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  1. #include <iostream>
  2. #include <iomanip>
  3. #include <random>
  4. #include <cmath>
  5.  
  6. using namespace std;
  7.  
  8. long double f(long double x) {
  9.     return 4.0L / (1.0L + x * x);
  10. }
  11.  
  12. int main() {
  13.  
  14.     // ===== USTAWIONA LICZBA ITERACJI =====
  15.     const unsigned long long n = 1000000ULL;
  16.  
  17.     // ======================
  18.     // 1. MONTE CARLO
  19.     // ======================
  20.     mt19937_64 gen(123456); // stałe ziarno
  21.     uniform_real_distribution<long double> dist(-1.0L, 1.0L);
  22.  
  23.     unsigned long long inside = 0;
  24.  
  25.     for (unsigned long long i = 0; i < n; i++) {
  26.         long double x = dist(gen);
  27.         long double y = dist(gen);
  28.         if (x*x + y*y <= 1.0L)
  29.             inside++;
  30.     }
  31.  
  32.     long double pi_monte = 4.0L * inside / n;
  33.  
  34.     // ======================
  35.     // 2. PROSTOKĄTY
  36.     // ======================
  37.     long double h = 1.0L / n;
  38.     long double sum_rect = 0.0L;
  39.  
  40.     for (unsigned long long i = 0; i < n; i++) {
  41.         long double x = i * h;
  42.         sum_rect += f(x);
  43.     }
  44.  
  45.     long double pi_rect = h * sum_rect;
  46.  
  47.     // ======================
  48.     // 3. TRAPEZY
  49.     // ======================
  50.     long double sum_trap = (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_trap += f(x);
  55.     }
  56.  
  57.     long double pi_trap = h * sum_trap;
  58.  
  59.     // ======================
  60.     // WYNIKI
  61.     // ======================
  62.     cout << fixed << setprecision(20);
  63.     cout << "Monte Carlo : " << pi_monte << endl;
  64.     cout << "Prostokaty  : " << pi_rect  << endl;
  65.     cout << "Trapezy     : " << pi_trap  << endl;
  66.  
  67.     return 0;
  68. }
Success #stdin #stdout 0.04s 5316KB
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stdin
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Standard input is empty
stdout
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Monte Carlo : 3.14205599999999999998
Prostokaty  : 3.14159365358962659200
Trapezy     : 3.14159265358962659187
https://ideone.com/EC9n4w
language:
C++ (gcc 8.3)
created:
16 hours ago
visibility:
public

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