C Tower of Hanoi,

Question

I wrote the code, but I don't understand why it works. For example, when Hanoi is recursively called the second time (on pythontutor.com's C visualization):

disk - 1 = 1, start = 1, end = 3, and temp = 2.

I think it should be: disk - 1 = 1, start = 1, end (which is now temp) = 2, and temp (which is now end) = 3.

Why is my assumption about the arguments of the function wrong? I was playing around with the order of the last three lines of code in the Hanoi function when it printed out the correct answer, so I don't know how I did it. I appreciate any help you can provide.

#include <stdio.h> //inputs and more

void hanoi(int disks, int start, int end, int temp);

int main(void)
{

    int d = 3, s = 1, e = 3, t = 2;
    
    hanoi(d, s, e, t);

    return 0;

}//end of main function

void hanoi(int disks, int start, int end, int temp)
{
    if (1 == disks) 
    {
        printf("%d --> %d\n", start, end);
    }
    else 
    {
        hanoi(disks - 1, start, temp, end);
        printf("%d --> %d\n", start, end);
        hanoi(disks - 1, temp, end, start);
    }
}

The C code is correct and prints:

1 --> 3
1 --> 2
3 --> 2
1 --> 3
2 --> 1
2 --> 3
1 --> 3

Answer 1

The initial call is:

  hanoi(3, 1, 3, 2)

Thus the first recursive call is:

  hanoi(3-1, 1, 2, 3)

and the second recursive call is:

  hanoi(3-1-1, 1, 3, 2)

The last 3 lines of the hanoi() function are correct as they are now. Try to visualize it: To move D disks from "start" to "end":

• first move D-1 disks from "start" to "temp", then
• move the last (i.e. the largest) disk from "start" to "end", and finally
• move the D-1 disks from "temp" to "end"

This corresponds to the three lines of code.