Question
Towers of Hanoi. There is a story about Buddhist monks who are playing this puzzle with 64 stone disks. The story claims that when the monks finish moving the disks from one post to a second via the third post, time will end. Eschatology (concerns about the end of time) and theology will be left to those better qualified; our interest is limited to the recursive solution to the problem.
A stack of n disks of decreasing size is placed on one of three posts. The task is to move the disks one at a time from the first post to the second. To do this, any disk can be moved from any post to any other post, subject to the rule that you can never place a larger disk over a smaller disk. The (spare) third post is provided to make the solution possible. Your task is to write a recursive function that describes instructions for a solution to this problem. We do not have graphics available, so you should output a sequence of instructions that will solve the problem.
Hint: If you could move n-1 of the disks from the first post to the third post using the second post as a spare, the last disk could be moved from the first post to the second post. Then by using the same technique (whatever that may be), you can move the n-1 disks from the third post to the second post, using the first post as a spare. There! You have the puzzle solved. You have only to decide what the nonrecursive case is, what the recursive case is, and when to output instructions to move the disks.
Answer
C++ program code:
//header section
#include <iostream>
using namespace std;
void solveTowersOfHanoi(int n, char source, char destination, char spare)
{
// Base case: If there is only one disk, move it from source to destination
if (n == 1) {
cout << "Move disk 1 from " << source << " to " << destination << endl;
return;
}
// Recursive case: Move n-1 disks from source to spare using destination as spare
solveTowersOfHanoi(n - 1, source, spare, destination);
// Move the nth disk from source to destination
cout << "Move disk " << n << " from " << source << " to " << destination << endl;
// Move the n-1 disks from spare to destination using source as spare
solveTowersOfHanoi(n - 1, spare, destination, source);
}
int main()
{
int numDisks = 3; // Change this value to adjust the number of disks
// Call the recursive function to solve the Towers of Hanoi puzzle
solveTowersOfHanoi(numDisks, 'A', 'B', 'C');
return 0;
}
Output of the program code:
Move disk 1 from A to B
Move disk 2 from A to C
Move disk 1 from B to C
Move disk 3 from A to B
Move disk 1 from C to A
Move disk 2 from C to B
Move disk 1 from A to B