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  1. #include <iostream>
  2. #include <iomanip>
  3. #include <random>
  4. #include <cmath>
  5.  
  6. using namespace std;
  7.  
  8. // ================= MONTE CARLO =================
  9. long double monteCarlo(unsigned long long n) {
  10.     mt19937_64 gen(123456); // stałe ziarno dla powtarzalności
  11.     uniform_real_distribution<long double> dist(-1.0L, 1.0L);
  12.  
  13.     unsigned long long inside = 0;
  14.  
  15.     for (unsigned long long i = 0; i < n; ++i) {
  16.         long double x = dist(gen);
  17.         long double y = dist(gen);
  18.  
  19.         if (x * x + y * y <= 1.0L)
  20.             inside++;
  21.     }
  22.  
  23.     return 4.0L * (long double)inside / (long double)n;
  24. }
  25.  
  26. // ================= METODA PROSTOKĄTÓW =================
  27. long double rectangleMethod(unsigned long long n) {
  28.     long double h = 1.0L / (long double)n;
  29.     long double sum = 0.0L;
  30.  
  31.     for (unsigned long long i = 0; i < n; ++i) {
  32.         long double x = i * h;
  33.         sum += 1.0L / (1.0L + x * x);
  34.     }
  35.  
  36.     return 4.0L * h * sum;
  37. }
  38.  
  39. // ================= METODA TRAPEZÓW =================
  40. long double trapezoidalMethod(unsigned long long n) {
  41.     long double h = 1.0L / (long double)n;
  42.     long double sum = 0.0L;
  43.  
  44.     sum += 0.5L * (1.0L / (1.0L + 0.0L * 0.0L));
  45.     sum += 0.5L * (1.0L / (1.0L + 1.0L * 1.0L));
  46.  
  47.     for (unsigned long long i = 1; i < n; ++i) {
  48.         long double x = i * h;
  49.         sum += 1.0L / (1.0L + x * x);
  50.     }
  51.  
  52.     return 4.0L * h * sum;
  53. }
  54.  
  55. // ================= MAIN =================
  56. int main() {
  57.     unsigned long long nMonteCarlo = 100000000ULL; // 100 mln punktów
  58.     unsigned long long nIntegral = 100000000ULL;
  59.  
  60.     cout << fixed << setprecision(30);
  61.  
  62.     long double piMonteCarlo = monteCarlo(nMonteCarlo);
  63.     long double piRectangle  = rectangleMethod(nIntegral);
  64.     long double piTrapezoid  = trapezoidalMethod(nIntegral);
  65.  
  66.     cout << "Monte Carlo (100 000 000 punktów):\n";
  67.     cout << piMonteCarlo << endl << endl;
  68.  
  69.     cout << "Metoda prostokatow:\n";
  70.     cout << piRectangle << endl << endl;
  71.  
  72.     cout << "Metoda trapezow:\n";
  73.     cout << piTrapezoid << endl;
  74.  
  75.     return 0;
  76. }
Success #stdin #stdout 4.36s 5320KB
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Standard input is empty
stdout
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Monte Carlo (100 000 000 punktów):
3.141445999999999999898261937581

Metoda prostokatow:
3.141592663589793947955322583887

Metoda trapezow:
3.141592653589793948014710633920
https://ideone.com/bWDVuj
language:
C++ (gcc 8.3)
created:
2 days ago
visibility:
public

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