

    • The towerOfHanoi function takes four parameters: the number of disks, and the source, auxiliary, and destination pegs.
    • The function initializes three stacks to represent the three rods and performs the iterative Tower of Hanoi algorithm.
    • The total number of moves required is calculated as 2^n - 1, where n is the number of disks.

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    Description

    A quiz on the Tower of Hanoi problem, a classic mathematical puzzle that involves three rods and a set of disks of different sizes. This quiz will test your understanding of the problem and its iterative solution.

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