# Towers of Hanoi Recursive Ananlysis

Recursive program to towers of hanoi problem

```package algorithms.recursion;

/**
* @author ntallapa
*
*/
public class TowersOfHanoi {

/**
* This recursive algorithm takes (2^n-1) iterations to complete the task
*
* @param n number of disks
* @param startPole
* @param endPole
*/
public static void move(int n, int startPole, int endPole) {
if (n== 0){
return;
}
// here 6 is summation of poles, i.e, sigma(3) = 3+2+1 = 6
int intermediatePole = 6 - startPole - endPole;

// Move nā1 disks from disk 1 to disk 2, using disk 3 as a temporary holding area.
move(n-1, startPole, intermediatePole);

// Move the last disk (the largest) from disk 1 to disk 3.
System.out.println("Move " +n + " from " + startPole + " to " +endPole);

//  Move nā1 disks from disk 2 to disk 3, using disk 1 as a temporary holding area.
move(n-1, intermediatePole, endPole);
}

public static void main(String[] args) {
move(4, 1, 3);
}
}
```

For 2 discs we need 3 iterations, 3 discs we need 7 iterations, 4 discs we need 15 iterations, etc… from this it can be realized that to move ‘n’ discs we need (2^n)-1 iterations.

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