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  1. #include <iostream>
  2. #include <iomanip>
  3. #include <cmath>
  4.  
  5. using namespace std;
  6.  
  7. int main()
  8. {
  9.     ios::sync_with_stdio(false);
  10.     cin.tie(nullptr);
  11.  
  12.     const long long N = 1000000;   // 1 milion punktów
  13.  
  14.     // ===== Monte Carlo =====
  15.     unsigned long long seed = 123456789ULL;
  16.     auto fastRand = [&seed]() {
  17.         seed = seed * 2862933555777941757ULL + 3037000493ULL;
  18.         return (seed >> 33) * (1.0 / (1ULL << 31));
  19.     };
  20.  
  21.     long long inside = 0;
  22.  
  23.     // ===== Całkowanie =====
  24.     double h = 1.0 / N;
  25.     double sumRect = 0.0;
  26.     double sumTrap = 0.0;
  27.  
  28.     sumTrap = 0.5 * (1.0 + 1.0 / (1.0 + 1.0));
  29.  
  30.     for(long long i = 0; i < N; i++)
  31.     {
  32.         // Monte Carlo
  33.         double x = fastRand() * 2.0 - 1.0;
  34.         double y = fastRand() * 2.0 - 1.0;
  35.         if (x*x + y*y <= 1.0)
  36.             inside++;
  37.  
  38.         // Prostokąty (midpoint)
  39.         double xr = (i + 0.5) * h;
  40.         sumRect += 1.0 / (1.0 + xr*xr);
  41.  
  42.         // Trapezy
  43.         if (i > 0)
  44.         {
  45.             double xt = i * h;
  46.             sumTrap += 1.0 / (1.0 + xt*xt);
  47.         }
  48.     }
  49.  
  50.     double piMonte = 4.0 * inside / N;
  51.     double piRect  = 4.0 * h * sumRect;
  52.     double piTrap  = 4.0 * h * sumTrap;
  53.  
  54.     cout << fixed << setprecision(20);
  55.     cout << piMonte << "\n";
  56.     cout << piRect  << "\n";
  57.     cout << piTrap  << "\n";
  58.  
  59.     return 0;
  60. }
Success #stdin #stdout 0.02s 5324KB
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stdin
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Standard input is empty
stdout
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3.14483999999999985775
3.14159265358976425020
3.14159265358979267191
https://ideone.com/nTQgKm
language:
C++ (gcc 8.3)
created:
16 hours ago
visibility:
public

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