Question

Implement an iterator that produces the moves for the Towers of Hanoi puzzle described in Worked Example 11.2. Provide methods hasMorexoves and nexthove. The nextNove method should yield a string describing the next move. For example, the following code prints all moves needed to move five disks from peg 1 to peg 3 : nover = DiskNover \((5,1,3)\) while mover.hasMoreMoves \(\mathrm{O}\) : print (nover. nextMove(O) Hint: A disk mover that moves a single disk from one peg to another simply has a nextMove method that returns a string Move disk from peg sotree to target A disk mover with more than one disk to move must work harder. It needs another Disklover to help it move the first \(d-1\) disks. The nextrove asks that disk mover for its next move until it is done. Then the nextmove method issues a command to move the \(d\) th disk. Finally, it constructs another disk mover that generates the remaining moves. It helps to keep track of the state of the disk mover: \- BEFORE LARCEST: A helper mover moves the smaller pile to the other peg. \- LARCEST: Move the largest disk from the source to the destination. \- Arter LARCEST: The helper mover moves the smaller pile from the other peg to the target. \- DONE: All moves are done.

Short answer

An iterator for Towers of Hanoi is implemented using states and recursive `DiskMover` instances.

Step-by-step solution

Understanding the Problem

We need to implement an iterator for the Towers of Hanoi puzzle which can output the moves required to solve the puzzle for a given number of disks. The iterator should have methods `hasMoreMoves` and `nextMove`.

Class Structure Design

Design a class `DiskMover` that takes three parameters: number of disks `d`, source `s`, and target `t`. Include a third parameter called `intermediate` as the peg used for intermediate moves. The class should keep track of the current move state using state variables.

Initializing the Class

Define the `__init__` method in the `DiskMover` class that initializes the parameters. If only one disk is required to be moved, directly set the state to 'LARGEST', otherwise set it to 'BEFORE_LARGEST'.

hasMoreMoves Method

Implement the `hasMoreMoves` method to return `True` if the current state is not 'DONE'. It will check the current state of our iterator object.

nextMove Method for One Disk

For a single disk, implement `nextMove` to move the disk from the source peg to the target peg and return the move as a string. Transition the state to 'DONE' after the move.

nextMove Method for Multiple Disks

For multiple disks, utilize helper `DiskMover` instances to manage the recursive move strategy. Define logic for the 'BEFORE_LARGEST', 'LARGEST', and 'AFTER_LARGEST' states to recursively call `nextMove` on helper instances (small pile movers) and switch states appropriately.

Implementing Recursive Helper Movers

In the 'BEFORE_LARGEST' state, initialize a helper `DiskMover` to move the top `d-1` disks to the intermediate peg. In the 'AFTER_LARGEST' state, initialize another helper `DiskMover` to move these disks from the intermediate peg to the target peg.

Testing the Implementation

Test the implementation with a loop running while `hasMoreMoves` returns `True`, calling `nextMove` and printing the result to ensure the moves are correct for a given number of disks (e.g., 5 disks).

Key concepts

Recursion and the Towers of Hanoi

The Towers of Hanoi is a classic puzzle that provides an excellent opportunity to explore the concept of recursion. To understand recursion, think of it as a process where a function calls itself with a modified set of parameters. In the context of Towers of Hanoi, the goal is to move disks from one peg to another, obeying specific rules:
- Only one disk can be moved at a time.
- A disk can only be placed on top of a larger disk or an empty peg.
- The disks can be moved using three pegs: source, destination, and intermediate.

Recursion is ideal for breaking down this seemingly complex task. We solve the problem for a specific number of disks by:
1. Moving the top \(d-1\) disks to the intermediate peg.
2. Moving the largest disk directly to the destination.
3. Moving the \(d-1\) disks from the intermediate peg to the destination peg.

This recursive approach simplifies our thinking. Each instance of the problem reduces in size until only one disk is left to move, directly solvable without further recursion. This logical division is why recursion is central to the Towers of Hanoi solution.

Iterator Implementation for Elegant Move Progression

Implementing an iterator in Python lets us manage the flow of moves within our Towers of Hanoi solution in an organized way. An iterator simplifies the task by controlling how and when each move is executed, which is vital for our problem where each disk must be moved in a precise order.

Our iterator within the `DiskMover` class should include methods such as:
- `hasMoreMoves`: Checks if there are any moves left to execute by reviewing the current state of the disk mover.
- `nextMove`: Executes the next move in the sequence and advances the state accordingly.

This setup follows Python's iterator protocol, where `hasMoreMoves` keeps the iteration going until all moves are complete. This design enables us to handle recursive calls efficiently and ensures that each move is processed accurately. The iterator, therefore, serves as a useful abstraction, making the movement calculation smooth and logical.

State Management for Tracking Progress

State management in software applications is critical for tracking progress and current activity, especially in iterative and recursive problems like Towers of Hanoi. In our implementation, different states signify different stages in our iterative process:
- `BEFORE_LARGEST`: Represents the phase where the smaller disks are moved to an intermediate peg.
- `LARGEST`: Indicates the time to move the largest disk from the source peg to the target peg.
- `AFTER_LARGEST`: Involves moving the smaller disks from the intermediate peg to the target peg.
- `DONE`: Signals that all moves have been completed.

By managing these states, our program keeps track of what needs to be done next. State management ensures our algorithm knows precisely which actions to trigger and when. Transitioning between these states happens seamlessly due to our iterator's recursive nature, reflecting each step's completion accurately.

Class Design in Python for Structured Solutions

Class design in Python provides a structural scaffold for complex solutions like the Towers of Hanoi. In this scenario, the `DiskMover` class is central. It encapsulates the logic necessary to solve our puzzle, maintaining clear boundaries and responsibilities.

Here are some key points in designing the `DiskMover` class:
- **Initialization**: The `__init__` method sets up necessary variables, such as the number of disks, the source, target, intermediate pegs, and the state of the operation. This initial setup gives the class a specific and extensible task.
- **Encapsulation**: With integration of state management and recursion, the class becomes self-sufficient. This autonomy allows for modifications and scaling without disrupting the internal operations.

Class design is about organizing logic in a way that is both powerful and intuitive. It eases maintenance and enhances readability. By separating concerns into methods like `hasMoreMoves` and `nextMove`, the `DiskMover` class provides a neat framework to handle the intricate task of managing moves within our Towers of Hanoi solution.