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)))
t = 'abaaba$'
b = bwtViaBwm(t)
b
'abba$aa'
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
ranks, tots = rankBwt(b)
print zip(b, ranks) # print characters of BWT(T) in order, along with rank
[('a', 0), ('b', 0), ('b', 1), ('a', 1), ('$', 0), ('a', 2), ('a', 3)]
def firstCol(tots):
''' Return map from character to the range of rows prefixed by
the character. '''
first = {}
totc = 0
for c, count in sorted(tots.items()):
first[c] = (totc, totc + count)
totc += count
return first
firstCol(tots)
{'$': (0, 1), 'a': (1, 5), 'b': (5, 7)}
# confirm that the representation of the first column above is sensible
print('\n'.join(bwm(t)))
$abaaba a$abaab aaba$ab aba$aba abaaba$ ba$abaa baaba$a
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
reverseBwt(b)
'abaaba$'
reverseBwt(bwtViaBwm('In_the_jingle_jangle_morning$'))
'In_the_jingle_jangle_morning$'