# ----------
# User Instructions:
#
# Implement the function optimum_policy2D below.
#
# You are given a car in grid with initial state
# init. Your task is to compute and return the car's
# optimal path to the position specified in goal;
# the costs for each motion are as defined in cost.
#
# There are four motion directions: up, left, down, and right.
# Increasing the index in this array corresponds to making a
# a left turn, and decreasing the index corresponds to making a
# right turn.forward = [[-1,  0], # go up[ 0, -1], # go left[ 1,  0], # go down[ 0,  1]] # go right
forward_name = ['up', 'left', 'down', 'right']# action has 3 values: right turn, no turn, left turn
action = [-1, 0, 1]
action_name = ['R', '#', 'L']# EXAMPLE INPUTS:
# grid format:
#     0 = navigable space
#     1 = unnavigable space
grid = [[1, 1, 1, 0, 0, 0],[1, 1, 1, 0, 1, 0],[0, 0, 0, 0, 0, 0],[1, 1, 1, 0, 1, 1],[1, 1, 1, 0, 1, 1]]init = [4, 3, 0] # given in the form [row,col,direction]# direction = 0: up#             1: left#             2: down#             3: rightgoal = [2, 0] # given in the form [row,col]cost = [2, 1, 20] # cost has 3 values, corresponding to making # a right turn, no turn, and a left turn# EXAMPLE OUTPUT:
# calling optimum_policy2D with the given parameters should return
# [[' ', ' ', ' ', 'R', '#', 'R'],
#  [' ', ' ', ' ', '#', ' ', '#'],
#  ['*', '#', '#', '#', '#', 'R'],
#  [' ', ' ', ' ', '#', ' ', ' '],
#  [' ', ' ', ' ', '#', ' ', ' ']]
# ----------# ----------------------------------------
# modify code below
# ----------------------------------------def optimum_policy2D(grid,init,goal,cost):value = [ [[999 for row in range(len(grid[0]))] for col in range(len(grid))],[[999 for row in range(len(grid[0]))] for col in range(len(grid))],[[999 for row in range(len(grid[0]))] for col in range(len(grid))],[[999 for row in range(len(grid[0]))] for col in range(len(grid))] ]policy = [ [[' ' for row in range(len(grid[0]))] for col in range(len(grid))],[[' ' for row in range(len(grid[0]))] for col in range(len(grid))],[[' ' for row in range(len(grid[0]))] for col in range(len(grid))],[[' ' for row in range(len(grid[0]))] for col in range(len(grid))] ]policy2D =  [[' ' for row in range(len(grid[0]))] for col in range(len(grid))]change =  Truewhile change:change =  Falsefor x in range(len(grid)):for y in range(len(grid[0])):for orientation in range(4):if goal[0] == x and goal[1] == y:if value[orientation][x][y] > 0:change = Truevalue[orientation][x][y] = 0policy[orientation][x][y] = '*'elif grid[x][y] == 0:for i in range(3):# The reason why moduler 4 is for the cycular buffer for the simulated grid.o2 = (orientation + action[i]) % 4# this is the motion modelx2 = x + forward[o2][0]y2 = y + forward[o2][1]if x2 >= 0 and x2 < len(grid) and y2 >=0 and y2 < len(grid[0]) and grid[x2][y2] == 0:v2 = value[o2][x2][y2] + cost[i]if v2 < value[orientation][x][y]:value[orientation][x][y] = v2policy[orientation][x][y] = action_name[i]change = Truex = init[0]y = init[1]orientation = init[2]policy2D[x][y] = policy[orientation][x][y]while policy[orientation][x][y] != '*':if policy[orientation][x][y] == '#':o2 = orientationelif policy[orientation][x][y] == 'R':o2 =  (orientation -1 ) % 4elif policy[orientation][x][y] == 'L':o2 = (orientation + 1) % 4x = x + forward[o2][0]y = y + forward[o2][1]orientation = o2policy2D[x][y] = policy[orientation][x][y]return policy2Dpolicy = optimum_policy2D(grid,init,goal,cost)for i in range(len(policy)):print(policy[i])