words = ['<s>', 'the', 'aged', 'bottle', 'flies', 'fast', '</s>']
k = len(words)


T = ['<s>', 'adj', 'adv', 'det', 'n', 'v', '</s>']
cardT = len(T)
a = [[0.0, 0.4, 0.2, 0.2, 0.1, 0.1, 0.0],
     [0.0, 0.2, 0.1, 0.0, 0.3, 0.2, 0.2],
     [0.0, 0.2, 0.2, 0.1, 0.1, 0.2, 0.2],
     [0.0, 0.3, 0.1, 0.0, 0.5, 0.1, 0.0],
     [0.0, 0.1, 0.1, 0.1, 0.2, 0.3, 0.2],
     [0.0, 0.2, 0.3, 0.1, 0.2, 0.0, 0.2], 
     [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]


b = [[1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], 
     [0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0],
     [0.0, 0.1, 0.0, 0.0, 0.0, 0.01, 0.0],
     [0.0, 0.0, 0.0, 0.0, 0.1, 0.1, 0.0],
     [0.0, 0.0, 0.0, 0.0, 0.1, 0.2, 0.0],
     [0.0, 0.1, 0.3, 0.0, 0.01, 0.1,0.0],
     [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]]  

b = dict(zip(words,b))      

alpha = [None for _ in range(k)]
alpha[0] = b["<s>"]
for t in range(1,k):
    alpha[t] = [sum([alpha[t-1][i] *  a[i][j] for i in range(cardT)])*b[words[t]][j] for j in range(cardT)]


for group in alpha:
    print group