import numpy as np #hint: np.log
import sys
from collections import defaultdict,Counter
from gtnlplib import scorer, most_common,preproc
from gtnlplib.constants import OFFSET

def estimate_nb(x,y,smoothing):
    """estimate a naive bayes model

    :param x: list of dictionaries of base feature counts
    :param y: list of labels
    :param smoothing: smoothing constant
    :returns: weights
    :rtype: defaultdict 

    """
    #hint: use your solution from pset 1
    raise NotImplementedError

def estimate_nb_tagger(counters,smoothing):
    """build a tagger based on the naive bayes classifier, which correctly accounts for the prior P(Y)

    :param counters: dict of word-tag counters, from most_common.get_tag_word_counts
    :param smoothing: value for lidstone smoothing
    :returns: classifier weights
    :rtype: defaultdict

    """
    # hint: call estimate_nb, then modify the output
    raise NotImplementedError