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

# In[1]:


def rotations(t):
    ''' Return list of rotations of input string t '''
    tt = t * 2
    return [ tt[i:i+len(t)] for i in range(0, len(t)) ]

def bwm(t):
    ''' Return lexicographically sorted list of t’s rotations '''
    return sorted(rotations(t))

def bwtViaBwm(t):
    ''' Given T, returns BWT(T) by way of the BWM '''
    return ''.join(map(lambda x: x[-1], bwm(t)))


# In[2]:


t = 'abaaba$'
b = bwtViaBwm(t)
b


# In[3]:


def rankBwt(bw):
    ''' Given BWT string bw, return parallel list of B-ranks.  Also
        returns tots: map from character to # times it appears. '''
    tots = dict()
    ranks = []
    for c in bw:
        if c not in tots:
            tots[c] = 0
        ranks.append(tots[c])
        tots[c] += 1
    return ranks, tots


# In[4]:


ranks, tots = rankBwt(b)
print zip(b, ranks) # print characters of BWT(T) in order, along with rank


# In[5]:


def firstCol(tots):
    ''' Return map from character to the range of rows prefixed by
        the character. '''
    first = {}
    totc = 0
    for c, count in sorted(tots.items()):
        first[c] = (totc, totc + count)
        totc += count
    return first


# In[6]:


firstCol(tots)


# In[7]:


# confirm that the representation of the first column above is sensible
print('\n'.join(bwm(t)))


# In[8]:


def reverseBwt(bw):
    ''' Make T from BWT(T) '''
    ranks, tots = rankBwt(bw)
    first = firstCol(tots)
    rowi = 0 # start in first row
    t = '$' # start with rightmost character
    while bw[rowi] != '$':
        c = bw[rowi]
        t = c + t # prepend to answer
        # jump to row that starts with c of same rank
        rowi = first[c][0] + ranks[rowi]
    return t


# In[9]:


reverseBwt(b)


# In[10]:


reverseBwt(bwtViaBwm('In_the_jingle_jangle_morning$'))