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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
  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.     cin >> n;   // liczba losowań / podziałów
  16.  
  17.     // =========================
  18.     // 1. MONTE CARLO
  19.     // =========================
  20.     mt19937_64 gen(random_device{}());
  21.     uniform_real_distribution<long double> dist(-1.0L, 1.0L);
  22.  
  23.     long long inside = 0;
  24.  
  25.     for (long long i = 0; i < n; i++) {
  26.         long double x = dist(gen);
  27.         long double y = dist(gen);
  28.  
  29.         if (x * x + y * y <= 1.0L)
  30.             inside++;
  31.     }
  32.  
  33.     long double pi_monte = 4.0L * inside / n;
  34.  
  35.     // =========================
  36.     // 2. METODA PROSTOKĄTÓW
  37.     // =========================
  38.     long double dx = 1.0L / n;
  39.     long double sum_rect = 0.0L;
  40.  
  41.     for (long long i = 0; i < n; i++) {
  42.         long double x = (i + 0.5L) * dx;  // punkt środkowy
  43.         sum_rect += f(x);
  44.     }
  45.  
  46.     long double pi_rect = sum_rect * dx;
  47.  
  48.     // =========================
  49.     // 3. METODA TRAPEZÓW
  50.     // =========================
  51.     long double sum_trap = (f(0.0L) + f(1.0L)) / 2.0L;
  52.  
  53.     for (long long i = 1; i < n; i++) {
  54.         long double x = i * dx;
  55.         sum_trap += f(x);
  56.     }
  57.  
  58.     long double pi_trap = sum_trap * dx;
  59.  
  60.     // =========================
  61.     // WYNIKI
  62.     // =========================
  63.     cout << fixed << setprecision(20);
  64.     cout << pi_monte << endl;
  65.     cout << pi_rect << endl;
  66.     cout << pi_trap << endl;
  67.  
  68.     return 0;
  69. }
Success #stdin #stdout 0.01s 5320KB
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Standard input is empty
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-nan
-nan
inf
https://ideone.com/KkvTW6
language:
C++ (gcc 8.3)
created:
15 hours ago
visibility:
public

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