使用 Monte Carlo 估计 Pi 的值 |并行计算方法

给定两个整数N和K ，表示并行处理中的试验次数和总线程数。任务是使用 Monte Carlo 算法找到 PI 的估计值，该算法使用并行化程序部分的开放式多处理 (OpenMP) 技术。

例子：

Input: N = 100000, K = 8
Output: Final Estimation of Pi = 3.146600

Input: N = 10, K = 8
Output: Final Estimation of Pi = 3.24

Input: N = 100, K = 8
Output: Final Estimation of Pi = 3.0916

编程需要懂一点英语

方法：上面给出的使用蒙特卡洛估计 Pi 值的问题已经使用标准算法解决了。这里的想法是使用 OpenMp 的并行计算来解决问题。请按照以下步骤解决问题：

初始化 3 个变量，例如x、y和d ，以存储随机点的X和Y坐标以及随机点到原点的距离的平方。
初始化 2 个变量，例如pCircle和pSquare ，其值为0以存储位于半径为 0.5的圆和边长为1的正方形内的点。
现在开始使用 OpenMp 和以下部分的 reduction() 进行并行处理：
- 迭代范围[0, N]并在每次迭代中使用srand48()和drand48()找到x和y ，然后找到点 ( x, y)与原点的距离的平方，然后如果距离小于或等于到1然后将pCircle增加1 。
- 在上述步骤的每次迭代中，将pSquare的计数增加1 。
最后，经过上述步骤计算估计的 pi 的值如下，然后打印得到的值。
- Pi = 4.0 * ((double)pCircle / (double)(pSquare))

下面是上述方法的实现：

C++

// C++ program for the above approach
#include 
using namespace std;
 
// Function to find estimated
// value of PI using Monte
// Carlo algorithm
void monteCarlo(int N, int K)
{
   
    // Stores X and Y coordinates
    // of a random point
    double x, y;
   
    // Stores distance of a random
    // point from origin
    double d;
 
    // Stores number of points
    // lying inside circle
    int pCircle = 0;
 
    // Stores number of points
    // lying inside square
    int pSquare = 0;
    int i = 0;
 
// Parallel calculation of random
// points lying inside a circle
#pragma omp parallel firstprivate(x, y, d, i) reduction(+ : pCircle, pSquare) num_threads(K)
    {
       
        // Initializes random points
        // with a seed
        srand48((int)time(NULL));
 
        for (i = 0; i < N; i++)
        {
           
            // Finds random X co-ordinate
            x = (double)drand48();
 
            // Finds random X co-ordinate
            y = (double)drand48();
 
            // Finds the square of distance
            // of point (x, y) from origin
            d = ((x * x) + (y * y));
 
            // If d is less than or
            // equal to 1
            if (d <= 1)
            {
               
                // Increment pCircle by 1
                pCircle++;
            }
           
            // Increment pSquare by 1
            pSquare++;
        }
    }
   
    // Stores the estimated value of PI
    double pi = 4.0 * ((double)pCircle / (double)(pSquare));
 
    // Prints the value in pi
    cout << "Final Estimation of Pi = "<< pi;
}
 
// Driver Code
int main()
{
   
    // Input
    int N = 100000;
    int K = 8;
   
    // Function call
    monteCarlo(N, K);
}
 
// This code is contributed by shivanisinghss2110

C

// C program for the above approach
 
#include 
#include 
#include 
#include 
 
// Function to find estimated
// value of PI using Monte
// Carlo algorithm
void monteCarlo(int N, int K)
{
    // Stores X and Y coordinates
    // of a random point
    double x, y;
    // Stores distance of a random
    // point from origin
    double d;
 
    // Stores number of points
    // lying inside circle
    int pCircle = 0;
 
    // Stores number of points
    // lying inside square
    int pSquare = 0;
 
    int i = 0;
 
// Parallel calculation of random
// points lying inside a circle
#pragma omp parallel firstprivate(x, y, d, i) reduction(+ : pCircle, pSquare) num_threads(K)
    {
        // Initializes random points
        // with a seed
        srand48((int)time(NULL));
 
        for (i = 0; i < N; i++) {
            // Finds random X co-ordinate
            x = (double)drand48();
 
            // Finds random X co-ordinate
            y = (double)drand48();
 
            // Finds the square of distance
            // of point (x, y) from origin
            d = ((x * x) + (y * y));
 
            // If d is less than or
            // equal to 1
            if (d <= 1) {
                // Increment pCircle by 1
                pCircle++;
            }
            // Increment pSquare by 1
            pSquare++;
        }
    }
    // Stores the estimated value of PI
    double pi = 4.0 * ((double)pCircle / (double)(pSquare));
 
    // Prints the value in pi
    printf("Final Estimation of Pi = %f\n", pi);
}
 
// Driver Code
int main()
{
    // Input
    int N = 100000;
    int K = 8;
    // Function call
    monteCarlo(N, K);
}

输出

Final Estimation of Pi = 3.146600

上述C程序的输出

时间复杂度： O(N*K)
辅助空间： O(1)