#include<stdio.h>
#include<math.h>
#include<stdlib.h>
#define pi  3.1415
#define L  20
#define T  18

double* mkarr(int n, int l)
{
    double* arr = (double*) malloc(l * n * sizeof(double));
    return arr;
}
double* solve_analitic(double K, double h)
{
    double t = h * K;
    int n = lround(T / t + 1);
    int l = lround(L / h + 1);
    double* arr = mkarr(n,l);

        for(int i = 0; i < l; i++)
        for(int j = 0; j < n; j++)
            arr[j, i] = sin(4 * pi * (h * i - t * j)/ L);
    return arr;
}
double* solve_corner(double K, double h)
{
    double t = h * K;
    int n = lround(T / t + 1);
    int l = lround(L / h + 1);
    double* arr = mkarr(n, l);

    arr [0, 0] = 0;
    for(int i = 0; i < l; i++)
        arr[0, i] = sin(4 * pi * (i) * h/L);
    for(int i = 1; i < n; i++)
    {
        arr[i, 0] = arr[i - 1, l] * t / h + arr[i - 1, 0] * (1-t / h);
        for(int j = 0; j < l; j++)
            arr[i, j] = arr[i - 1, j - 1] * t / h + arr[i - 1,j] * (1 - t / h);
        arr[i,0] = arr[i, l - 1];
    }
    return arr;
}
double* solve_LV(double K, double h)
{
    double t = h * K;
    int n = lround(T / t + 1);
    int l = lround(L / h + 1);
    double* arr = mkarr(n, l);
    int j = 0;
    arr[0, 0] = 0;
        for(int i = 0; i < l; i++)
            arr[0, i] = sin(4 * pi * i * h / L);
        for(j = 1; j < l; j++)
    {
            arr[j, 0] = arr[j - 1,0] * (1 - t * t / h * h) + (arr[j - 1, 1] + arr[j - 1,n - 1]) * (t * t / 2 / h * h) - (arr[j,1] - arr[j - 1,n - 1]) * t / 2 /h;
            for(int i = 1; i < n; i++)
                arr[j,i] = arr[j - 1,i] * (1 - t * t / h * h) + (arr[j - 1,i + 1] + arr[j - 1, i - 1]) * (t * t / 2 / h * h) - (arr[j - 1 , i + 1] - arr[j - 1, i - 1]) * t / 2 /h;
    }
    arr[j, n] = arr[j, 0];
    return arr;
}


int main ()
{
    FILE* out = fopen("out.txt", "w");
    if( out  == 0)
        perror("err");
    double K = 1;
    double h = 0.5;
    double t = h * K;
    int n = lround(T / t + 1);
    int l = lround(L / h + 1);
        double* analitic = solve_analitic(K,h);
    double* corner = solve_corner(K,h);
    double* LV = solve_LV(K,h);
    printf("%d %d \n", n, l);
    int x = 0;
    for (int i = 0; i < l; i++)
    {
        for(int j = 0; j < n; j++)
        {
            fprintf(out,"%f ",(analitic[i,j]));
        }
        x++;
        fprintf(out, "\n");
    }
    printf("%d \n", x);
    fclose(out);
    free (analitic);
    free (corner);
    free (LV);
    return 0;
}