import random
import math
from pprint import pprint

CYCLE = 10000

def resetGrid(grid):
	for key, value in grid.items():
		value[0] = 0

def selectRoute(routes):
	'''
	Generates a random number then decides which way to go
	according to the probabilities
	'''
	prob = random.uniform(0, 1)
	routesProb = 0
	for i, route in enumerate(routes):
		routesProb += route[1]
		if prob < routesProb:
			return i
	return None

def displayResults(grid, opt, reps, steps):
	''' display function '''
	print("RUN WITH {} REPETITIONS AND {} STEPS".format(reps, steps))
	if opt == 3:
		for key, value in grid.items():
			print("CELL %d, turtle crosses it %d times, which probability is : %.3f" % (key, value[0], value[0] / (reps)))
	elif opt == 4:
		for key, value in grid.items():
			print("CELL %d, turtle crosses it %d times, which probability is : %.3f" % (key, value[0], value[0] / (reps * steps)))

def standardDeviation(samples):
	# compute standard deviation, by calculing the average of samples, the variance and standard deviation
	stdDev = {}
	for key, sample in samples.items():
		if len(sample) > 0:
			average = sum(sample) / len(sample)
			variance = sum([(value - average) ** 2 for value in sample]) / len(sample)
			stdDev[key] = math.sqrt(variance)
		else:
			stdDev[key] = 0
	print("standard deviations : ")
	for key, value in stdDev.items():
		print("CELL %d, standard deviation : %.3f" % (key, round(value, 3)))

def simulation(grid, samples, steps, opt):
	'''
	one repetition process, choose a route
	then increments cell traffic at the end of steps (for task 3)
	'''
	pos = 1
	for i, step in enumerate(range(steps)):
		route = selectRoute(grid[pos][1])
		if route != None:
			pos = grid[pos][1][route][0]
		if opt == 4:
			grid[pos][0] += 1
			if i != 0 and i % CYCLE == 0:
				for key in samples.keys():
					samples[key].append(grid[key][0] / step)
	if opt == 3:
		grid[pos][0] += 1
	return pos

def taskThree(grid):
	REPETITIONS = 10000
	STEPS = 3
	OPTION = 3
	# dict to store probabilities states
	resetGrid(grid)
	samples = {1: [], 3: [], 9: []}
	for rep in range(REPETITIONS):
		pos = simulation(grid, samples, STEPS, OPTION)
		if pos in samples.keys():
			samples[pos].append((grid[pos][0]) / (REPETITIONS))
	displayResults(grid, OPTION, REPETITIONS, STEPS)
	return samples

def taskFour(grid):
	REPETITIONS = 1
	STEPS = 1000000
	OPTION = 4
	# dict to store probabilities states
	resetGrid(grid)
	samples = {1: [], 3: [], 9: []}
	for rep in range(REPETITIONS):
		pos = simulation(grid, samples, STEPS, OPTION)
	displayResults(grid, OPTION, REPETITIONS, STEPS)
	return samples

def main():
	'''
	entry point, defines grid with an index for each node,
	a number of crossing on the cell,
	a list of nodes with their transition probabilities
	'''
	grid = {1: [0, [(2, 1/4), (4, 1/4)]],
			2: [0, [(1, 1/4), (5, 1/4), (3, 1/4)]],
			3: [0, [(2, 1/4), (6, 1/4)]],
			4: [0, [(1, 1/8), (5, 1/4), (7, 1/4)]],
			5: [0, [(4, 1/4), (8, 1/4), (6, 1/4), (2, 1/8)]],
			6: [0, [(3, 1/8), (5, 1/4), (9, 1/4)]],
			7: [0, [(4, 1/6), (8, 1/4)]],
			8: [0, [(7, 1/4), (5, 1/6), (9, 1/4)]],
			9: [0, [(8, 1/4), (6, 1/6)]]}

	standardDeviation(taskThree(grid))
	standardDeviation(taskFour(grid))

if __name__ == '__main__':
	main()