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Recursive Tower of Hanoi using 4 pegs / rods
  • Difficulty Level : Hard
  • Last Updated : 18 Aug, 2020

Tower of Hanoi is a mathematical puzzle. Traditionally, It consists of three poles and a number of disks of different sizes which can slide onto any poles. The puzzle starts with the disk in a neat stack in ascending order of size in one pole, the smallest at the top thus making a conical shape. The objective of the puzzle is to move all the disks from one pole (say ‘source pole’) to another pole (say ‘destination pole’) with the help of third pole (say auxiliary pole).

The puzzle has the following two rules:

1. You can’t place a larger disk onto smaller disk
2. Only one disk can be moved at a time

We’ve already discussed recursive solution for Tower of Hanoi with time complexity O(2^n). Using 4 rods, same approach shows significant decrease in time complexity.

Examples:



Input : 3
Output :
Move disk 1 from rod A to rod B
Move disk 2 from rod A to rod C
Move disk 3 from rod A to rod D
Move disk 2 from rod C to rod D
Move disk 1 from rod B to rod D

Input : 5
Output : 
Move disk 1 from rod A to rod C
Move disk 2 from rod A to rod D
Move disk 3 from rod A to rod B
Move disk 2 from rod D to rod B
Move disk 1 from rod C to rod B
Move disk 4 from rod A to rod C
Move disk 5 from rod A to rod D
Move disk 4 from rod C to rod D
Move disk 1 from rod B to rod A
Move disk 2 from rod B to rod C
Move disk 3 from rod B to rod D
Move disk 2 from rod C to rod D
Move disk 1 from rod A to rod D

C++




// C++ Recursive program for Tower of Hanoi
#include
using namespace std;

// Recursive function to solve Tower
// of Hanoi puzzle
void towerOfHanoi(int n, char from_rod, char to_rod,
char aux_rod1, char aux_rod2)
{
if (n == 0)
return;
if (n == 1)
{
cout << "\n Move disk" <


C




// Recursive program for Tower of Hanoi
#include

// Recursive function to solve Tower
// of Hanoi puzzle
void towerOfHanoi(int n, char from_rod, char to_rod,
char aux_rod1, char aux_rod2)
{
if (n == 0)
return;
if (n == 1) {
printf(“\n Move disk %d from rod %c to rod %c”,
n, from_rod, to_rod);
return;
}

towerOfHanoi(n – 2, from_rod, aux_rod1, aux_rod2,
to_rod);
printf(“\n Move disk %d from rod %c to rod %c “,
n – 1, from_rod, aux_rod2);
printf(“\n Move disk %d from rod %c to rod %c “,
n, from_rod, to_rod);
printf(“\n Move disk %d from rod %c to rod %c “,
n – 1, aux_rod2, to_rod);
towerOfHanoi(n – 2, aux_rod1, to_rod, from_rod,
aux_rod2);
}

// driver program
int main()
{
int n = 4; // Number of disks

// A, B, C and D are names of rods
towerOfHanoi(n, ‘A’, ‘D’, ‘B’, ‘C’);
return 0;
}


Java




// Recursive program for Tower of Hanoi
public class GFG {

// recursive function to solve
// Tower of Hanoi puzzle
static void towerOfHanoi(int n, char from_rod,
char to_rod, char aux_rod1,
char aux_rod2)
{
if (n == 0)
return;
if (n == 1) {
System.out.println(“Move disk ” + n +
” from rod ” + from_rod +
” to rod ” + to_rod);
return;
}



towerOfHanoi(n – 2, from_rod, aux_rod1, aux_rod2,
to_rod);
System.out.println(“Move disk ” + (n – 1) +
” from rod ” + from_rod +
” to rod ” + aux_rod2);
System.out.println(“Move disk ” + n +
” from rod ” + from_rod +
” to rod ” + to_rod);
System.out.println(“Move disk ” + (n – 1) +
” from rod ” + aux_rod2 +
” to rod ” + to_rod);
towerOfHanoi(n – 2, aux_rod1, to_rod, from_rod,
aux_rod2);
}

// Driver method
public static void main(String args[])
{
int n = 4; // Number of disks

// A, B, C and D are names of rods
towerOfHanoi(n, ‘A’, ‘D’, ‘B’, ‘C’);
}
}


Python 3




# Recursive program for Tower of Hanoi

# Recursive function to solve Tower
# of Hanoi puzzle
def towerOfHanoi(n, from_rod, to_rod, aux_rod1,
aux_rod2):

if (n == 0):
return
if (n == 1):
print(“Move disk”, n, “from rod”,
from_rod, “c to rod”, to_rod)
return

towerOfHanoi(n – 2, from_rod, aux_rod1,
aux_rod2, to_rod)
print(“Move disk”, n-1, “from rod”, from_rod,
“c to rod”, aux_rod2)

print(“Move disk”, n, “from rod”, from_rod,
“c to rod”, to_rod)

print(“Move disk”, n-1, “from rod”, aux_rod2,
“c to rod”, to_rod)

towerOfHanoi(n – 2, aux_rod1, to_rod,
from_rod, aux_rod2)

# driver program
n = 4 # Number of disks

# A, B, C and D are names of rods
towerOfHanoi(n, ‘A’, ‘D’, ‘B’, ‘C’)

# This code is contributed by Smitha.


C#




// Recursive program for Tower of Hanoi
using System;

public class GFG {

// recursive function to solve
// Tower of Hanoi puzzle
static void towerOfHanoi(int n, char from_rod,
char to_rod, char aux_rod1,
char aux_rod2)
{
if (n == 0)
return;
if (n == 1) {
Console.WriteLine(“Move disk ” + n +
” from rod ” + from_rod +
” to rod ” + to_rod);
return;
}

towerOfHanoi(n – 2, from_rod, aux_rod1,
aux_rod2, to_rod);
Console.WriteLine(“Move disk ” + (n – 1)
+ ” from rod ” + from_rod
+ ” to rod ” + aux_rod2);
Console.WriteLine(“Move disk ” + n +
” from rod ” + from_rod
+ ” to rod ” + to_rod);
Console.WriteLine(“Move disk ” + (n – 1)
+ ” from rod ” + aux_rod2
+ ” to rod ” + to_rod);
towerOfHanoi(n – 2, aux_rod1, to_rod,
from_rod, aux_rod2);
}

// Driver method
public static void Main()
{
int n = 4; // Number of disks

// A, B, C and D are names of rods
towerOfHanoi(n, ‘A’, ‘D’, ‘B’, ‘C’);
}
}

// This code is contributed by Anant Agarwal.


PHP






Output:

Move disk 1 from rod A to rod D
Move disk 2 from rod A to rod B
Move disk 1 from rod D to rod B
Move disk 3 from rod A to rod C
Move disk 4 from rod A to rod D
Move disk 3 from rod C to rod D
Move disk 1 from rod B to rod C
Move disk 2 from rod B to rod D
Move disk 1 from rod C to rod D

Time Complexity: O(2^(N/2))

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