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def SA(A):
def SA_IS(A):
def equal(pos1, pos2):
end1, end2 = LMS.find('*', pos1+1), LMS.find('*', pos2+1)
return A[pos1:end1+1] == A[pos2:end2+1]
def IS(stars):
sa = [n] + [-1] * n
tails = list(accumulate(bucket))
for i in stars[::-1]:
sa[tails[A[i]]] = i
tails[A[i]] -= 1
heads = list(accumulate([1] + bucket[:-1]))
for i in range(n + 1):
j = sa[i] - 1
if j >= 0 and types[j] == 'L':
sa[heads[A[j]]] = j
heads[A[j]] += 1
tails = list(accumulate(bucket))
for i in range(n, -1, -1):
j = sa[i] - 1
if j >= 0 and types[j] == 'S':
sa[tails[A[j]]] = j
tails[A[j]] -= 1
return sa[1:]
n = len(A)
types = list('0' * (n - 1) + 'LS')
for i in range(n - 2, -1, -1):
types[i] = 'S' if A[i] < A[i + 1] else 'L' if A[i] > A[i + 1] else types[i + 1]
LMS = ''.join('*' if types[i - 1:i + 1] == ['L', 'S'] else ' ' for i in range(n + 1))
ct = Counter(A)
bucket = [ct[x] for x in range(max(ct) + 1)]
stars = [i for i in range(n) if LMS[i] == '*']
sa = IS(stars)
d, cnt, prev = {}, 0, -1
for pos in sa:
if LMS[pos] == '*':
cnt += prev < 0 or not equal(prev, pos)
d[pos] = cnt
prev = pos
B = [d[pos] for pos in stars]
d1 = {x-1:i for i,x in enumerate(B)}
sa1 = [d1[x] for x in range(cnt)] if cnt == len(B) else SA_IS(B)
return IS([stars[pos] for pos in sa1])
def SA_h(A,sa):
n = len(A)
rk, height, h = [0]*n,[0]*n,0
for i in range(n):
rk[sa[i]] = i
for i in range(n):
h = max(0, h-1)
j = sa[rk[i]-1] if rk[i] else n
while max(i,j)+h<n and A[i+h]==A[j+h]:
h += 1
height[rk[i]] = h
return rk, height
sa = SA_IS(A) # sa[i]:第i小的后缀编号
rk, height = SA_h(A,sa) # rk[i]:后缀i的排名
return sa,rk,height # height[i]:lcp(sa[i],sa[i-1])
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