Tower of Hanoi is a puzzle problem. Where we have three stands and n discs. Initially, Discs are placed in the first stand. We have to place discs into the third or destination stand, the second or auxiliary stand can be used as a helping stand.
- But there are some rules to follow.
- We can transfer only one disc for each movement.
- Only the topmost disc can be picked up from a stand.
- No bigger disc will be placed at the top of the smaller disc.
This problem can be solved easily by recursion. At first, using recursion the top (n-1) discs are placed from source to auxiliary stand, then place the last disc from source to destination, then again place (n-1) disc from auxiliary stand to destination stand by recursion.
Input and Output
Input: Number of discs: 3 Output: 1. Move disk 1 from A to C 2. Move disk 2 from A to B 3. Move disk 1 from C to B 4. Move disk 3 from A to C 5. Move disk 1 from B to A 6. Move disk 2 from B to C 7. Move disk 1 from A to C
Algorithm
toh(n, s, a, d)
Input: Number of discs, source, auxiliary, destination.
Output: Steps to move discs from source to destination maintaining proper rules.
Begin if n = 1, then display move disc from s to d toh(n-1, s, d, a) display move disc from s to d toh(n-1, a, s, d) End
Example
#include<iostream>
using namespace std;
void TOH(int n, char s, char a, char d) {
static int count = 0; //store number of counts
if(n == 1) {
count++;
cout << count<< ". Move disk " << n << " from "<<s <<" to "<<d<<endl;
return; //base case, when only one disk
}
TOH(n-1, s, d, a); //recursive call the function
count++;
cout << count<< ". Move disk " << n << " from "<<s <<" to"<<d<<endl;
TOH(n-1, a, s, d);
}
int main() {
int n;
cout << "Enter the number of disks: ";
cin >> n;
TOH(n, 'A','B','C');
}Output
Enter the number of disks: 3 1. Move disk 1 from A to C 2. Move disk 2 from A to B 3. Move disk 1 from C to B 4. Move disk 3 from A to C 5. Move disk 1 from B to A 6. Move disk 2 from B to C 7. Move disk 1 from A to C