#include <iostream>
#include <cmath>

using namespace std;

int main() {

        const int x_max=20 ,y_max=20;
        const float y_max_v=1.0, mu=1.0;
        int counter=1;


        float V[x_max][y_max];

        for (int i=0; i<=y_max-1; i++) {
                        V[0][i]=0.0;
                        V[x_max-1][i]=1.0;
                                   }

        for (int i=0; i<=x_max-1;i++){
                        V[i][0]=(y_max_v/(y_max-1))*i;
                        V[i][y_max-1]=(y_max_v/(y_max-1))*i;
                                  }



        for(int i=1;i<=x_max-2;i++) {
                            for(int j=1;j<=y_max-2;j++) {V[i][j]=mu;}
                                     }



        while(2>1){

        bool converged = false;
        int c_x, c_y;
        counter=counter+1;


        for(int i=1;i<=x_max-2;i++) {



                            for(int j=1;j<=y_max-2;j++) {
                                                    if(fabs(((V[i+1][j]+V[i-1][j]+V[i][j+1]+V[i][j-1])/4.0)-V[i][j])>=0.000001) {

                                                                                             V[i][j]=(V[i+1][j]+V[i-1][j]+V[i][j+1]+V[i][j-1])/4.0;


                                                                                                                           }
                                                    else {
                                                            converged=true; c_x=i; c_y=j;
                                                          }

                                                           //cout<<"The solution is "<<V[i][j]; break;}

                                                         }

                                     }

                            if(converged) { cout<<"The solution is "<<V[x_max/2][y_max/2]<<" and it took "<<counter<<" iterations to complete"<<endl;
                                            break;
                                           }
                    }

            return 0;

            }