C++ Blatt 10 A24.cc

#include <iostream>
#include <cmath>
#include <random>
using namespace std;

class normal_generator {
  bool status;
  double cache;
  public:
    normal_generator() {
      status = false;
    }
    double random_number() {
      return 2.0 * double (rand()) / RAND_MAX - 1;
    }
    double update() {
      while (true) {
        double v1 = random_number(), v2 = random_number();
        double s = v1 * v1 + v2 * v2;

        if (s < 1 && s != 0) {
          cache = v1 * sqrt((-2 * log(s)) / s);
          return v2 * sqrt((-2 * log(s)) / s);
        }
      }
    }
    double get() {
      status = !status;
      return status ? update() : cache;
    }
};

int main() {
  srand(time(NULL));
  normal_generator rnd;

  double m = 0, s = 0;

  for (int i = 0; i < pow(10, 5); i++) {
    double x = rnd.get();
    m += x;
    s += x*x;
  }

  m *= pow(10, -5);
  s *= pow(10, -5);
  cout << "m: " << m << endl;
  cout << "σ: " << sqrt(s - m*m) << endl;

  int s1 = 0, s2 = 0, s3 = 0;

  for (int i = 0; i < pow(10, 5); i++) {
    double x = rnd.get();
    if (abs(x) > 1)
      s1++;
    if (abs(x) > 2)
      s2++;
    if (abs(x) > 3)
      s3++;
  }

  cout << "Betrag > σ: " << s1 * pow(10, -3) << "%" << endl;
  cout << "Betrag > 2σ: " << s2 * pow(10, -3) << "%" << endl;
  cout << "Betrag > 3σ: " << s3 * pow(10, -3) << "%" << endl;
}

C++ Blatt 10 A25.cc

#include <iostream>
#include <vector>
using namespace std;

int num = 1;

void print(vector<int> board) {
  cout << endl << "Solution " << num++ << endl;
  for (int row = 0; row < board.size(); row++) {
    cout << string(board[row], 'O') << "X" << string(board.size() - board[row] - 1, 'O') << endl;
  }
}

bool check(int row, int col, vector<int> board) {
  for (int i = 0; i < row; i++) {
    if (board[i] == col || board[i] == col + (row - i) || board[i] == col - (row - i))
      return false;
  }
  return true;
}

void place(int row, vector<int> board) {
  if (row == board.size())
    return print(board);

  for (int col = 0; col < board.size(); col++) {
    if (check(row, col, board)) {
      board[row] = col;
      place(row + 1, board);
    }
  }
}

int main () {
  vector<int> board(8, 0);
  place(0, board);
}