ps5_ghost binary search

import random

# -----------------------------------
# Helper code
# (you don't need to understand this helper code)

import string

WORDLIST_FILENAME = "words.txt"

def load_words():
    """
    Returns a list of valid words. Words are strings of lowercase letters.
    Depending on the size of the word list, this function may
    take a while to finish.
    """
    print "Loading word list from file..."
    # inFile: file
    inFile = open(WORDLIST_FILENAME, 'r', 0)
    # wordlist: list of strings
    wordlist = []
    for line in inFile:
        wordlist.append(line.strip().lower())
    print "  ", len(wordlist), "words loaded."
    return wordlist

def get_frequency_dict(sequence):
    """
    Returns a dictionary where the keys are elements of the sequence
    and the values are integer counts, for the number of times that
    an element is repeated in the sequence.
    sequence: string or list
    return: dictionary
    """
    # freqs: dictionary (element_type -> int)
    freq = {}
    for x in sequence:
        freq[x] = freq.get(x,0) + 1
    return freq

# (end of helper code)
# -----------------------------------

# Actually load the dictionary of words and point to it with
# the wordlist variable so that it can be accessed from anywhere
# in the program.

wordlist = load_words()

# TO DO: your code begins here!

def ghost():
    frag = ''
    count = 0
    while True:
        print 'Current word fragment: ', frag
        if count%2 == 0:
            player = 'Player 1'
        else: player = 'Player 2'

        print player,
        lettera = raw_input('says: ')
        letter = lettera.lower()
        first = 0
        last = len(wordlist)-1

        if letter in string.ascii_letters:
            frag += letter
            exists = exist_word(wordlist,frag,first,last)# set variable so it will run only once
            if exists == False:
                print player, 'loses because no word begins with', frag.upper()
                break
            if exists == True and len(frag)>3:
                    print player, 'loses because',frag.upper(), 'is a word!'
                    break
            count += 1
        else: print 'Invalid character. Try again.'
    return frag

def fragment(frag, word):
    if word.startswith(frag)==True:
        return True
    else: return False

def exist_word(wordlist, frag, first, last):
    """
    Binary search. If either last 2 words left is the frag, return True.
    """
    #print first, last, call, wordlist[last], frag
    mid = first + ((last-first)/2)
    #print mid, wordlist[mid]

    ##End Test. Function runs until there are 2 words left
    ##Note: The wordlist[last] is always less than word fragment or, if it exists,
    ##1 before the fragment. Therefore, compare wordlist[last+1]

    if last-first<2:
            if wordlist[first]==frag or wordlist[last]==frag:
                return True
            elif fragment(frag, wordlist[last+1]) == False:
                return False
            else:
                return None

    if wordlist[mid] == frag:
            return True
    if wordlist[mid] > frag:
            return exist_word(wordlist, frag, first, mid-1)
    return exist_word(wordlist, frag, mid + 1, last)

ghost()