Tower of Hanoi C / C++ / Python Program

Tower of hanoi is a mathematical game or puzzle. It 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 simple rules:

1. Only one disk can be moved at a time.
2. 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.
3. No larger disk may be placed on top of a smaller disk.

With 3 disks, the puzzle can be solved in 7 moves. The minimal number of moves required to solve a Tower of Hanoi puzzle is 2ⁿ − 1, where n is the number of disks.

For example consider 3 disks ,it can be solved in 2³ -1 steps :

Steps required to be performed for solving tower of hanoi problem  :

The universal way (steps ) to solve this type of problem are:

N=number of disks :
A,B,C are rods :
1) move N-1 disks from A to B using C
2) move the remaining single disk in A to C
3) move N-1 disks from B to C using A 

The Recursive Function based on the above steps is defined below

void TOH(int n,char a,char b,char c){
     if(n>0){
         TOH(n-1,a,c,b);
         printf("%d from %c to %c\n",n,a,c);
         TOH(n-1,b,a,c);
         s++;
     }
 }

Output :

For N=3:

For N=7

C / C++ Source Code :

#include <stdio.h>
#include<conio.h>
#include<time.h>
#include<direct.h>
#include<dos.h>
#include<unistd.h>
#include<windows.h>
static int s=0;
void TOH(int n,char a,char b,char c);
int main(int argc, char *argv[]) {
 int n;
 time_t t1=time(NULL);
 printf("Enter number of discs ");
 scanf("%d",&n);
 TOH(n,'A','B','C');
 time_t t2=time(NULL);
 time_t t=t2-t1;
 printf("\n\nsteps=%d time elapsed=%d seconds ",s,t);
 getch();
 return 0;
}
void TOH(int n,char a,char b,char c){
 if(n>0){
  TOH(n-1,a,c,b);
  printf("%d from %c to %c\n",n,a,c);
  TOH(n-1,b,a,c);
  s++;
 }
}

Python Source code :

s = 0


def TOH(n, a, b, c):
    global s
    if n > 0:
        TOH(n - 1, a, c, b)
        print("Move %d from %s to %s\n" % (n, a, c))
        TOH(n - 1, b, a, c)
        s += 1


if __name__ == '__main__':
    n = int(input("Enter number of discs : "))
    TOH(n, "A", "B", "C")
    print("\n\nsteps=%d \n" % s)


if any doubts or queries please comment