#!/usr/bin/env python
# coding: utf-8

# In[1]:


from bisect import bisect_left, bisect_right # for binary search
import random
random.seed(77) # so that you and I get same random lists


# In[2]:


a = [1, 2, 3, 3, 3, 4, 5]
bisect_left(a, 3), bisect_right(a, 3)


# In[3]:


a = [2, 4, 6, 8, 10]
bisect_left(a, 5), bisect_right(a, 5)


# In[4]:


# make a list of pseudo-random integers in [1, 99]
ls = [ random.randint(1, 99) for _ in range(30) ]
ls # show it


# In[5]:


ls.sort() # sort the list in-place
ls # show the sorted list; note there are some repeated elements


# In[6]:


# The number 40 is not in the sorted list.  If it were, where would it go?
bisect_left(ls, 40)


# In[7]:


# insert it
ls.insert(13, 40)
ls # show the new list


# In[8]:


# The number 19 appears in the list multiple times.
# Say we want a range [st, en) where st is the first element
# (inclusive) and en is last element (exclusive) that contains a 19
st, en = bisect_left(ls, 19), bisect_right(ls, 19)


# In[9]:


st, en


# In[10]:


ls[st:en]


# In[11]:


# Of course, there also exists a total ordering over strings
# (lexicographical ordering), so we can do all the same things
# with strings
strls = ['a', 'awkward', 'awl', 'awls', 'axe', 'axes', 'bee']


# In[12]:


strls == sorted(strls)


# In[13]:


# We want to get the range of elements that equal a query string:
st, en = bisect_left(strls, 'awl'), bisect_right(strls, 'awl')
st, en


# In[14]:


# Say we want to get the range of elements that have some prefix,
# e.g. 'aw' and say that 'z' is the lexicographically greatest
# character in the alphabet.
st, en = bisect_left(strls, 'aw'), bisect_left(strls, 'ax')
st, en


# In[15]:


strls[st:en]


# In[16]:


# If we can do it for any sorted list of strings, we can do it for
# a sorted list of suffixes
t = 'abaaba$'
suffixes = sorted([t[i:] for i in range(len(t))])
suffixes


# In[17]:


st, en = bisect_left(suffixes, 'aba'), bisect_left(suffixes, 'abb')
st, en