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  1.  
  2. #include <iostream>
  3. #include <iomanip>
  4. #include <random>
  5. #include <cmath>
  6.  
  7. using namespace std;
  8.  
  9. // Funkcja podcałkowa
  10. long double f(long double x) {
  11.     return sqrt(1.0L - x * x);
  12. }
  13.  
  14. int main() {
  15.  
  16.     // Tu ustawiasz liczbę losowań / podziałów
  17.     const long long n = 1000000;   // możesz zmienić np. na 10000000
  18.  
  19.     cout << fixed << setprecision(20);
  20.  
  21.     // =========================
  22.     // 1. METODA MONTE CARLO
  23.     // =========================
  24.     mt19937_64 gen(123456);  // stałe ziarno dla powtarzalnych wyników
  25.     uniform_real_distribution<long double> dist(-1.0L, 1.0L);
  26.  
  27.     long long inside = 0;
  28.  
  29.     for (long long i = 0; i < n; i++) {
  30.         long double x = dist(gen);
  31.         long double y = dist(gen);
  32.  
  33.         if (x * x + y * y <= 1.0L)
  34.             inside++;
  35.     }
  36.  
  37.     long double pi_monte = 4.0L * inside / n;
  38.  
  39.     // =========================
  40.     // 2. METODA PROSTOKĄTÓW (punkty środkowe)
  41.     // =========================
  42.     long double h = 1.0L / n;
  43.     long double sum_rect = 0.0L;
  44.  
  45.     for (long long i = 0; i < n; i++) {
  46.         long double x = (i + 0.5L) * h;
  47.         sum_rect += f(x);
  48.     }
  49.  
  50.     long double pi_rect = 4.0L * h * sum_rect;
  51.  
  52.     // =========================
  53.     // 3. METODA TRAPEZÓW
  54.     // =========================
  55.     long double sum_trap = (f(0.0L) + f(1.0L)) / 2.0L;
  56.  
  57.     for (long long i = 1; i < n; i++) {
  58.         long double x = i * h;
  59.         sum_trap += f(x);
  60.     }
  61.  
  62.     long double pi_trap = 4.0L * h * sum_trap;
  63.  
  64.     // =========================
  65.     // WYNIKI
  66.     // =========================
  67.     cout << "Przyblizenie liczby pi (n = " << n << "):\n\n";
  68.     cout << "Monte Carlo  : " << pi_monte << endl;
  69.     cout << "Prostokaty   : " << pi_rect << endl;
  70.     cout << "Trapezy      : " << pi_trap << endl;
  71.  
  72.     return 0;
  73. }
Success #stdin #stdout 0.04s 5312KB
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Przyblizenie liczby pi (n = 1000000):

Monte Carlo  : 3.14205599999999999998
Prostokaty   : 3.14159265393423042215
Trapezy      : 3.14159265241381118004
https://ideone.com/BaAxZi
language:
C++ (gcc 8.3)
created:
15 hours ago
visibility:
public

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