"""
Markov Decision Processes (Chapter 16)

First we define an MDP, and the special case of a GridMDP, in which
states are laid out in a 2-dimensional grid. We also represent a policy
as a dictionary of {state: action} pairs, and a Utility function as a
dictionary of {state: number} pairs. We then define the value_iteration
and policy_iteration algorithms.
"""

import random
from collections import defaultdict

import numpy as np

from utils4e import vector_add, orientations, turn_right, turn_left


class MDP:
    """A Markov Decision Process, defined by an initial state, transition model,
    and reward function. We also keep track of a gamma value, for use by
    algorithms. The transition model is represented somewhat differently from
    the text. Instead of P(s' | s, a) being a probability number for each
    state/state/action triplet, we instead have T(s, a) return a
    list of (p, s') pairs. We also keep track of the possible states,
    terminal states, and actions for each state. [Page 646]"""

    def __init__(self, init, actlist, terminals, transitions=None, reward=None, states=None, gamma=0.9):
        if not (0 < gamma