def init_farthest_distance(far_mat, dist_mat, s):
    """initialize matrix to keep track of distance from set 
    Parameters:
    ------------------
    far_mat  :  python list length = dist_mat.shape[0]
        the minimum distance from solution set to all the points
    dist_mat :  numpy.array (n, n)
        distance matrix  
    s        :  the last added index
        solution index

    Returns:
    ------------------
    far_mat  :  python list length = dist_mat.shape[0]
        the minimum distance from solution set to all the points
    """
    for i in range(far_mat.shape[0]):
        far_mat[i] = dist_mat[i,s]
    return far_mat