利用蒙特卡罗方法求积分

函数y=f(x)=sin(x)/x 在区间[1,2]的积分，refer to http://www.cnblogs.com/leoo2sk/archive/2009/05/29/1491526.html

代码如下：

#include<iostream>
#include<cmath>
#include<ctime>
#define COUNT 500000 
using namespace std;
bool InCircle(double x, double y)
{
        if( sin(x) / x >= y )
        {
                return true;
        }
        else
        {
                return false;
        }
}
int main()
{
        double x, y;
        int a = 1, b = 2;
        int num = 0;
        int i;
        srand((unsigned)time(NULL));
        for(i = 0; i < COUNT; i++)
        {
                x=rand() * 1.0 / RAND_MAX;
                y=rand() * 1.0 / RAND_MAX;
                x = a + (b - a) * x;
                y = (b - a) * y;
                if(InCircle(x,y)) 
                {
                        num++;
                }
        }
        double res = (double)num / COUNT;
        cout << "result is " << res << endl;
}

结果如下：

/home/a/j/nomad2:./a.out 
result is 0.658302

思想：将面积转化为求落在函数下方的点与长度为(b-a)的正方形内的点数之比，类似的还有求圆周率。

#include<iostream>
#include<cmath>
#include<ctime>
#define COUNT 500000 
using namespace std;
bool InCircle(double x,double y)
{
    if((x*x+y*y)<=1)return true;
    return false;
}
int main()
{
    double x,y;
    int num=0;
    int i;
    srand((unsigned)time(NULL));
    for(i=0;i<COUNT;i++)
    {
        x=rand()*1.0/RAND_MAX;
        y=rand()*1.0/RAND_MAX;
        if(InCircle(x,y)) num++;
    }
    cout<<"PI:"<<(num*4.0)/COUNT<<endl;
}

运行结果：

/home/a/j/nomad2:./a.out 
PI:3.14107