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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 całkowania: 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 losowan / podzialow n: ";
  16.     cin >> n;
  17.  
  18.     // ==========================
  19.     // 1. METODA MONTE CARLO
  20.     // ==========================
  21.     mt19937_64 gen(random_device{}());
  22.     uniform_real_distribution<long double> dist(-1.0L, 1.0L);
  23.  
  24.     long long inside = 0;
  25.  
  26.     for(long long i = 0; i < n; i++) {
  27.         long double x = dist(gen);
  28.         long double y = dist(gen);
  29.  
  30.         if(x*x + y*y <= 1.0L)
  31.             inside++;
  32.     }
  33.  
  34.     long double pi_monte_carlo = 4.0L * inside / n;
  35.  
  36.     // ==========================
  37.     // 2. METODA PROSTOKĄTÓW
  38.     // ==========================
  39.     long double dx = 1.0L / n;
  40.     long double sum_rect = 0.0L;
  41.  
  42.     for(long long i = 0; i < n; i++) {
  43.         long double x = i * dx;
  44.         sum_rect += f(x);
  45.     }
  46.  
  47.     long double pi_rect = sum_rect * dx;
  48.  
  49.     // ==========================
  50.     // 3. METODA TRAPEZÓW
  51.     // ==========================
  52.     long double sum_trap = (f(0.0L) + f(1.0L)) / 2.0L;
  53.  
  54.     for(long long i = 1; i < n; i++) {
  55.         long double x = i * dx;
  56.         sum_trap += f(x);
  57.     }
  58.  
  59.     long double pi_trap = sum_trap * dx;
  60.  
  61.     // ==========================
  62.     // WYNIKI
  63.     // ==========================
  64.     cout << fixed << setprecision(20);
  65.     cout << "\nPrzyblizenie liczby pi:\n";
  66.     cout << "Monte Carlo : " << pi_monte_carlo << endl;
  67.     cout << "Prostokaty  : " << pi_rect << endl;
  68.     cout << "Trapezy     : " << pi_trap << endl;
  69.  
  70.     return 0;
  71. }
Success #stdin #stdout 0s 5308KB
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Standard input is empty
stdout
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Podaj liczbe losowan / podzialow n: 
Przyblizenie liczby pi:
Monte Carlo : -nan
Prostokaty  : -nan
Trapezy     : inf
https://ideone.com/0FDxI6
language:
C++ (gcc 8.3)
created:
16 hours ago
visibility:
public

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