exp2.cpp

使用C++用蒙特卡洛方法求解圆周率pi的值

#include <iostream>
#include <cmath>
#include <ctime>

using namespace std;


void fun1()                    //计算pi值
{
	int i,num=0;
	int total=10000000;
	double pi;
	srand(time(NULL));
	double x,y;
	for(i=1;i<=total;i++)
	{
		x=double(rand())/RAND_MAX;
		y=double(rand())/RAND_MAX;
		x=x*2-1;
		y=y*2-1;
		if(x*x+y*y<=1.0)
			num++;
	}
	pi=4.0*(double)num/total;
	cout<<"The calculated value of PI is "<<pi<<endl;
}

void fun2()                   //用撒点体积法求二重积分结果
{
	int i;
    int total=1000000;
	double sum=0;
	srand(time(NULL));
	double x,y;
	for(i=1;i<=total;i++)
	{
		x=double(rand())/RAND_MAX;
		y=double(rand())/RAND_MAX;
		y=y*2;
		sum=sum+x*x+y*y;		
	}
	sum=sum/total;
	cout<<"method1: The result of the integral is "<<2*sum<<endl;

}

void fun3()                    //用随机变量期望的方法求解二重积分结果
{
    int i,num=0;
    int total=1000000;
	double sum=0;
	srand(time(NULL));
	double x,y,z;
	for(i=1;i<=total;i++)
	{
		x=double(rand())/RAND_MAX;
		y=double(rand())/RAND_MAX;
		z=double(rand())/RAND_MAX;
		y=y*2;
		z=z*5;
		if(z<=x*x+y*y)
			num++;
	}
	
	cout<<"method2: The result of the integral is "<<10*double(num)/total<<endl;

}
void main()
{
	fun1();
	fun2();
	fun3();

}