/**********************************************
* Section : 10
* Roll No. : 20CS10000 / 20CS30000
* Name : Aritra Hazra
* Assignment No : 3
* Description : Continued Fraction Explorations
* Date : 20-Apr-2021
**********************************************/

#include<stdio.h>
#include<math.h>

#define ERROR 0.000001
#define MAX_FRACTION 1000000

int main()
{
    int choice;
    unsigned int x, y, num, i, temp, gcd, rem;
    double root, next, b, c, real;
    do{ // menu of options
        printf("\n====================================================\
                \n++ Determine the Following using Continued Fraction:\
                \n  --> 1. Representation of Rational Fractions\
                \n  --> 2. Representation of Finite Reals\
                \n  --> 3. Square Root of Positive Integer\
                \n  --> 4. Roots of Quadratic Equation\
                \n  --> 0. Exit\
                \n====================================================");
        printf("\n++ Enter Your Choice: ");
        scanf("%d", &choice);
        
        switch(choice) { // choice selection
            case 0: // exit from program loop
                printf("\n** Thank You! Bye ...\n");
                break;
            
            case 1: // representing rationals using continued fractions
                printf("\n++ Enter Two Positive Integers (space-separated): ");
                scanf("%u%u", &x, &y);
                printf("\n** The Continued Fraction Representation of %u/%u = ", x, y);
                // computing GCD of x and y
                gcd = x; temp = y;
                while(temp > 0){
                  rem = gcd % temp;
                  gcd = temp;
                  temp = rem;
                }
                // normalized fraction
                x = x/gcd; y = y/gcd;
                printf("%u/%u : [ ", x, y);
                do { // iterating over quotients and reminders in continued fraction
                    printf("%u ", x/y);
                    temp = y;
                    y = x - y*(x/y);
                    x = temp;
                }while(y > 0);
                printf("]\n");
                break;
            
            case 2: // representing finite reals using continued fractions
                printf("\n++ Enter a Positive Real Number: ");
                scanf("%lf", &real);
                printf("\n** The Continued Fraction Representation of %lf: [ %u ", real, (unsigned int)real);
                // extracting the fractional part (6 digits after decimal point)
                x = MAX_FRACTION; y = real*MAX_FRACTION - (unsigned int)real*MAX_FRACTION;
                do { // iterating over quotients and reminders in continued fraction
                    printf("%u ", x/y);
                    temp = y;
                    y = x - y*(x/y);
                    x = temp;
                }while(y > 0);
                printf("]\n");
                break;
            
            case 3: // square-root determination
                printf("\n++ Enter a Positive Integer: ");
                scanf("%u", &num);
                printf("\n** Iteration-wise Square-Root Values:");
                next = 1.0; i = 0;
                do{ // iterating over root values through continued fraction
                    root = next;
                    next = 1.0 + (num-1)/(1.0+root);
                    printf("\nIteration ## %6u : SQRT(%u) = %lf", i+1, num, root);
                    i++;
                }while(fabs(next-root) > ERROR);
                printf("\n\n** The Final Square-Root = %lf", next);
                printf("\n** The MATH FORMULA Square-Root = %lf", sqrt(num)); // formula wise square root determination
                printf("\n");
                break;
            
            case 4: // quadratic equation root determination
                printf("\n++ For Quadratic Equation x^2 + Bx + C = 0,\
                        \n   Enter B and C (space-separated real-values ensuring B^2 >= 4C) : " );
                scanf("%lf%lf", &b, &c);
                printf("\n** The Quadratic Equation: x^2 + (%lf)x + (%lf) = 0", b, c);
                printf("\n** Iteration-wise Root Values:");
                next = b; i = 0;
                do{ // iterating over root values through continued fraction
                    root = next;
                    next = -b - c/root;
                    printf("\nIteration ## %6u : Root = %lf", i+1, root);
                    i++;
                }while(fabs(next-root) > ERROR);
                printf("\n\n** The Final Root = (%lf)\
                        \n   The Other Root = (%lf)", next, c/next); // finding other root
                printf("\n** The MATH FORMULA Roots = (%lf) and (%lf)", (-b+sqrt(b*b-4*c))/2, (-b-sqrt(b*b-4*c))/2); // formula wise roots determination
                printf("\n");
                break;
            
            default: // handling wrong choices
                printf("\n** Wrong Choice Entered! Please Try Again ...\n");
                break;
        }
    }while(choice != 0);

    return 0;
}