# The function localize takes the following arguments:
 #
 # colors:
 #        2D list, each entry either 'R' (for red cell) or 'G' (for green cell)
 #
 # measurements:
 #        list of measurements taken by the robot, each entry either 'R' or 'G'
 #
 # motions:
 #        list of actions taken by the robot, each entry of the form [dy,dx],
 #        where dx refers to the change in the x-direction (positive meaning
 #        movement to the right) and dy refers to the change in the y-direction
 #        (positive meaning movement downward)
 #        NOTE: the *first* coordinate is change in y; the *second* coordinate is
 #              change in x
 #
 # sensor_right:
 #        float between 0 and 1, giving the probability that any given
 #        measurement is correct; the probability that the measurement is
 #        incorrect is 1-sensor_right
 #
 # p_move:
 #        float between 0 and 1, giving the probability that any given movement
 #        command takes place; the probability that the movement command fails
 #        (and the robot remains still) is 1-p_move; the robot will NOT overshoot
 #        its destination in this exercise
 #
 # The function should RETURN (not just show or print) a 2D list (of the same
 # dimensions as colors) that gives the probabilities that the robot occupies
 # each cell in the world.
 #
 # Compute the probabilities by assuming the robot initially has a uniform
 # probability of being in any cell.
 #
 # Also assume that at each step, the robot:
 # 1) first makes a movement,
 # 2) then takes a measurement.
 #
 # Motion:
 #  [0,0] - stay
 #  [0,1] - right
 #  [0,-1] - left
 #  [1,0] - down
 #  [-1,0] - up
 def sense(p,colors,measurement,sensor_right):
     q=[]
     for row in range(len(colors)):
         temp=[]
         for col in range(len(colors[0])):
             hit = (measurement == colors[row][col])
             temp.append(p[row][col] * (hit * sensor_right + (1-hit) * (1-sensor_right)))
         q.append(temp)
     s=0
     for row in range(len(q)):
         for col in range(len(q[0])):
             s += q[row][col]
     for row in range(len(p)):
         for col in range(len(q[0])):
             q[row][col] = q[row][col]/s
     return q

 def move(p, motion, p_move):
     q = []
     for row in range(len(colors)):
         temp=[]
         for col in range(len(colors[0])):
             s = p_move * p[(row - motion[0]) % len(colors)][(col - motion[1]) % len(colors[0])]
             s += (1-p_move) * p[row][col]
             temp.append(s)
         q.append(temp)
     return q

 def localize(colors,measurements,motions,sensor_right,p_move):
     # initializes p to a uniform distribution over a grid of the same dimensions as colors
     pinit = 1.0 / float(len(colors)) / float(len(colors[0]))
     p = [[pinit for row in range(len(colors[0]))] for col in range(len(colors))]

     # >>> Insert your code here <<<

     for k in range(len(motions)):
         p = move(p, motions[k],p_move)
         p = sense(p,colors,measurements[k],sensor_right)

     return p

 def show(p):
     rows = ['[' + ','.join(map(lambda x: '{0:.5f}'.format(x),r)) + ']' for r in p]
     print '[' + ',\n '.join(rows) + ']'

 #############################################################
 # For the following test case, your output should be
 # [[0.01105, 0.02464, 0.06799, 0.04472, 0.02465],
 #  [0.00715, 0.01017, 0.08696, 0.07988, 0.00935],
 #  [0.00739, 0.00894, 0.11272, 0.35350, 0.04065],
 #  [0.00910, 0.00715, 0.01434, 0.04313, 0.03642]]
 # (within a tolerance of +/- 0.001 for each entry)

 colors = [['R','G','G','R','R'],
           ['R','R','G','R','R'],
           ['R','R','G','G','R'],
           ['R','R','R','R','R']]
 measurements = ['G','G','G','G','G']
 motions = [[0,0],[0,1],[1,0],[1,0],[0,1]]
 p = localize(colors,measurements,motions,sensor_right = 0.7, p_move = 0.8)
 show(p) # displays your answer