/*
Program: binary-search-square-root.c (Report comments/bugs to chikh@yuntech.edu.tw)
Function:
*/
 
#include <stdio.h>
#include <stdlib.h>
#include <math.h>

int main()
{
	int    i;
	float  x;
    double a = 0, b, c;
    
    printf("\n*** 輸入x值(x>0)計算其平方根 ***\n\n輸入x => ");
    scanf("%f",&x);
    b = (x < 1)? 1: x;
    
    printf("\n二元搜尋法求解過程如下 ...\n\n迭代 區間                               中間值\n"
	       "----+----------------------------------+----------------\n");
    for (i = 0;;) {
    	c = (a+b)/2;
    	printf("#%-2d  [%.10f,%.10f]\t解=%.10f\n",++i,a,b,c);
    	if (fabs(c*c-x) < 1e-10) break;
    	if (c*c < x) 
			a = c;
    	else
    		b = c;
	}
	printf("\n[二元搜尋法] sqrt(%g)=%.10f，相較於C內建函數解誤差%.1f%%\n",x,c,fabs(c-sqrt(x))/sqrt(x)*100);
	
	system("pause");
	return 0;
}