Problem Statement
Tower of Hanoi Puzzle Solver
You're developing an educational game that teaches algorithmic thinking through classic puzzles. One of the puzzles you want to include is the Tower of Hanoi, a mathematical puzzle that helps players understand recursive problem-solving.
The Tower of Hanoi consists of three rods and a number of disks of different sizes, which can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape.
The objective of the puzzle is to move the entire stack to another rod, obeying the following rules:
- Only one disk can be moved at a time.
- Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod.
- No disk may be placed on top of a smaller disk.
Your task is to implement a function that prints the sequence of moves required to solve the Tower of Hanoi puzzle for n disks.
Examples
Example 1:
Input: n = 1, source = 'A', auxiliary = 'B', target = 'C'
Output: Move disk 1 from A to C
Explanation: With only one disk, we can move it directly from the source to the target.
Example 2:
Input: n = 2, source = 'A', auxiliary = 'B', target = 'C'
Output: Move disk 1 from A to B
Move disk 2 from A to C
Move disk 1 from B to C
Explanation: With two disks, we first move the smaller disk to the auxiliary rod, then move the larger disk to the target rod, and finally move the smaller disk from the auxiliary rod to the target rod.
Example 3:
Input: n = 3, source = 'A', auxiliary = 'B', target = '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
Explanation: With three disks, the solution requires 7 moves following the recursive pattern.
Constraints
- The number of disks n is a positive integer.
- The function should print the sequence of moves in the correct order.
- The function should handle inputs where 1 ≤ n ≤ 20 (beyond this, the number of moves becomes very large).
- The three rods are labeled as source, auxiliary, and target.
Problem Breakdown
To solve this problem, we need to:
- The Tower of Hanoi is a classic example of a problem that can be solved elegantly using recursion.
- The minimum number of moves required to solve the puzzle with n disks is 2^n - 1.
- The problem can be broken down into three steps: move n-1 disks to the auxiliary rod, move the largest disk to the target rod, then move the n-1 disks from the auxiliary rod to the target rod.
- This problem demonstrates the power of the recursive approach for solving complex problems by breaking them down into simpler subproblems.
String Problems
Learning Objective
Apply string manipulation concepts to solve a real-world problem.
Tower of Hanoi Puzzle Solver
You're developing an educational game that teaches algorithmic thinking through classic puzzles. One of the puzzles you want to include is the Tower of Hanoi, a mathematical puzzle that helps players understand recursive problem-solving.
The Tower of Hanoi consists of three rods and a number of disks of different sizes, which can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape.
The objective of the puzzle is to move the entire stack to another rod, obeying the following rules:
- Only one disk can be moved at a time.
- Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod.
- No disk may be placed on top of a smaller disk.
Your task is to implement a function that prints the sequence of moves required to solve the Tower of Hanoi puzzle for n disks.
Examples
Example 1:
With only one disk, we can move it directly from the source to the target.
Example 2:
With two disks, we first move the smaller disk to the auxiliary rod, then move the larger disk to the target rod, and finally move the smaller disk from the auxiliary rod to the target rod.
Example 3:
With three disks, the solution requires 7 moves following the recursive pattern.
Problem Breakdown
Constraints:
- The number of disks n is a positive integer.
- The function should print the sequence of moves in the correct order.
- The function should handle inputs where 1 ≤ n ≤ 20 (beyond this, the number of moves becomes very large).
- The three rods are labeled as source, auxiliary, and target.
Key Insights:
The Tower of Hanoi is a classic example of a problem that can be solved elegantly using recursion.
The minimum number of moves required to solve the puzzle with n disks is 2^n - 1.
The problem can be broken down into three steps: move n-1 disks to the auxiliary rod, move the largest disk to the target rod, then move the n-1 disks from the auxiliary rod to the target rod.
This problem demonstrates the power of the recursive approach for solving complex problems by breaking them down into simpler subproblems.
Real-World Application
This problem has several practical applications:
Educational Games
The Tower of Hanoi is used in educational settings to teach recursive thinking and problem-solving strategies.
Cognitive Assessment
The puzzle is used in cognitive psychology to assess problem-solving abilities and planning skills.
Algorithm Design
The recursive solution to the Tower of Hanoi serves as a model for designing algorithms for other complex problems.