Given two integers N and K representing number of trials and number of total threads in parallel processing. The task is to find the estimated value of PI using the Monte Carlo algorithm using the Open Multi-processing (OpenMP) technique of parallelizing sections of the program.
Examples:
Input: N = 100000, K = 8
Output: Final Estimation of Pi = 3.146600Input: N = 10, K = 8
Output: Final Estimation of Pi = 3.24Input: N = 100, K = 8
Output: Final Estimation of Pi = 3.0916
Approach: The above given problem Estimating the value of Pi using Monte Carlo is already been solved using standard algorithm. Here the idea is to use parallel computing using OpenMp to solve the problem. Follow the steps below to solve the problem:
- Initialize 3 variables say x, y, and d to store the X and Y co-ordinates of a random point and the square of the distance of the random point from origin.
- Initialize 2 variables say pCircle and pSquare with values 0 to store the points lying inside circle of radius 0.5 and square of side length 1.
- Now starts the parallel processing with OpenMp together with reduction() of the following section:
- Iterate over the range [0, N] and find x and y in each iteration using srand48() and drand48() then find the square of distance of point (x, y) from origin and then if the distance is less than or equal to 1 then increment pCircle by 1.
- In each iteration of the above step, increment the count of pSquare by 1.
- Finally, after the above step calculate the value of estimated pi as below and then print the obtained value.
- Pi = 4.0 * ((double)pCircle / (double)(pSquare))
Below is the implementation of the above approach:
C++
// C++ program for the above approach#include <iostream>using namespace std;// Function to find estimated// value of PI using Monte// Carlo algorithmvoid 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 Codeint 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 <omp.h>#include <stdio.h>#include <stdlib.h>#include <time.h>// Function to find estimated// value of PI using Monte// Carlo algorithmvoid 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 Codeint main(){ // Input int N = 100000; int K = 8; // Function call monteCarlo(N, K);} |
Java
// Java implementation of the approachimport java.util.*;class GFG { // Function to find estimated // value of PI using Monte // Carlo algorithm static 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; // Initializes random points // with a seed Random rand = new Random(); // Loop through each iteration for (int i = 0; i < N; i++) { // Finds random X co-ordinate x = rand.nextDouble(); // Finds random Y co-ordinate y = rand.nextDouble(); // 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 of pi System.out.println("Final Estimation of Pi = " + pi); } // Driver Code public static void main(String[] args) { // Input int N = 100000; int K = 8; // Function call monteCarlo(N, K); }}// This code is contributed by phasing17 |
Python3
# Python3 program for the above approachimport randomimport time# Function to find estimated# value of PI using Monte# Carlo algorithmdef monteCarlo(N, K): # Stores X and Y coordinates # of a random point x = 0 y = 0 # Stores distance of a random # point from origin d = 0 # Stores number of points # lying inside circle pCircle = 0 # Stores number of points # lying inside square pSquare = 0 # Initializes random points # with a seed random.seed(time.time()) for i in range(N): # Finds random X co-ordinate x = random.random() # Finds random X co-ordinate y = random.random() # 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 += 1 # Increment pSquare by 1 pSquare += 1 # Stores the estimated value of PI pi = 4.0 * (pCircle / pSquare) # Prints the value in pi print("Final Estimation of Pi = ", pi)# Driver Code# InputN = 100000K = 8# Function callmonteCarlo(N, K)# This code is contributed by phasing17. |
C#
// C# equivalent of the above codeusing System;namespace MonteCarloPi { class GFG { // Function to find estimated // value of PI using Monte // Carlo algorithm static 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; // Initializes random points // with a seed Random rand = new Random(); // Loop through each iteration for (int i = 0; i < N; i++) { // Finds random X co-ordinate x = rand.NextDouble(); // Finds random Y co-ordinate y = rand.NextDouble(); // 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 of pi Console.WriteLine("Final Estimation of Pi = " + pi); } // Driver Code static void Main(string[] args) { // Input int N = 100000; int K = 8; // Function call monteCarlo(N, K); } }}// This code is contributed by phasing17 |
Javascript
// JS program for the above approach// Function to find estimated value of PI using Monte Carlo algorithmfunction monteCarlo(N, K) { // Stores X and Y coordinates of a random point let x = 0; let y = 0; // Stores distance of a random point from origin let d = 0; // Stores number of points lying inside circle let pCircle = 0; // Stores number of points lying inside square let pSquare = 0; let pi; for (let i = 0; i < N; i++) { // Finds random X co-ordinate x = Math.random(); // Finds random Y co-ordinate y = Math.random(); // 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 pi = 4.0 * (pCircle / pSquare); } // Prints the value of pi console.log("Final Estimation of Pi = " + pi);}// Driver Code// Inputconst N = 100000;const K = 8;// Function callmonteCarlo(N, K);// This code is contributed by phasing17. |
Output
Final Estimation of Pi = 3.146600
Output of above C program
Time Complexity: O(N*K)
Auxiliary Space: O(1)
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