1 
	Implement the functions forward() and backward() in hmm.py:
	• forward(π, A, B,O) takes the model parameters π, A, B and the observation sequence O as input
	  and output a numpy array α, where α[j, t − 1] = P(Zt = sj, X1:t = x1:t). Note that this is α[j, t − 1]
	  instead of α[j, t] just because the index of an array starts from 0.
	• backward(π, A, B,O) takes the model parameters π, A, B and the observation sequence O as input
	  and output a numpy array β, where β[j, t − 1] = P(Xt+1:N = xt+1:N | Zt = sj). Note the same index
	  difference.

2 
	Calculate P(X1:N = O) from the output of your forward and backward algorithms. Implement the function seqprob_forward() 
and seqprob_backward() in hmm.py. Both of them should return P(X1:N = O). Note that in seqprob_forward() the input is only 
the forward messages, while in seqprob backward() you have access to the model parameters too.

3 
	Find the most likely state path based on the observation O, namely,
		argmax z∗ 1:N P(Z1:N = z∗ 1:N | X1:N = O).
	Implement the Viterbi algorithm viterbi() in hmm.py. The function viterbi(π, A, B,O) takes
the model parameters π, A, B and the observation sequence O as inputs and outputs a list path which contains
the most likely state path z∗ 1:N (in terms of the state index) you have found.