def compute_transition_matrix(order, l0, l1, l2, C_t, C_tt, C_ttt, num_tokens):
    """
    """
    # for order = 2
    if order == 2:
        transition_matrix = defaultdict(lambda: defaultdict(int))
        for key1 in C_tt:
            for key2 in C_tt[key1]:
                if C_t[key1] != 0:
                    transition_matrix[key1][key2] = l1 * (C_tt[key1][key2] / float(C_t[key1])) + l0 * (C_t[key2] / float(num_tokens))

    # for order = 3
    else:
        transition_matrix = defaultdict(lambda: defaultdict(lambda: defaultdict(int)))
        for key1 in C_ttt:
            for key2 in C_ttt[key1]:
                for key3 in C_ttt[key2]:
                    if C_tt[key1][key2] == 0:
                        transition_matrix[key1][key2][key3] = l1 * (C_tt[key2][key3] / float(C_t[key2])) + l0 * (C_t[key3] / float(num_tokens))
                    elif C_tt[key1][key2] != 0 and C_t[key2] != 0:
                        transition_matrix[key1][key2][key3] = l2 * (C_ttt[key1][key2][key3] / float(C_tt[key1][key2])) + l1 * (C_tt[key2][key3] / float(C_t[key2])) + l0 * (C_t[key3] / float(num_tokens))

    return transition_matrix