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Code Implementation

Tower of Hanoi Puzzle Solver Implementation

Below is the implementation of the tower of hanoi puzzle solver:

solution.js

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function towerOfHanoi(n, source, auxiliary, target) {
  // Base case: only one disk to move
  if (n === 1) {
    console.log(`Move disk 1 from ${source} to ${target}`);
    return;
  }
 
  // Step 1: Move n-1 disks from source to auxiliary
  towerOfHanoi(n - 1, source, target, auxiliary);
 
  // Step 2: Move the largest disk from source to target
  console.log(`Move disk ${n} from ${source} to ${target}`);
 
  // Step 3: Move n-1 disks from auxiliary to target
  towerOfHanoi(n - 1, auxiliary, source, target);
}
 
// Test cases
console.log("Tower of Hanoi with 1 disk:");
towerOfHanoi(1, 'A', 'B', 'C');
// Output: Move disk 1 from A to C
 
console.log("\nTower of Hanoi with 2 disks:");
towerOfHanoi(2, 'A', 'B', 'C');
// Output:
// Move disk 1 from A to B
// Move disk 2 from A to C
// Move disk 1 from B to C
 
console.log("\nTower of Hanoi with 3 disks:");
towerOfHanoi(3, 'A', 'B', 'C');
// Output:
// Move disk 1 from A to C
// Move disk 2 from A to B
// Move disk 1 from C to B
// Move disk 3 from A to C
// Move disk 1 from B to A
// Move disk 2 from B to C
// Move disk 1 from A to C
 
// Calculate the number of moves for n disks
function calculateMoves(n) {
  return Math.pow(2, n) - 1;
}
 
console.log("\nNumber of moves required:");
for (let i = 1; i <= 5; i++) {
  console.log(`For ${i} disk(s): ${calculateMoves(i)} moves`);
}

Step-by-Step Explanation

Let's break down the implementation:

Understand the Problem: The Tower of Hanoi puzzle involves moving a stack of disks from one rod to another, following specific rules about disk movement.
Identify the Recursive Structure: Recognize that moving n disks can be broken down into moving n-1 disks, then moving the largest disk, then moving n-1 disks again.
Define the Base Case: The simplest case is moving a single disk directly from the source to the target rod.
Implement the Recursive Solution: Write a function that handles the base case and implements the three-step recursive approach for the general case.
Analyze the Solution: Understand that the number of moves required is 2^n - 1, which grows exponentially with the number of disks.

Previous Next

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Determine if a string reads the same forward and backward.

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Message Encryption

Reverse a string to create a simple encryption system.

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Word Puzzle Challenge

Check if two strings are anagrams of each other.

EasyString Manipulation

Learning Objective

Implement the tower of hanoi puzzle solver solution in different programming languages.

Tower of Hanoi Puzzle Solver Implementation

Below is the implementation of the tower of hanoi puzzle solver in different programming languages. Select a language tab to view the corresponding code.

solution.js

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function towerOfHanoi(n, source, auxiliary, target) {
  // Base case: only one disk to move
  if (n === 1) {
    console.log(`Move disk 1 from ${source} to ${target}`);
    return;
  }
 
  // Step 1: Move n-1 disks from source to auxiliary
  towerOfHanoi(n - 1, source, target, auxiliary);
 
  // Step 2: Move the largest disk from source to target
  console.log(`Move disk ${n} from ${source} to ${target}`);
 
  // Step 3: Move n-1 disks from auxiliary to target
  towerOfHanoi(n - 1, auxiliary, source, target);
}
 
// Test cases
console.log("Tower of Hanoi with 1 disk:");
towerOfHanoi(1, 'A', 'B', 'C');
// Output: Move disk 1 from A to C
 
console.log("\nTower of Hanoi with 2 disks:");
towerOfHanoi(2, 'A', 'B', 'C');
// Output:
// Move disk 1 from A to B
// Move disk 2 from A to C
// Move disk 1 from B to C
 
console.log("\nTower of Hanoi with 3 disks:");
towerOfHanoi(3, 'A', 'B', 'C');
// Output:
// Move disk 1 from A to C
// Move disk 2 from A to B
// Move disk 1 from C to B
// Move disk 3 from A to C
// Move disk 1 from B to A
// Move disk 2 from B to C
// Move disk 1 from A to C
 
// Calculate the number of moves for n disks
function calculateMoves(n) {
  return Math.pow(2, n) - 1;
}
 
console.log("\nNumber of moves required:");
for (let i = 1; i <= 5; i++) {
  console.log(`For ${i} disk(s): ${calculateMoves(i)} moves`);
}

Step-by-Step Explanation

1Understand the Problem

The Tower of Hanoi puzzle involves moving a stack of disks from one rod to another, following specific rules about disk movement.

2Identify the Recursive Structure

Recognize that moving n disks can be broken down into moving n-1 disks, then moving the largest disk, then moving n-1 disks again.

3Define the Base Case

The simplest case is moving a single disk directly from the source to the target rod.

4Implement the Recursive Solution

Write a function that handles the base case and implements the three-step recursive approach for the general case.

5Analyze the Solution

Understand that the number of moves required is 2^n - 1, which grows exponentially with the number of disks.

Language-Specific Notes

JavaScript

Uses template literals (backticks) for string interpolation in the output messages.
Implements a separate function to calculate the number of moves using Math.pow().
The recursive function follows the standard three-step approach for solving the Tower of Hanoi.

Python

Uses f-strings for string interpolation in the output messages.
Implements a separate function to calculate the number of moves using the ** operator.
The recursive function follows the standard three-step approach for solving the Tower of Hanoi.

Java

Uses string concatenation for building the output messages.
Implements a separate method to calculate the number of moves using Math.pow().
The recursive method follows the standard three-step approach for solving the Tower of Hanoi.

C++

Uses the iostream library for output and the cmath library for the pow() function.
Implements a separate function to calculate the number of moves.
The recursive function follows the standard three-step approach for solving the Tower of Hanoi.

Key Takeaways

The Tower of Hanoi is a classic example of a problem that can be solved elegantly using recursion.
The recursive solution breaks down the problem into three steps: move n-1 disks to auxiliary, move the largest disk to target, then move n-1 disks from auxiliary to target.
The number of moves required to solve the puzzle with n disks is 2^n - 1, which grows exponentially.
This problem demonstrates the power of recursive thinking for solving complex problems by breaking them down into simpler subproblems.
The solution is remarkably concise and elegant, despite the complexity of the problem.

Try It Yourself

Modify the code to implement an alternative approach and test it with the same examples.

Challenge:

Implement a function that solves the tower of hanoi puzzle solver problem using a different approach than shown above.

Common Edge Cases

Single Disk

With only one disk, the solution is trivial: move the disk directly from source to target.

towerOfHanoi(1, 'A', 'B', 'C') → Move disk 1 from A to C

Large Number of Disks

The number of moves grows exponentially with the number of disks, potentially leading to very long output.

For 20 disks, the solution requires 2^20 - 1 = 1,048,575 moves

Rod Naming

The algorithm works regardless of how the rods are named, as long as the names are used consistently.

towerOfHanoi(2, 'Source', 'Auxiliary', 'Target') works just as well

Solution Approach Practice Problems

Problem Solution Code

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Tower of Hanoi Puzzle Solver - Implementation

Code Implementation

Tower of Hanoi Puzzle Solver Implementation

Below is the implementation of the tower of hanoi puzzle solver:

solution.js

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function towerOfHanoi(n, source, auxiliary, target) {
  // Base case: only one disk to move
  if (n === 1) {
    console.log(`Move disk 1 from ${source} to ${target}`);
    return;
  }
 
  // Step 1: Move n-1 disks from source to auxiliary
  towerOfHanoi(n - 1, source, target, auxiliary);
 
  // Step 2: Move the largest disk from source to target
  console.log(`Move disk ${n} from ${source} to ${target}`);
 
  // Step 3: Move n-1 disks from auxiliary to target
  towerOfHanoi(n - 1, auxiliary, source, target);
}
 
// Test cases
console.log("Tower of Hanoi with 1 disk:");
towerOfHanoi(1, 'A', 'B', 'C');
// Output: Move disk 1 from A to C
 
console.log("\nTower of Hanoi with 2 disks:");
towerOfHanoi(2, 'A', 'B', 'C');
// Output:
// Move disk 1 from A to B
// Move disk 2 from A to C
// Move disk 1 from B to C
 
console.log("\nTower of Hanoi with 3 disks:");
towerOfHanoi(3, 'A', 'B', 'C');
// Output:
// Move disk 1 from A to C
// Move disk 2 from A to B
// Move disk 1 from C to B
// Move disk 3 from A to C
// Move disk 1 from B to A
// Move disk 2 from B to C
// Move disk 1 from A to C
 
// Calculate the number of moves for n disks
function calculateMoves(n) {
  return Math.pow(2, n) - 1;
}
 
console.log("\nNumber of moves required:");
for (let i = 1; i <= 5; i++) {
  console.log(`For ${i} disk(s): ${calculateMoves(i)} moves`);
}

Step-by-Step Explanation

Let's break down the implementation:

Understand the Problem: The Tower of Hanoi puzzle involves moving a stack of disks from one rod to another, following specific rules about disk movement.
Identify the Recursive Structure: Recognize that moving n disks can be broken down into moving n-1 disks, then moving the largest disk, then moving n-1 disks again.
Define the Base Case: The simplest case is moving a single disk directly from the source to the target rod.
Implement the Recursive Solution: Write a function that handles the base case and implements the three-step recursive approach for the general case.
Analyze the Solution: Understand that the number of moves required is 2^n - 1, which grows exponentially with the number of disks.

Previous Next

String Problems

Palindrome Checker

Determine if a string reads the same forward and backward.

EasyString Manipulation

Message Encryption

Reverse a string to create a simple encryption system.

EasyString Manipulation

Word Puzzle Challenge

Check if two strings are anagrams of each other.

EasyString Manipulation

Learning Objective

Implement the tower of hanoi puzzle solver solution in different programming languages.

Tower of Hanoi Puzzle Solver Implementation

Below is the implementation of the tower of hanoi puzzle solver in different programming languages. Select a language tab to view the corresponding code.

solution.js

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function towerOfHanoi(n, source, auxiliary, target) {
  // Base case: only one disk to move
  if (n === 1) {
    console.log(`Move disk 1 from ${source} to ${target}`);
    return;
  }
 
  // Step 1: Move n-1 disks from source to auxiliary
  towerOfHanoi(n - 1, source, target, auxiliary);
 
  // Step 2: Move the largest disk from source to target
  console.log(`Move disk ${n} from ${source} to ${target}`);
 
  // Step 3: Move n-1 disks from auxiliary to target
  towerOfHanoi(n - 1, auxiliary, source, target);
}
 
// Test cases
console.log("Tower of Hanoi with 1 disk:");
towerOfHanoi(1, 'A', 'B', 'C');
// Output: Move disk 1 from A to C
 
console.log("\nTower of Hanoi with 2 disks:");
towerOfHanoi(2, 'A', 'B', 'C');
// Output:
// Move disk 1 from A to B
// Move disk 2 from A to C
// Move disk 1 from B to C
 
console.log("\nTower of Hanoi with 3 disks:");
towerOfHanoi(3, 'A', 'B', 'C');
// Output:
// Move disk 1 from A to C
// Move disk 2 from A to B
// Move disk 1 from C to B
// Move disk 3 from A to C
// Move disk 1 from B to A
// Move disk 2 from B to C
// Move disk 1 from A to C
 
// Calculate the number of moves for n disks
function calculateMoves(n) {
  return Math.pow(2, n) - 1;
}
 
console.log("\nNumber of moves required:");
for (let i = 1; i <= 5; i++) {
  console.log(`For ${i} disk(s): ${calculateMoves(i)} moves`);
}

Step-by-Step Explanation

1Understand the Problem

The Tower of Hanoi puzzle involves moving a stack of disks from one rod to another, following specific rules about disk movement.

2Identify the Recursive Structure

Recognize that moving n disks can be broken down into moving n-1 disks, then moving the largest disk, then moving n-1 disks again.

3Define the Base Case

The simplest case is moving a single disk directly from the source to the target rod.

4Implement the Recursive Solution

Write a function that handles the base case and implements the three-step recursive approach for the general case.

5Analyze the Solution

Understand that the number of moves required is 2^n - 1, which grows exponentially with the number of disks.

Language-Specific Notes

JavaScript

Uses template literals (backticks) for string interpolation in the output messages.
Implements a separate function to calculate the number of moves using Math.pow().
The recursive function follows the standard three-step approach for solving the Tower of Hanoi.

Python

Uses f-strings for string interpolation in the output messages.
Implements a separate function to calculate the number of moves using the ** operator.
The recursive function follows the standard three-step approach for solving the Tower of Hanoi.

Java

Uses string concatenation for building the output messages.
Implements a separate method to calculate the number of moves using Math.pow().
The recursive method follows the standard three-step approach for solving the Tower of Hanoi.

C++

Uses the iostream library for output and the cmath library for the pow() function.
Implements a separate function to calculate the number of moves.
The recursive function follows the standard three-step approach for solving the Tower of Hanoi.

Key Takeaways

The Tower of Hanoi is a classic example of a problem that can be solved elegantly using recursion.
The recursive solution breaks down the problem into three steps: move n-1 disks to auxiliary, move the largest disk to target, then move n-1 disks from auxiliary to target.
The number of moves required to solve the puzzle with n disks is 2^n - 1, which grows exponentially.
This problem demonstrates the power of recursive thinking for solving complex problems by breaking them down into simpler subproblems.
The solution is remarkably concise and elegant, despite the complexity of the problem.

Try It Yourself

Modify the code to implement an alternative approach and test it with the same examples.

Challenge:

Implement a function that solves the tower of hanoi puzzle solver problem using a different approach than shown above.

Common Edge Cases

Single Disk

With only one disk, the solution is trivial: move the disk directly from source to target.

towerOfHanoi(1, 'A', 'B', 'C') → Move disk 1 from A to C

Large Number of Disks

The number of moves grows exponentially with the number of disks, potentially leading to very long output.

For 20 disks, the solution requires 2^20 - 1 = 1,048,575 moves

Rod Naming

The algorithm works regardless of how the rods are named, as long as the names are used consistently.

towerOfHanoi(2, 'Source', 'Auxiliary', 'Target') works just as well

Solution Approach Practice Problems

Code Implementation

Tower of Hanoi Puzzle Solver Implementation

Step-by-Step Explanation

String ProblemsShow All

Palindrome Checker

Message Encryption

Word Puzzle Challenge

Learning Objective

Tower of Hanoi Puzzle Solver Implementation

Step-by-Step Explanation

1Understand the Problem

2Identify the Recursive Structure

3Define the Base Case

4Implement the Recursive Solution

5Analyze the Solution

Language-Specific Notes

JavaScript

Python

Java

C++

Key Takeaways

Try It Yourself

Challenge:

Common Edge Cases

Single Disk

Large Number of Disks

Rod Naming

Tower of Hanoi Puzzle Solver - Implementation

Code Implementation

Tower of Hanoi Puzzle Solver Implementation

Step-by-Step Explanation

String ProblemsShow All

Palindrome Checker

Message Encryption

Word Puzzle Challenge

Learning Objective

Tower of Hanoi Puzzle Solver Implementation

Step-by-Step Explanation

1Understand the Problem

2Identify the Recursive Structure

3Define the Base Case

4Implement the Recursive Solution

5Analyze the Solution

Language-Specific Notes

JavaScript

Python

Java

C++

Key Takeaways

Try It Yourself

Challenge:

Common Edge Cases

Single Disk

Large Number of Disks

Rod Naming

String Problems

String Problems