import sys;

def difference_eq_print1(f, x0, N):
    xp = x0;
    for n in range(N):
        x = f(xp);
        print(x)
        
        # Update variables 
        xp = x;

def difference_eq_print2(f,x0,x1, N):
    xp = x1;
    xpp = x0;
    for n in range(N):
        x = f(xpp, xp);
        print(x)
        # Update variables 
        xpp = xp;
        xp = x;

def difference_eq_print3(f,x0,x1,x2, N):
    xp = x2;
    xpp = x1;
    xppp = x0;
    for n in range(N):
        x = f(xppp, xpp, xp);
        print(x)
        
        # Update variables 
        xppp = xpp;
        xpp = xp;
        xp = x;

def difference_eq_print_general(f,x_list,N):
    """
    Assume x_list = [x0,...,xn];
    """
    for n in range(N):
        x_value = f(x_list)
        x_list = x_list[1:];
        x_list.append(x_value);
        print(x_value);

def fibonacci2(xpp,xp):
    return xp + xpp;

def fibonacci3(xppp,xpp,xp):
    return xppp + xpp + xp;


def fibonacci2_general(x):
    return x[0] + x[1];    

def difference_eq2(f,x0,x1, N):
    xp = x1;
    xpp = x0;
    x_list = []
    for n in range(N):
        x = f(xpp, xp);
        print(x);
        x_list.append(x);
        # Update variables 
        xpp = xp;
        xp = x;
    return x_list;

if __name__ == "__main__":
    
    if (len(sys.argv) < 2):
        N = 10;
    else:
        N = int(sys.argv[1]); 
    
     
        
    #python3 difference_eps.py 10 "f = lambda xpp,xp: xp+xpp"
    
    x0 = 1;
    x1 = 1;
    difference_eq_print2(fibonacci2, x0, x1, N);
    print('---------')
    x_list = [x0,x1];
    difference_eq_print_general(fibonacci2_general, x_list, N);
    print('---------')

    x2 = 1;
    difference_eq_print3(fibonacci3, x0, x1, x2, N);
    print('---------')
    
    if (len(sys.argv) == 3):
        exec(sys.argv[2]); # Someone has provided a function f(xpp,xp) on the command line
        
        difference_eq_print2(f,x0,x1,N);
    print('---------')
    
    x_list = difference_eq2(fibonacci2, x0, x1, N);