LR Factorization Doolittle

#include <stdio.h>
#include <stdlib.h>
int n, i, j, k, h;
float a[100][100], S, piv, aux;
int main()
{
    scanf("%d", &n);
    for (i = 1; i <= n; i++)
        for (j = 1; j <= n + 1; j++)
            scanf("%f", &a[i][j]);
    if (a[1][1] == 0)
    {
        i = 1;
        do
        {
            i++;
        } while (a[i][1] == 0 && i <= n);
        if (i > n)
        {
            printf("The system does not unique solution");
            return 0;
        }
        for (j = 1; j <= n + 1; j++)
        {
            aux = a[1][j];
            a[1][j] = a[i][j];
            a[i][j] = aux;
        }
    }
    for (i = 2; i <= n; i++)
        a[1][i] = a[1][i] / a[1][1];
    for (k = 2; k <= n; k++)
    {
        i = k;
        do
        {
            S = 0;
            piv = 0;
            for (h = 1; h <= k - 1; h++)
                S = S + a[i][h] * a[h][k];
            piv = a[i][k] - S;
            i++;
        } while (piv == 0 && i <= n);
        if (piv == 0)
        {
            printf("The system does not have unique solution");
            return 0;
        }
        if (i != k + 1)
        {
            for (j = 1; j <= n + 1; j++)
            {
                aux = a[k][j];
                a[k][j] = a[i - 1][j];
                a[i - 1][j] = aux;
            }
        }
        for (i = k; i <= n; i++)
        {
            S = 0;
            for (h = 1; h <= k - 1; h++)
                S = S + a[i][h] * a[h][k];
            a[i][k] = a[i][k] - S;
        }
        for (j = k + 1; j <= n; j++)
        {
            S = 0;
            for (h = 1; h <= k - 1; h++)
                S = S + a[k][h] * a[h][k];
            a[k][j] = (a[k][j] - S) / a[k][k];
        }
    }
    for (i = 2; i <= n; i++)
    {
        S = 0;
        for (k = 1; k <= i - 1; k++)
            S = S + a[i][k] * a[k][n + 1];
        a[i][n + 1] = a[i][n + 1] - S;
    }
    a[n][n + 1] = a[n][n + 1] / a[n][n];
    for (i = n - 1; i >= 1; i--)
    {
        S = 0;
        for (j = i + 1; j <= n; j++)
            S = S + a[i][j] * a[j][n + 1];
        a[i][n + 1] = (a[i][n + 1] - S) / a[i][i];
    }
    for (i = 1; i <= n; i++)
        printf("x%d = %f ", i, a[i][n + 1]);
    printf("\n");
    system("pause");
    return 0;
}