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  1. #include <iostream>
  2. #include <iomanip>
  3. #include <random>
  4. #include <cmath>
  5.  
  6. using namespace std;
  7.  
  8. // Funkcja podcałkowa
  9. long double f(long double x) {
  10.     return 4.0L / (1.0L + x * x);
  11. }
  12.  
  13. // Metoda Monte Carlo
  14. long double monteCarloPi(unsigned long long points) {
  15.     mt19937_64 gen(random_device{}());
  16.     uniform_real_distribution<long double> dist(0.0L, 1.0L);
  17.  
  18.     unsigned long long inside = 0;
  19.  
  20.     for (unsigned long long i = 0; i < points; ++i) {
  21.         long double x = dist(gen);
  22.         long double y = dist(gen);
  23.  
  24.         if (x * x + y * y <= 1.0L)
  25.             ++inside;
  26.     }
  27.  
  28.     return 4.0L * inside / points;
  29. }
  30.  
  31. // Metoda prostokątów (lewych)
  32. long double rectangleMethod(unsigned long long n) {
  33.     long double h = 1.0L / n;
  34.     long double sum = 0.0L;
  35.  
  36.     for (unsigned long long i = 0; i < n; ++i) {
  37.         long double x = i * h;
  38.         sum += f(x);
  39.     }
  40.  
  41.     return h * sum;
  42. }
  43.  
  44. // Metoda trapezów
  45. long double trapezoidalMethod(unsigned long long n) {
  46.     long double h = 1.0L / n;
  47.     long double sum = (f(0.0L) + f(1.0L)) / 2.0L;
  48.  
  49.     for (unsigned long long i = 1; i < n; ++i) {
  50.         long double x = i * h;
  51.         sum += f(x);
  52.     }
  53.  
  54.     return h * sum;
  55. }
  56.  
  57. int main() {
  58.     // Liczba punktów/przedziałów
  59.     unsigned long long monteCarloPoints = 100000000;   // 1e8
  60.     unsigned long long intervals = 100000000;          // 1e8
  61.  
  62.     cout << fixed << setprecision(20);
  63.  
  64.     long double piMonteCarlo = monteCarloPi(monteCarloPoints);
  65.     long double piRectangle = rectangleMethod(intervals);
  66.     long double piTrapezoid = trapezoidalMethod(intervals);
  67.  
  68.     cout << "Monte Carlo:      " << piMonteCarlo << endl;
  69.     cout << "Metoda prostokatow: " << piRectangle << endl;
  70.     cout << "Metoda trapezow:    " << piTrapezoid << endl;
  71.  
  72.     return 0;
  73. }
Success #stdin #stdout 4.29s 5320KB
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stdin
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Standard input is empty
stdout
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Monte Carlo:      3.14163996000000000008
Metoda prostokatow: 3.14159266358979394796
Metoda trapezow:    3.14159265358979394801
https://ideone.com/IriiQt
language:
C++ (gcc 8.3)
created:
15 hours ago
visibility:
public

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