Step by Step solution about How to resolve the algorithm Continued fraction/Arithmetic/Construct from rational number step by step in the C programming language

The code you provided is a C program that implements a function called r2cf to convert a fraction to a continued fraction. A continued fraction is a representation of a number as a sequence of fractions, where each fraction has a numerator and a denominator.

The r2cf function takes two pointers to integers as arguments, representing the numerator and denominator of a fraction. It uses integer division to compute the quotient of the numerator by the denominator, and then updates the numerator and denominator to be the remainder of the division and the original denominator, respectively. The function returns the quotient.

The main function of the program runs the r2cf function on a series of example fractions, including the square root of 2 and pi. It prints the results of the function, which are the sequence of quotients that represent the continued fraction expansion of the original fraction, For example, the output for the fraction 1/2 is "0 1", which means that the continued fraction expansion of 1/2 is 0 + 1/(1 + 0). The output for the square root of 2 is "1 4 1 1 4 1 1 4 ...", which means that the continued fraction expansion of the square root of 2 is 1 + 1/(4 + 1/(1 + 1/(4 + 1/(1 + 1/(4 + ...))))).

Here is a breakdown of the code:

• The fraction struct is used to represent a fraction with a numerator and a denominator. Several arrays of fraction structs are defined to represent different examples, including the square root of 2 and pi.

• The r2cf function implements the algorithm to convert a fraction to a continued fraction. It takes two pointers to integers as arguments, representing the numerator and denominator of a fraction. It uses integer division to compute the quotient of the numerator by the denominator, and then updates the numerator and denominator to be the remainder of the division and the original denominator, respectively. The function returns the quotient.

• The main function of the program runs the r2cf function on a series of example fractions, including the square root of 2 and pi. It prints the results of the function, which are the sequence of quotients that represent the continued fraction expansion of the original fraction.

#include<stdio.h>

typedef struct{
	int num,den;
	}fraction;

fraction examples[] = {{1,2}, {3,1}, {23,8}, {13,11}, {22,7}, {-151,77}}; 
fraction sqrt2[] = {{14142,10000}, {141421,100000}, {1414214,1000000}, {14142136,10000000}};
fraction pi[] = {{31,10}, {314,100}, {3142,1000}, {31428,10000}, {314285,100000}, {3142857,1000000}, {31428571,10000000}, {314285714,100000000}};

int r2cf(int *numerator,int *denominator)
{
	int quotient=0,temp;
	
	if(denominator != 0)
	{
		quotient = *numerator / *denominator;
		
		temp = *numerator;
		
		*numerator = *denominator;
		
		*denominator = temp % *denominator;
	}
	
	return quotient;
}

int main()
{
	int i;
	
	printf("Running the examples :");
	
	for(i=0;i<sizeof(examples)/sizeof(fraction);i++)
	{
		printf("\nFor N = %d, D = %d :",examples[i].num,examples[i].den);
		
		while(examples[i].den != 0){
			printf(" %d ",r2cf(&examples[i].num,&examples[i].den));
			}
	}
	
	printf("\n\nRunning for %c2 :",251); /* 251 is the ASCII code for the square root symbol */
	
	for(i=0;i<sizeof(sqrt2)/sizeof(fraction);i++)
	{
		printf("\nFor N = %d, D = %d :",sqrt2[i].num,sqrt2[i].den);
		
		while(sqrt2[i].den != 0){
			printf(" %d ",r2cf(&sqrt2[i].num,&sqrt2[i].den));
			}
	}
	
	printf("\n\nRunning for %c :",227); /* 227 is the ASCII code for Pi's symbol */
	
	for(i=0;i<sizeof(pi)/sizeof(fraction);i++)
	{
		printf("\nFor N = %d, D = %d :",pi[i].num,pi[i].den);
		
		while(pi[i].den != 0){
			printf(" %d ",r2cf(&pi[i].num,&pi[i].den));
			}
	}
	
	
	
	return 0;
}