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#Problem Parameters
class jcp:
    @staticmethod
    def max_cars():
        return 20
    
    @staticmethod
    def γ():
        return 0.9
    

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class poisson_:
    
    def __init__(self, λ):
        self.λ = λ
        
        ε = 0.01
        
        # [α , β] is the range of n's for which the pmf value is above ε
        self.α = 0
        state = 1

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α = 0
β = 8

vals = {0: 0.05127513134990861,
 1: 0.15084926808563653,
 2: 0.2255298706374324,
 3: 0.2255298706374324,
 4: 0.1695194187235855,
 5: 0.10230687642696924,
 6: 0.051897469704506906,

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#A class holding the properties of a location together

class location:
    
    def __init__(self, req, ret):
        self.α = req                        #value of lambda for requests
        self.β = ret                        #value of lambda for returns
        self.poissonα = poisson_(self.α)
        self.poissonβ = poisson_(self.β)

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#IMPORTS
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from scipy.stats import poisson
import sys

#Problem Parameters
class jcp:
    @staticmethod

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#Initializing the value and policy matrices. Initial policy has zero value for all states.

value = np.zeros((jcp.max_cars()+1, jcp.max_cars()+1))
policy = value.copy().astype(int)

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def expected_reward(state, action):
    global value
    """
    state  : It's a pair of integers, # of cars at A and at B
    action : # of cars transferred from A to B,  -5 <= action <= 5 
    """
    
    ψ = 0 #reward
    new_state = [max(min(state[0] - action, jcp.max_cars()),0) , max(min(state[1] + action, jcp.max_cars()),0)]
    

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def policy_improvement():
    
    global policy
    
    policy_stable = True
    for i in range(value.shape[0]):
        for j in range(value.shape[1]):
            old_action = policy[i][j]
            
            max_act_val = None

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while(1):
    policy_evaluation()
    ρ = policy_improvement()
    save_value()
    save_policy()
    if ρ == True:
        break

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# adding reward for moving cars from one location to another (which is negative) 
    
if action <= 0:
    ψ = ψ + jcp.moving_reward() * abs(action)
else:
    ψ = ψ + jcp.moving_reward() * (action - 1)    #one car is moved by one of Jack's employees for free

# adding reward for second parking lot (which is also negative)

if new_state[0] > 10: