polygon.cpp

输入n条边的长度

#include <string>
#include <iostream>
#include <math.h>
#include <algorithm>
#include <vector>

using namespace std ;

const double pi = 3.1415926 ;
const double m_min = 0.0000001 ;

double area(double a ,double b,double c)
{
	double s = (a+b+c)/2 ;
	return sqrt(s*(s-a)*(s-b)*(s-c)) ;//There is a error in function area
}

double radian(double x,double r)
{
	return 2*asin(x/(2*r)) ;
} 

double radian_A(vector<double>A,double r)
{
	double num = 0 ;
	for(int i = 0;i<=A.size()-1 ;i++)
		num = num + radian(A[i],r) ;
	return num ;
}

int main()
{
	double x ;
	double max = 0 ;
	double sum = 0 ;
	int i = 0 ;
	int n = -1 ;
	int m = 0 ;
    double p_area = 0 ;
	vector <double> A ;
	while(cin>>x)
	{   n++ ; 
		sum += x ;
		if(x>max)
		{
			max = x ;
			m = n ;
		}
		A.push_back(x) ;
	}
	double R = max/2 ;
	double radi = 0 ;
	double low = 0 ;
	double high = 0 ;
	for(i = 0 ; i<=A.size()-1 ; i++)
	{
		if(i!=m)
		radi = radi + radian(A[i],R) ;
	}
	if(radi <= pi)
	{
		low = R ;
		high = sum/2 ;
		while(fabs(radian_A(A,R)-2*radian(max,R))>=m_min)
		{
			R = (low+high)/2 ;
			if(radian_A(A,R) < 2*radian(max,R))
			{
				low = R ;
				
			}   
			else
			{
				high = R ;
		
			}
		}
		for(i = 0 ;i<=A.size()-1&&(i!=m) ;i++)
			p_area += area(R,R,A[i]) ;
		p_area -=area(R,R,max) ;
    }
	else 
	{
        low = R ;
	    high = sum/2 ;
		while(fabs(radian_A(A,R)-2*pi)>=m_min)
		{
			R = (low+high)/2 ;
			if(radian_A(A,R) < 2*pi)
				high = R ;
			else
				low = R ;
		}
		for(i = 0 ;i<=A.size()-1 ;i++)
			p_area += area(R,R,A[i]) ;
	}
	cout << p_area <<endl;
	return 0 ;
}