import math
import numpy as np

X = {1,2,3,4,5,6}
A = {"Up","Down","Right","Left"}


Pup=np.array([[0.8, 0.1,   0, 0.1,   0,   0],
            [  0.1, 0.7, 0.1,   0, 0.1,   0],
            [    0, 0.1, 0.8,   0,   0, 0.1],
            [  0.6,   0,   0, 0.3, 0.1,   0],
            [    0, 0.6,   0, 0.1, 0.2, 0.1],
            [    0,   0, 0.6,   0, 0.1, 0.3],
           ])

Pdown=np.array([[0.3, 0.1,   0, 0.6,   0,   0],  #1
            [    0.1, 0.2, 0.1,   0, 0.6,   0],  #2
            [      0, 0.1, 0.3,   0,   0, 0.6],  #3
            [    0.1,   0,   0, 0.8, 0.1,   0],  #4
            [      0, 0.1,   0, 0.1, 0.7, 0.1],  #5
            [      0,   0, 0.1,   0, 0.1, 0.8],  #6
           ])

Pright=np.array([[0.3, 0.6,   0, 0.1,   0,   0],  #1
            [     0.1, 0.2, 0.6,   0, 0.1,   0],  #2
            [       0, 0.1, 0.8,   0,   0, 0.1],  #3
            [     0.1,   0,   0, 0.3, 0.6,   0],  #4
            [       0, 0.1,   0, 0.1, 0.2, 0.6],  #5
            [       0,   0, 0.1,   0, 0.1, 0.8],  #6
           ])

Pleft=np.array([[0.8, 0.1,   0, 0.1,   0,   0],  #1
            [    0.6, 0.2, 0.1,   0, 0.1,   0],  #2
            [      0, 0.6, 0.3,   0,   0, 0.1],  #3
            [    0.1,   0,   0, 0.8, 0.1,   0],  #4
            [      0, 0.1,   0, 0.6, 0.2, 0.1],  #5
            [      0,   0, 0.1,   0, 0.6, 0.3],  #6
           ])
            #   UP   DOWN   RIGHT  LEFT
C = np.array([[0.15, 0.15, 0.15, 0.15],  #1
            [  0.15,    1, 0.15, 0.15],  #2
            [  0.15,    0, 0.15, 0.15],  #3
            [  0.15, 0.15,    1, 0.15],  #4
            [  0.15,    1, 0.15, 0.15],  #5
            [  0.15,    0,    0,    1],  #6
           ])# Insert your code here

print("State List: \n", X)

print("Action List: \n", A)

print("Transition UP: \n", Pup)
print("Transition DOWN: \n", Pdown)
print("Transition RIGHT: \n", Pright)
print("Transition LEFT: \n", Pleft)

print("Cost Matrix: \n", C)