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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: 4 / (1 + x^2)
  9. long double f(long double x) {
  10.     return 4.0L / (1.0L + x * x);
  11. }
  12.  
  13. int main() {
  14.     long long n;
  15.     cout << "Podaj liczbe n: ";
  16.     cin >> n;
  17.  
  18.     // ==========================
  19.     // 1. METODA MONTE CARLO
  20.     // ==========================
  21.     random_device rd;
  22.     mt19937_64 gen(rd());
  23.     uniform_real_distribution<long double> dist(-1.0L, 1.0L);
  24.  
  25.     long long inside = 0;
  26.  
  27.     for (long long i = 0; i < n; ++i) {
  28.         long double x = dist(gen);
  29.         long double y = dist(gen);
  30.  
  31.         if (x * x + y * y <= 1.0L)
  32.             inside++;
  33.     }
  34.  
  35.     long double pi_monte_carlo = 4.0L * inside / n;
  36.  
  37.     // ==========================
  38.     // 2. METODA PROSTOKĄTÓW
  39.     // ==========================
  40.     long double h = 1.0L / n;
  41.     long double sum_rect = 0.0L;
  42.  
  43.     for (long long i = 0; i < n; ++i) {
  44.         long double x = i * h;
  45.         sum_rect += f(x);
  46.     }
  47.  
  48.     long double pi_rect = h * sum_rect;
  49.  
  50.     // ==========================
  51.     // 3. METODA TRAPEZÓW
  52.     // ==========================
  53.     long double sum_trap = (f(0.0L) + f(1.0L)) / 2.0L;
  54.  
  55.     for (long long i = 1; i < n; ++i) {
  56.         long double x = i * h;
  57.         sum_trap += f(x);
  58.     }
  59.  
  60.     long double pi_trap = h * sum_trap;
  61.  
  62.     // ==========================
  63.     // WYNIKI
  64.     // ==========================
  65.     cout << fixed << setprecision(20);
  66.     cout << "\nPrzyblizenie liczby pi:\n";
  67.     cout << "Monte Carlo  : " << pi_monte_carlo << endl;
  68.     cout << "Prostokaty   : " << pi_rect << endl;
  69.     cout << "Trapezy      : " << pi_trap << endl;
  70.  
  71.     return 0;
  72. }
Success #stdin #stdout 0.01s 5280KB
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Standard input is empty
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Podaj liczbe n: 
Przyblizenie liczby pi:
Monte Carlo  : -nan
Prostokaty   : -nan
Trapezy      : inf
https://ideone.com/FPGXe5
language:
C++ (gcc 8.3)
created:
15 hours ago
visibility:
public

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