# CG_BWT_Reverse

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In :

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)))

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In :

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

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Out:

'abba\$aa'

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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

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In :

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

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[('a', 0), ('b', 0), ('b', 1), ('a', 1), ('\$', 0), ('a', 2), ('a', 3)]

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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.iteritems()):
first[c] = (totc, totc + count)
totc += count
return first

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In :

firstCol(tots)

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Out:

{'\$': (0, 1), 'a': (1, 5), 'b': (5, 7)}

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

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\$abaaba
a\$abaab
aaba\$ab
aba\$aba
abaaba\$
ba\$abaa
baaba\$a

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def reverseBwt(bw):
''' Make T from BWT(T) '''
ranks, tots = rankBwt(bw)
first = firstCol(tots)
rowi = 0 # start in first row
while bw[rowi] != '\$':
c = bw[rowi]
t = c + t # prepend to answer
rowi = first[c] + ranks[rowi]
return t

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reverseBwt(b)

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Out:

'abaaba\$'

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In :

reverseBwt(bwtViaBwm('In_the_jingle_jangle_morning\$'))

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Out:

'In_the_jingle_jangle_morning\$'

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