import operator
MIN_FLOAT = -3.14e100
MIN_INF = float("-inf")

def get_top_states(t_state_v, K=4):
    topK = sorted(t_state_v.items(), key=operator.itemgetter(1), reverse=True)[:K]
    return [x[0] for x in topK]

def viterbi(obs, states, start_p, trans_p, emit_p):
    V = [{}] #tabular
    mem_path = [{}]
    all_states = trans_p.keys()
    for y in states.get(obs[0], all_states): #init
        V[0][y] = start_p[y] + emit_p[y].get(obs[0], MIN_FLOAT)
        mem_path[0][y] = ''
    for t in range(1, len(obs)):
        V.append({})
        mem_path.append({})
        #prev_states = get_top_states(V[t-1])
        prev_states = [x for x in mem_path[t-1].keys() if len(trans_p[x]) > 0]

        prev_states_expect_next = set((y for x in prev_states for y in trans_p[x].keys()))
        obs_states = set(states.get(obs[t], all_states)) & prev_states_expect_next

        if not obs_states:
            obs_states = prev_states_expect_next if prev_states_expect_next else all_states

        for y in obs_states:
            prob, state = max([(V[t-1][y0] + trans_p[y0].get(y,MIN_INF) + emit_p[y].get(obs[t],MIN_FLOAT), y0) for y0 in prev_states])
            V[t][y] = prob
            mem_path[t][y] = state

    last = [(V[-1][y], y) for y in mem_path[-1].keys()]
    #if len(last)==0:
        #print obs
    prob, state = max(last)

    route = [None] * len(obs)
    i = len(obs) - 1
    while i >= 0:
        route[i] = state
        state = mem_path[i][state]
        i -= 1
    return (prob, route)