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  1. #include <iostream>
  2. #include <iomanip>
  3. #include <random>
  4. #include <cmath>
  5.  
  6. using namespace std;
  7.  
  8. // Funkcja podcałkowa
  9. long double f(long double x) {
  10.     return sqrt(1.0L - x * x);
  11. }
  12.  
  13. int main() {
  14.  
  15.     // 🔴 TU ustawiasz liczbę losowań / podziałów
  16.     const long long n = 1000000;   // możesz zmienić np. na 10000000
  17.  
  18.     cout << fixed << setprecision(20);
  19.  
  20.     // =========================
  21.     // 1. METODA MONTE CARLO
  22.     // =========================
  23.     mt19937_64 gen(123456);  // stałe ziarno dla powtarzalnych wyników
  24.     uniform_real_distribution<long double> dist(-1.0L, 1.0L);
  25.  
  26.     long long inside = 0;
  27.  
  28.     for (long long i = 0; i < n; i++) {
  29.         long double x = dist(gen);
  30.         long double y = dist(gen);
  31.  
  32.         if (x * x + y * y <= 1.0L)
  33.             inside++;
  34.     }
  35.  
  36.     long double pi_monte = 4.0L * inside / n;
  37.  
  38.     // =========================
  39.     // 2. METODA PROSTOKĄTÓW (punkty środkowe)
  40.     // =========================
  41.     long double h = 1.0L / n;
  42.     long double sum_rect = 0.0L;
  43.  
  44.     for (long long i = 0; i < n; i++) {
  45.         long double x = (i + 0.5L) * h;
  46.         sum_rect += f(x);
  47.     }
  48.  
  49.     long double pi_rect = 4.0L * h * sum_rect;
  50.  
  51.     // =========================
  52.     // 3. METODA TRAPEZÓW
  53.     // =========================
  54.     long double sum_trap = (f(0.0L) + f(1.0L)) / 2.0L;
  55.  
  56.     for (long long i = 1; i < n; i++) {
  57.         long double x = i * h;
  58.         sum_trap += f(x);
  59.     }
  60.  
  61.     long double pi_trap = 4.0L * h * sum_trap;
  62.  
  63.     // =========================
  64.     // WYNIKI
  65.     // =========================
  66.     cout << "Przyblizenie liczby pi (n = " << n << "):\n\n";
  67.     cout << "Monte Carlo  : " << pi_monte << endl;
  68.     cout << "Prostokaty   : " << pi_rect << endl;
  69.     cout << "Trapezy      : " << pi_trap << endl;
  70.  
  71.     return 0;
  72. }
Success #stdin #stdout 0.05s 5316KB
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Przyblizenie liczby pi (n = 1000000):

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

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