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  1. #include <iostream>
  2. #include <iomanip>
  3. #include <random>
  4. #include <cmath>
  5.  
  6. using namespace std;
  7.  
  8. // ==========================
  9. // MONTE CARLO
  10. // ==========================
  11. long double monteCarloPi(unsigned long long n)
  12. {
  13.     unsigned long long inside = 0;
  14.  
  15.     random_device rd;
  16.     mt19937_64 gen(rd());
  17.     uniform_real_distribution<long double> dist(0.0L, 1.0L);
  18.  
  19.     for (unsigned long long i = 0; i < n; ++i)
  20.     {
  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 * (long double)inside / (long double)n;
  29. }
  30.  
  31. // ==========================
  32. // METODA PROSTOKĄTÓW
  33. // π = 4 ∫₀¹ 1/(1+x²) dx
  34. // ==========================
  35. long double rectanglePi(unsigned long long n)
  36. {
  37.     long double sum = 0.0L;
  38.     long double h = 1.0L / n;
  39.  
  40.     for (unsigned long long i = 0; i < n; ++i)
  41.     {
  42.         long double x = i * h;
  43.         sum += 1.0L / (1.0L + x * x);
  44.     }
  45.  
  46.     return 4.0L * h * sum;
  47. }
  48.  
  49. // ==========================
  50. // METODA TRAPEZÓW
  51. // ==========================
  52. long double trapezoidPi(unsigned long long n)
  53. {
  54.     long double h = 1.0L / n;
  55.     long double sum = 0.0L;
  56.  
  57.     sum += 0.5L * (1.0L / (1.0L + 0.0L));       // f(0)
  58.     sum += 0.5L * (1.0L / (1.0L + 1.0L));       // f(1)
  59.  
  60.     for (unsigned long long i = 1; i < n; ++i)
  61.     {
  62.         long double x = i * h;
  63.         sum += 1.0L / (1.0L + x * x);
  64.     }
  65.  
  66.     return 4.0L * h * sum;
  67. }
  68.  
  69. // ==========================
  70. // MAIN
  71. // ==========================
  72. int main()
  73. {
  74.     unsigned long long n = 100000000; // liczba iteracji/podziałów
  75.  
  76.     long double piMonte = monteCarloPi(n);
  77.     long double piRect = rectanglePi(n);
  78.     long double piTrap = trapezoidPi(n);
  79.  
  80.     cout << fixed << setprecision(20);
  81.  
  82.     cout << "Monte Carlo:      " << piMonte << endl;
  83.     cout << "Metoda prostokatow: " << piRect << endl;
  84.     cout << "Metoda trapezow:    " << piTrap << endl;
  85.  
  86.     return 0;
  87. }
Success #stdin #stdout 4.41s 5312KB
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stdin
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Standard input is empty
stdout
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Monte Carlo:      3.14145372000000000002
Metoda prostokatow: 3.14159266358979394796
Metoda trapezow:    3.14159265358979394801
https://ideone.com/LEDmI1
language:
C++ (gcc 8.3)
created:
16 hours ago
visibility:
public

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