#include <iostream>
#include <vector>
#include <string>
#include <random>
#include <ctime>
using namespace std;

void construire_passage (int i,int j,vector<vector<bool>>& libre,vector<vector<bool>>& passage);

int main () {

	char c;
	cin.get(c);
	int n(0);
	cin>>n;
	double p;
	cin>>p;
	int nbt;
	cin>>nbt;
	if ((p>1) or (p<0)) { return 0;}
	cout<<" "<<c<<" : "<<n<<" : "<<p<<" : "<<nbt<<endl;

	//building cells
    vector<vector<bool>>libre (n,vector<bool>(n));
    vector<vector<bool>>passage (n,vector<bool>(n));

	bernoulli_distribution b(p);
	default_random_engine e;

	//for (int k(0); k<nbt;++k) {  //generates random matrix
	//display the "libre" matrix
	   for (int i(0); i<n ;++i) {  //horizontal line
		  for (int j(0); j<n;++j) {   //vertical line
			libre[i][j]=b(e); //random cells
			cout<<libre[i][j];
		   }
		cout<<endl;
	    }
	cout<<endl;
    //}

    //buidling the "passage" matrix
    for(int j(0); j<n ;++j)
	{
	   construire_passage(0,j,libre,passage);
    }

    //display the passage matrix
	for (int i(0); i<n ;++i)
	 {
	 for (int j(0); j<n ;++j)
	    {cout<<passage[i][j];}
	  cout<<endl;

	  }

	  int compteur(0);

	  //Analyzing if there is "traversée"
   for (int l(0);l<nbt;++l) { //veryfing if there is "traversée for the nbt vectors
	    for (int j(0);j<n;++j){
		    if (passage[n-1][j]==0) {
			  cout<<"il y a bel et bien traversée"<<endl;
			  compteur+=1;
			  return compteur;}
			else {}
		}
	}

	//final step : display the probability to have "traversée"
	double pf(0);
	pf = compteur/nbt;
	cout<<"la probabilité d'avoir un passage est donc de : "<<pf<<endl;



}

void construire_passage (int i,int j,vector<vector<bool>>& libre,vector<vector<bool>>& passage)
{
   //step1 :: confirm that i,j are in the area
   int n;
   n=libre.size(); // warning :: libre is of dimension nXn
   if ((i<0) or (i>n-1) or (j<0) or (j>n-1)) {return;}  // if outside stop execution and get back
   //test if cell is "libre" => value=0  => not true...
   if (libre[i][j]==1)
          {return;} //cell closed -> stop
          else
          {
			  // test if it has been visited ??
			  if (passage[i][j]==0)
			     {return;} //cell already visited -> stop
			     else
			     {
					 passage[i][j]=0;  // cell is a free "passage"
					 // test all adajcent cells
					 construire_passage(i+1,j,libre,passage);
					 construire_passage(i-1,j,libre,passage);
					 construire_passage(i,j+1,libre,passage);
					 construire_passage(i,j-1,libre,passage);
					 }
	       }
}