/*
 * Recursive programming demonstration
 * CNIT 315
 * Tyler Philbrick
 * 2017-02-03
 */

#include <stdio.h>

/* Function prototypes */
int factorial(int);
int fibonacci(int);
void hanoi(int, char, char, char);

int main() {
	int sel;

	while (1) {

        printf("\nMenu:\n1: Factorial\n2: Fibonacci\n3: Tower of Hanoi\n");
        printf("4: Exit\nMake a choice: ");
        scanf("%i", &sel);
        fflush(stdin);
        while (sel > 4 || sel < 1) {
            printf("Invalid choice. Try again: ");
            scanf("%i", &sel);
            fflush(stdin);
        }
    
        /* Factorial */
		if (1 == sel) { 
			int fac_n;
			printf("Enter a desired number n for n! (0-12): ");
            scanf("%i", &fac_n);
            while (fac_n > 12 || fac_n < 0) {
                printf("Invalid choice. Try again: ");
                scanf("%i", &fac_n);
            }
			printf("\n%d! = %d\n", fac_n, factorial(fac_n));

        /* Fibonacci */
		} else if (2 == sel) {
			int fib_n;
			printf("Enter a desired number n for F_n (0-46): ");
            scanf("%i", &fib_n);
            while (fib_n > 46 || fib_n < 0) {
                printf("Invalid choice. Try again: ");
                scanf("%i", &fib_n);
            }
			printf("\nF_%d = %d\n", fib_n, fibonacci(fib_n));

        /* Hanoi */
		} else if (3 == sel) {
			int han_l;
			printf("Enter the number of disks for the Towe of Hanoi (1-1000): ");
            scanf("%i", &han_l);
            while (han_l > 1000 || han_l < 1) {
                printf("Invalid choice. Try again: ");
                scanf("%i", &han_l);
            }
			hanoi(han_l, 'A', 'B', 'C');

		} else if (4 == sel) {
			printf("Good bye!\n");
			break;

		} else {
			printf("Invalid choice. Try again.\n");
		}
	}
	return 0;
}

/* Return the product of all positive integers less than
 * or equal to n
 */
int factorial(int n) {
	if(1 >= n) {
		return 1;
	} else {
		return n * factorial(n-1);
	}
}

/* Return the n-th term of Fibonacci sequence */
int fibonacci(int n) {
	if(0 >= n) {
		return 0;
	} else if(1 == n) {
		return 1;
	} else {
		return fibonacci(n-1) + fibonacci(n-2);
	}
}

/* Move n discs from peg_a to peg_c. */
void hanoi(int n, char peg_a, char peg_b, char peg_c) {
	if(1 == n) {
		printf("Move the top disk: peg %c -> peg %c\n", peg_a, peg_c);
	} else { 
		hanoi(n-1, peg_a, peg_c, peg_b);
		hanoi(1, peg_a, peg_b, peg_c);
		hanoi(n-1, peg_b, peg_a, peg_c);
	}
}