### demo

>>> m = Fig[17,1]

>>> pi = best_policy(m, value_iteration(m, .01))

>>> pi
{(3, 2): None, (3, 1): None, (3, 0): (-1, 0), (2, 1): (0, 1), (0, 2): (1, 0), (1, 0): (1, 0), (0, 0): (0, 1), (1, 2): (1, 0), (2, 0): (0, 1), (0, 1): (0, 1), (2, 2): (1, 0)}

>>> m.to_arrows(pi)
[['>', '>', '>', '.'], ['^', None, '^', '.'], ['^', '>', '^', '<']]

>>> print_table(m.to_arrows(pi))
>   >      >   .  
^   None   ^   .  
^   >      ^   <  

>>> value_iteration(m, .01)
{(3, 2): 1.0, (3, 1): -1.0, (3, 0): 0.12958868267972745, (0, 1): 0.39810203830605462, (0, 2): 0.50928545646220924, (1, 0): 0.25348746162470537, (0, 0): 0.29543540628363629, (1, 2): 0.64958064617168676, (2, 0): 0.34461306281476806, (2, 1): 0.48643676237737926, (2, 2): 0.79536093684710951}

>>> policy_iteration(m)
{(3, 2): None, (3, 1): None, (3, 0): (0, -1), (2, 1): (-1, 0), (0, 2): (1, 0), (1, 0): (1, 0), (0, 0): (1, 0), (1, 2): (1, 0), (2, 0): (1, 0), (0, 1): (1, 0), (2, 2): (1, 0)}

>>> print_table(m.to_arrows(policy_iteration(m)))
>   >      >   .  
>   None   <   .  
>   >      >   v