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  1. #include <iostream>
  2. #include <iomanip>
  3. #include <random>
  4. #include <cmath>
  5.  
  6. using namespace std;
  7.  
  8. // Stała liczba losowań / podziałów
  9. const unsigned long long N = 100000000ULL;
  10.  
  11. // Funkcja podcałkowa
  12. long double f(long double x) {
  13.     return 4.0L / (1.0L + x * x);
  14. }
  15.  
  16. // ====================== MONTE CARLO ======================
  17. long double monteCarlo(unsigned long long &inside) {
  18.     mt19937_64 gen(random_device{}());
  19.     uniform_real_distribution<long double> dist(-1.0L, 1.0L);
  20.  
  21.     inside = 0;
  22.  
  23.     for (unsigned long long i = 0; i < N; ++i) {
  24.         long double x = dist(gen);
  25.         long double y = dist(gen);
  26.  
  27.         if (x * x + y * y <= 1.0L)
  28.             inside++;
  29.     }
  30.  
  31.     return 4.0L * inside / N;
  32. }
  33.  
  34. // ====================== METODA PROSTOKĄTÓW ======================
  35. long double rectangles() {
  36.     long double h = 1.0L / N;
  37.     long double sum = 0.0L;
  38.  
  39.     for (unsigned long long i = 0; i < N; ++i) {
  40.         long double x = i * h;
  41.         sum += f(x);
  42.     }
  43.  
  44.     return h * sum;
  45. }
  46.  
  47. // ====================== METODA TRAPEZÓW ======================
  48. long double trapezoids() {
  49.     long double h = 1.0L / N;
  50.     long double sum = (f(0.0L) + f(1.0L)) / 2.0L;
  51.  
  52.     for (unsigned long long i = 1; i < N; ++i) {
  53.         long double x = i * h;
  54.         sum += f(x);
  55.     }
  56.  
  57.     return h * sum;
  58. }
  59.  
  60. // ====================== MAIN ======================
  61. int main() {
  62.  
  63.     cout << fixed << setprecision(30);
  64.  
  65.     // Monte Carlo
  66.     unsigned long long inside;
  67.     long double pi_monte = monteCarlo(inside);
  68.  
  69.     cout << "--- Metoda Monte Carlo ---\n";
  70.     cout << "Liczba punktow w kole: " << inside << endl;
  71.     cout << "Przyblizenie pi:       " << pi_monte << endl;
  72.  
  73.     // Prostokąty
  74.     long double pi_rect = rectangles();
  75.     cout << "\n--- Metoda prostokatow ---\n";
  76.     cout << "Przyblizenie pi:       " << pi_rect << endl;
  77.  
  78.     // Trapezy
  79.     long double pi_trap = trapezoids();
  80.     cout << "\n--- Metoda trapezow ---\n";
  81.     cout << "Przyblizenie pi:       " << pi_trap << endl;
  82.  
  83.     return 0;
  84. }
Success #stdin #stdout 4.67s 5320KB
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stdin
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stdout
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--- Metoda Monte Carlo ---
Liczba punktow w kole: 78537716
Przyblizenie pi:       3.141508639999999999989702126335

--- Metoda prostokatow ---
Przyblizenie pi:       3.141592663589793947955322583887

--- Metoda trapezow ---
Przyblizenie pi:       3.141592653589793948014710633920
https://ideone.com/5kwP66
language:
C++ (gcc 8.3)
created:
2 days ago
visibility:
public

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