%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np

def discrete_prob(d):
    r = np.random.random()
    sum = 0
    for k in d:
        sum += d[k]
        if r < sum:
            return k

weather = {"Sunny":0.62, "Rainy":0.38}
for i in range(10):
    print discrete_prob(weather)

weather2 = {"Sunny":{"Sunny":0.8, "Rainy":0.2},
            "Rainy":{"Sunny":0.4, "Rainy":0.6}}

seq = ["Sunny"]
for i in range(10):
    seq.append(discrete_prob(weather2[seq[-1]]))

seq

fin = open("conway_weather.txt")
cw = []
for line in fin:
    cw.append(line.strip())

mc = {}
for i in range(1, len(cw)):
    p = cw[i - 1]
    if p not in mc:
        mc[p] = {}
    mc[p][cw[i]] = mc[p].get(cw[i], 0) + 1
for k in mc:
    sum = 0
    for k2 in mc[k]:
        sum += mc[k][k2]
    for k2 in mc[k]:
        mc[k][k2] /= float(sum)

mc

seq = ["clear"]
for i in range(100):
    seq.append(discrete_prob(mc[seq[-1]]))

seq

weighted = {"T":{"T":0.55,"H":0.45}, "H":{"T":0.45, "H":0.55}}

seq = ["T"]
for i in range(1000):
    seq.append(discrete_prob(weighted[seq[-1]]))

len(seq)

rc = 0.5 ** len(seq)

rc

prob = 1
for i in range(1, len(seq)):
    prob *= weighted[seq[i - 1]][seq[i]]

prob

prob / rc