Tower of Hanoi – Recursive Solution (C++)

Overview

The Tower of Hanoi is a classic problem in computer science that is commonly used to demonstrate and understand the concept of recursion and algorithmic thinking.

The problem consists of:

• Three rods: A (source), B (auxiliary), and C (destination)
• A number of disks of different sizes stacked on rod A
• The objective is to move all disks from rod A to rod C while respecting a set of rules

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Problem Rules

1. Only one disk can be moved at a time
2. A larger disk may never be placed on top of a smaller disk
3. All moves must use only the three given rods

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Solution Idea

The solution to the Tower of Hanoi problem is inherently recursive.

To move n disks from the source rod to the destination rod:

1. Move the top n-1 disks from the source rod to the auxiliary rod
2. Move the largest disk (n) directly to the destination rod
3. Move the n-1 disks from the auxiliary rod to the destination rod

This process repeats recursively until the base case (n = 1) is reached.

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Code Explanation

• The hanoi function implements the recursive solution
• Each valid disk movement is printed to the console
• The total number of moves is tracked using the moves variable
• The program reads the number of disks from user input and displays the complete sequence of moves

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Time Complexity

The time complexity of the algorithm is:# Tower of Hanoi – Recursive Solution (C++)

Overview

The Tower of Hanoi is a classic problem in computer science that is commonly used to demonstrate and understand the concept of recursion and algorithmic thinking.

The problem consists of:

• Three rods: A (source), B (auxiliary), and C (destination)
• A number of disks of different sizes stacked on rod A
• The objective is to move all disks from rod A to rod C while respecting a set of rules

---

Problem Rules

1. Only one disk can be moved at a time
2. A larger disk may never be placed on top of a smaller disk
3. All moves must use only the three given rods

---

Solution Idea

The solution to the Tower of Hanoi problem is inherently recursive.

To move n disks from the source rod to the destination rod:

1. Move the top n-1 disks from the source rod to the auxiliary rod
2. Move the largest disk (n) directly to the destination rod
3. Move the n-1 disks from the auxiliary rod to the destination rod

This process repeats recursively until the base case (n = 1) is reached.

---

Code Explanation

• The hanoi function implements the recursive solution
• Each valid disk movement is printed to the console
• The total number of moves is tracked using the moves variable
• The program reads the number of disks from user input and displays the complete sequence of moves

---

Time Complexity

The time complexity of the algorithm is:# Tower of Hanoi – Recursive Solution (C++)

Overview

The Tower of Hanoi is a classic problem in computer science that is commonly used to demonstrate and understand the concept of recursion and algorithmic thinking.

The problem consists of:

• Three rods: A (source), B (auxiliary), and C (destination)
• A number of disks of different sizes stacked on rod A
• The objective is to move all disks from rod A to rod C while respecting a set of rules

---

Problem Rules

1. Only one disk can be moved at a time
2. A larger disk may never be placed on top of a smaller disk
3. All moves must use only the three given rods

---

Solution Idea

The solution to the Tower of Hanoi problem is inherently recursive.

To move n disks from the source rod to the destination rod:

1. Move the top n-1 disks from the source rod to the auxiliary rod
2. Move the largest disk (n) directly to the destination rod
3. Move the n-1 disks from the auxiliary rod to the destination rod

This process repeats recursively until the base case (n = 1) is reached.

---

Code Explanation

• The hanoi function implements the recursive solution
• Each valid disk movement is printed to the console
• The total number of moves is tracked using the moves variable
• The program reads the number of disks from user input and displays the complete sequence of moves

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Time Complexity

The time complexity of the algorithm is: O(2^n) This indicates that the number of required moves grows exponentially as the number of disks increases.

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How to Run

1. Compile the source code using a C++ compiler (e.g., g++)
2. Run the executable
3. Enter the number of disks when prompted
4. The program will output all moves along with the total move count

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Project Purpose

This project is intended for educational purposes, focusing on:

• Understanding recursion
• Developing algorithmic problem-solving skills
• Analyzing time complexity of recursive algorithms