Recursion Algorithm

In this tutorial we will learn to solve Tower of Hanoi using recursion.

Tower of Hanoi is a very famous game. In this game there are 3 pegs and N number of disks placed one over the other in decreasing size.

The objective of this game is to move the disks one by one from the first peg to the last peg. And there is only **ONE** condition, we can not place a bigger disk on top of a smaller disk.

To solve this game we will follow 3 simple steps recursively.

```
We will use a general notation:
T(N, Beg, Aux, End)
Where,
T denotes our procedure
N denotes the number of disks
Beg is the initial peg
Aux is the auxiliary peg
End is the final peg
```

Following are the recursive steps to solve Tower of Hanoi.

```
1. T(N-1, Beg, End, Aux)
2. T(1, Beg, Aux, End)
3. T(N-1, Aux, Beg, End)
Step 1 says: Move top (N-1) disks from Beg to Aux peg.
Step 2 says: Move 1 disk from Beg to End peg.
Step 3 says: Move top (N-1) disks from Aux to End peg.
```

```
/*
N = Number of disks
Beg, Aux, End are the pegs
*/
T(N, Beg, Aux, End)
Begin
if N = 1 then
Print: Beg --> End;
else
Call T(N-1, Beg, End, Aux);
Call T(1, Beg, Aux, End);
Call T(N-1, Aux, Beg, End);
endif
End
```

If there are N disks then we can solve the game in minimum 2^{N} – 1 moves.

```
Example: N = 3
Minimum moves required = 2
```^{3} – 1 = 7

```
#include <stdio.h>
void t(int n, char beg, char aux, char end);
int main(){
printf("Moves\n");
t(3, 'a', 'b', 'c'); //N = 3 (no. of disks) a, b, c are the three pegs
return 0;
}//main() ends here
void t(int n, char beg, char aux, char end){
if(n == 1){
printf("%c --> %c\n", beg, end);
}else{
t(n-1, beg, end, aux);
t(1, beg, aux, end);
t(n-1, aux, beg, end);
}
}//t() ends here
```

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