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  1. #include <iostream>
  2. #include <iomanip>
  3. #include <random>
  4. #include <cmath>
  5.  
  6. using namespace std;
  7.  
  8. // Funkcja do obliczania pi metodą Monte Carlo
  9. long double monteCarloPi(long long n) {
  10.     random_device rd;
  11.     mt19937_64 gen(rd());
  12.     uniform_real_distribution<long double> dist(-1.0L, 1.0L);
  13.  
  14.     long long inside = 0;
  15.  
  16.     for (long long i = 0; i < n; i++) {
  17.         long double x = dist(gen);
  18.         long double y = dist(gen);
  19.  
  20.         if (x * x + y * y <= 1.0L)
  21.             inside++;
  22.     }
  23.  
  24.     return 4.0L * inside / n;
  25. }
  26.  
  27. // Funkcja f(x) = 4/(1+x^2)
  28. long double f(long double x) {
  29.     return 4.0L / (1.0L + x * x);
  30. }
  31.  
  32. // Metoda prostokątów
  33. long double rectangleMethod(long long n) {
  34.     long double h = 1.0L / n;
  35.     long double sum = 0.0L;
  36.  
  37.     for (long long i = 0; i < n; i++) {
  38.         long double x = (i + 0.5L) * h;  // środek przedziału
  39.         sum += f(x);
  40.     }
  41.  
  42.     return sum * h;
  43. }
  44.  
  45. // Metoda trapezów
  46. long double trapezoidalMethod(long long n) {
  47.     long double h = 1.0L / n;
  48.     long double sum = (f(0.0L) + f(1.0L)) / 2.0L;
  49.  
  50.     for (long long i = 1; i < n; i++) {
  51.         long double x = i * h;
  52.         sum += f(x);
  53.     }
  54.  
  55.     return sum * h;
  56. }
  57.  
  58. int main() {
  59.     const long long n = 1000000;
  60.  
  61.     cout << fixed << setprecision(20);
  62.  
  63.     long double piMonteCarlo = monteCarloPi(n);
  64.     long double piRectangle = rectangleMethod(n);
  65.     long double piTrapezoid = trapezoidalMethod(n);
  66.  
  67.     cout << "Liczba punktów (Monte Carlo): " << n << endl;
  68.     cout << "Pi (Monte Carlo):      " << piMonteCarlo << endl;
  69.     cout << "Pi (Prostokaty):       " << piRectangle << endl;
  70.     cout << "Pi (Trapezy):          " << piTrapezoid << endl;
  71.  
  72.     return 0;
  73. }
Success #stdin #stdout 0.05s 5320KB
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stdin
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Standard input is empty
stdout
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Liczba punktów (Monte Carlo): 1000000
Pi (Monte Carlo):      3.14089599999999999997
Pi (Prostokaty):       3.14159265358987658243
Pi (Trapezy):          3.14159265358962659187
https://ideone.com/sMgURY
language:
C++ (gcc 8.3)
created:
16 hours ago
visibility:
public

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