# Solution for Tower of Hanoi C++

### What is Tower of Hanoi?

All must be well aware of the problem of Tower of Hanoi, for those who don’t know, let’s discuss it once again.

The Tower of Hanoi (also called the Tower of Brahma or Lucas’ Tower, and sometimes pluralized) is a mathematical game or puzzle.

tower of hanoi

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:

• 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 i.e. a disk can only be moved if it is the uppermost disk on a stack.
• No disk may be placed on top of a smaller disk.

### We can solve it in 2 ways:

1. Using Recursion
2. Using Stacks

### Using Recursion:

```#include <iostream>
using namespace std;

void towers(int, char, char, char);

int main()
{
int num;

cout<<"Enter the number of disks : ";
cin>>num;
cout<<"The sequence of moves involved in the Tower of Hanoi are :n";
towers(num, 'A', 'C', 'B');
return 0;
}
void towers(int num, char frompeg, char topeg, char auxpeg)
{
if (num == 1)
{
cout<<"n Move disk 1 from peg "<<frompeg<<" to peg "<<topeg;
return;
}
towers(num - 1, frompeg, auxpeg, topeg);
cout<<"n Move disk "<<num<<" from peg "<<frompeg<<" to peg "<<topeg;
towers(num - 1, auxpeg, topeg, frompeg);
}
```

### Sample Output:

```Enter the number of disks : 3
The sequence of moves involved in the Tower of Hanoi are :

Move disk 1 from peg A to peg C
Move disk 2 from peg A to peg B
Move disk 1 from peg C to peg B
Move disk 3 from peg A to peg C
Move disk 1 from peg B to peg A
Move disk 2 from peg B to peg C
Move disk 1 from peg A to peg C```

## Program to solve Tower of Hanoi C++ using Stack

```#include<stdio.h>
#include<iostream>
#include<math.h>
using namespace std;
struct node1
{
int data1;
node1 *next1;
}*top1 = NULL, *p1 = NULL, *np1 = NULL;
struct node2
{
int data2;
node2 *next2;
}*top2 = NULL, *p2 = NULL, *np2 = NULL;
struct node3
{
int data3;
node3 *next3;
}*top3 = NULL, *p3 = NULL, *np3 = NULL;
void push1(int data)
{
np1 = new node1;
np1->data1 = data;
np1->next1 = NULL;
if (top1 == NULL)
{
top1 = np1;
}
else
{
np1->next1 = top1;
top1 = np1;
}
}
int pop1()
{
int b = 999;
if (top1 == NULL)
{
return b;
}
else
{
p1 = top1;
top1 = top1->next1;
return(p1->data1);
delete(p1);
}
}
void push2(int data)
{
np2 = new node2;
np2->data2 = data;
np2->next2 = NULL;
if (top2 == NULL)
{
top2 = np2;
}
else
{
np2->next2 = top2;
top2 = np2;
}
}
int pop2()
{
int b = 999;
if (top2 == NULL)
{
return b;
}
else
{
p2 = top2;
top2 = top2->next2;
return(p2->data2);
delete(p2);
}
}
void push3(int data)
{
np3 = new node3;
np3->data3 = data;
np3->next3 = NULL;
if (top3 == NULL)
{
top3 = np3;
}
else
{
np3->next3 = top3;
top3 = np3;
}
}
int pop3()
{
int b = 999;
if (top3 == NULL)
{
return b;
}
else
{
p3 = top3;
top3 = top3->next3;
return(p3->data3);
delete(p3);
}
}
int top_of_stack()
{
if (top1 != NULL && top1->data1 == 1 )
{
return 1;
}
else if (top2 != NULL && top2->data2 == 1)
{
return 2;
}
else if (top3 != NULL && top3->data3 == 1)
{
return 3;
}
}
void display1()
{
cout<<endl;
node1 *p1;
p1 = top1;
cout<<"Tower1-> "<<"t";
while (p1 != NULL)
{
cout<<p1->data1<<"t";
p1 = p1->next1;
}
cout<<endl;
}
void display2()
{
node2 *p2;
p2 = top2;
cout<<"Tower2-> "<<"t";
while (p2 != NULL)
{
cout<<p2->data2<<"t";
p2 = p2->next2;
}
cout<<endl;
}
void display3()
{
node3 *p3;
p3 = top3;
cout<<"Tower3-> "<<"t";
while (p3 != NULL)
{
cout<<p3->data3<<"t";
p3 = p3->next3;
}
cout<<endl;
cout<<endl;
}
void toh(int n)
{
int i, x, a, b;
for (i = 0; i < (pow(2,n)); i++)
{
display1();
display2();
display3();
x = top_of_stack();
if (i % 2 == 0)
{
if (x == 1)
{
push3(pop1());
}
else if (x == 2)
{
push1(pop2());
}
else if (x == 3)
{
push2(pop3());
}
}
else
{
if (x == 1)
{
a = pop2();
b = pop3();
if (a < b && b != 999)
{
push3(b);
push3(a);
}
else if (a > b && a != 999)
{
push2(a);
push2(b);
}
else if (b == 999)
{
push3(a);
}
else if (a == 999)
{
push2(b);
}
}
else if (x == 2)
{
a = pop1();
b = pop3();
if (a < b && b != 999)
{
push3(b);
push3(a);
}
else if (a > b && a != 999)
{
push1(a);
push1(b);
}
else if (b == 999)
{
push3(a);
}
else if (a == 999)
{
push1(b);
}
}
else if (x == 3)
{
a = pop1();
b = pop2();
if (a < b && b != 999)
{
push2(b);
push2(a);
}
else if (a > b && a != 999)
{
push1(a);
push1(b);
}
else if (b == 999)
{
push2(a);
}
else if (a == 999)
{
push1(b);
}
}
}
}
}
int main()
{
int n, i;
cout<<"enter the number of disksn";
cin>>n;
for (i = n; i >= 1; i--)
{
push1(i);
}
toh(n);
return 0;
}```

### Sample Output:

```enter the number of disks
5

Tower1->        1       2       3       4       5
Tower2->
Tower3->

Tower1->        2       3       4       5
Tower2->
Tower3->        1

Tower1->        3       4       5
Tower2->        2
Tower3->        1

Tower1->        3       4       5
Tower2->        1       2
Tower3->

Tower1->        4       5
Tower2->        1       2
Tower3->        3

Tower1->        1       4       5
Tower2->        2
Tower3->        3

Tower1->        1       4       5
Tower2->
Tower3->        2       3

Tower1->        4       5
Tower2->
Tower3->        1       2       3

Tower1->        5
Tower2->        4
Tower3->        1       2       3

Tower1->        5
Tower2->        1       4
Tower3->        2       3

Tower1->        2       5
Tower2->        1       4
Tower3->        3

Tower1->        1       2       5
Tower2->        4
Tower3->        3

Tower1->        1       2       5
Tower2->        3       4
Tower3->

Tower1->        2       5
Tower2->        3       4
Tower3->        1

Tower1->        5
Tower2->        2       3       4
Tower3->        1

Tower1->        5
Tower2->        1       2       3       4
Tower3->

Tower1->
Tower2->        1       2       3       4
Tower3->        5

Tower1->        1
Tower2->        2       3       4
Tower3->        5

Tower1->        1
Tower2->        3       4
Tower3->        2       5

Tower1->
Tower2->        3       4
Tower3->        1       2       5

Tower1->        3
Tower2->        4
Tower3->        1       2       5

Tower1->        3
Tower2->        1       4
Tower3->        2       5

Tower1->        2       3
Tower2->        1       4
Tower3->        5

Tower1->        1       2       3
Tower2->        4
Tower3->        5

Tower1->        1       2       3
Tower2->
Tower3->        4       5

Tower1->        2       3
Tower2->
Tower3->        1       4       5

Tower1->        3
Tower2->        2
Tower3->        1       4       5

Tower1->        3
Tower2->        1       2
Tower3->        4       5

Tower1->
Tower2->        1       2
Tower3->        3       4       5

Tower1->        1
Tower2->        2
Tower3->        3       4       5

Tower1->        1
Tower2->
Tower3->        2       3       4       5

Tower1->
Tower2->
Tower3->        1       2       3       4       5```

## 5 thoughts on “Solution for Tower of Hanoi C++”

1. //http://proprogramming.org/solution-for-tower-of-hanoi-c/
//corrected by James H H Rodríguez
#include
using namespace std;
void towers(int, char, char, char);
void towers(int num, char frompeg, char topeg, char auxpeg)
{
if (num == 1)
{
cout<<" Move disk 1 from peg "<<frompeg<<" to peg "<<topeg<< endl;
return;
}
towers(num – 1, frompeg, auxpeg, topeg);
cout<<" Move disk "<<num<<" from peg "<<frompeg<<" to peg "<<topeg<< endl;
//cout << " Move disk " << n << " from " << src << " to " << dest << endl;
towers(num – 1, auxpeg, topeg, frompeg);
}
int main()
{
int num;
cout<>num;
towers(num, ‘A’, ‘C’, ‘B’);
system(“PAUSE”);
return 0;
}

2. Enter the mumber or disks : 3
Move disk 1 from SRC to DEST
Move disk 2 from SRC to AUX
Move disk 1 from DEST to AUX
Move disk 3 from SRC to DEST
Move disk 1 from AUX to SRC
Move disk 2 from AUX to DEST
Move disk 1 from SRC to DEST
Presione una tecla para continuar . . .

3. venki says:

I am need to implement tours of hanoi
without recursion

4. lakshmi says:

how this code will executed… about tracing?

5. lakshmi says:

how to trace this code??