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string.py
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string.py
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#!/usr/bin/python3
#
# Copyright (c) 2013-2014, savrus
#
def ZFunction(s):
z = [len(s)] if len(s) > 0 else []
last = 0
lasti = 0
for i in range(1, len(s)):
t = 0
if i < last: t = min(z[i-lasti], last - i)
if i+t >= last:
lasti = i
while i+t < len(s) and s[i+t] == s[t]: t += 1
last = i + t
z.append(t)
return z
def PrefixFunction(s):
p = [0] if len(s) > 0 else []
for i in range(1,len(s)):
t = p[i-1]
while t > 0 and s[t] != s[i]: t = p[t-1]
if s[t] == s[i]: t += 1
else: assert(t == 0)
p.append(t)
return(p)
def ZFunction2PrefixFunction(z):
p = [0] if len(z) > 0 else []
last = 1
for i in range(1, len(z)):
for j in range(last, i+z[i]): p.append(j-i+1)
last = max(last,i+z[i])
if last == len(z)-1: p.append(0)
return p
def PrefixFunction2ZFunction(p):
z = [len(p)] if len(p) > 0 else []
last = 0
lasti = 0
for i in range(1, len(p)):
t = 0
if i < last: t = min(z[i-lasti], last - i)
if i+t >= last:
lasti = i
while i+t < len(p) and p[i+t] == t+1: t += 1
last = i + t
z.append(t)
return z
class SuffixTree:
# Nodes are of class Node. Node.out is a dict which contains outgoing edges. Keys are first characters.
# Edges are lists of 3 element: [start, end, target node].
# If target node is a leaf, it is None and so is the end.
# Tree is traversed by Position. If Position.edge is None, we are at a node Position.node.
# Oherwise we are at edge Position.edge skipping Position.skip characters.
# After Position.way() and Position.link() we are either at a node or in the middle of edge.
# After split() we are at the end of the edge (skip equals edge length), but we don't go there
# because our link is at the beginning of the edge and we are going to use it right after split()
class Node:
def __init__(self):
self.out = {}
self.link = None
def way(self, c):
return self.out.get(c, None)
class Position:
def __init__(self, s, node):
self.s = s
self.node = node
self.edge = None
self.skip = None
# Try to extend position by character 'c'. Returns True on success, False otherwise
def way(self, c):
if self.edge == None:
self.edge = self.node.way(c)
if self.edge == None: return False
self.skip = 1
else:
if c == self.s[self.edge[0]+self.skip]: self.skip += 1
else: return False
if self.edge[0] + self.skip == self.edge[1]:
self.node = self.edge[2]
self.edge = None
return True
# Go by link. Return True on success, False otherwise (= we are already at root)
def link(self):
if self.edge == None:
if self.node.link == None: return False
self.node = self.node.link
else:
k = self.edge[0]
if self.node.link == None:
k += 1
self.skip -= 1
else:
self.node = self.node.link
edge = None
while self.skip > 0 and edge == None:
edge = self.node.out[self.s[k]]
if edge[1] != None and edge[1]-edge[0] <= self.skip:
#assert(self.s[edge[0]:edge[1]] == self.s[k:k+edge[1]-edge[0]])
self.skip -= edge[1]-edge[0]
k += edge[1]-edge[0]
self.node = edge[2]
edge = None
self.edge = edge
return True
# Append new leaf to the node
def addleaf(self, node, i):
assert(node.way(self.s[i]) == None)
node.out[self.s[i]] = [i, None, None]
# Split edge at current position. We stay at old node
def split(self, p):
assert(p.skip > 0 and (p.edge[1] == None or p.edge[0] + p.skip < p.edge[1]))
node = self.Node()
node.out[self.s[p.edge[0]+p.skip]] = [p.edge[0]+p.skip, p.edge[1], p.edge[2]]
p.edge[1:3] = [p.edge[0] + p.skip, node]
# Construct Suffix Tree
def __init__(self, s):
self.endsymbol = chr(0)
self.s = s + self.endsymbol
self.root = self.Node()
p = self.Position(self.s, self.root)
for i in range(len(self.s)):
prev = None
while not p.way(self.s[i]):
n = p.node
if p.edge != None:
self.split(p)
n = p.edge[2]
if prev:
assert(prev.link == None or prev.link == n)
prev.link = n
prev = n
self.addleaf(n,i)
if not p.link():
assert(p.node == self.root)
break
# if We are at edge, next time we will split it and create a node for link
# but if we are already at a node, there is no guarantee that the loop will continue
if p.edge == None:
assert(prev.link == None or prev.link == p.node)
prev.link = p.node
# Search string in the tree. Succes if we finish matching at a leaf.
def __contains__(self, string):
string += self.endsymbol
i = 0
n = self.root
e = None
while i < len(string):
if string[i] not in n.out.keys(): return False
e = n.out[string[i]]
eend = e[1] if e[1] != None else len(self.s)
#if string[i:i + eend-e[0]] != self.s[e[0]:eend]: return False
if not self.s.startswith(string[i:i + eend-e[0]], e[0], eend): return False
i += eend-e[0]
n = e[2]
return e == None or e[1] == None
# Iterate over all strings in the tree
def __iter__(self):
stack = [ (self.root, iter(sorted(self.root.out.items())), 0) ]
ss = ""
while len(stack) > 0:
node, it, plen = stack[-1]
try: k, edge = next(it)
except StopIteration:
stack.pop()
ss = ss[:-plen]
continue
if edge[2] == None: yield ss + self.s[edge[0]:-len(self.endsymbol)]
else:
stack.append((edge[2], iter(sorted(edge[2].out.items())), edge[1]-edge[0]))
ss += self.s[edge[0]:edge[1]]
# Return Suffix Array
def SA(self):
stack = [ (self.root, iter(sorted(self.root.out.items())), 0) ]
l = 0
sa = []
while len(stack) > 0:
node, it, plen = stack[-1]
try: k, edge = next(it)
except StopIteration:
stack.pop()
l -= plen
continue
if edge[2] == None:
ll = l + len(self.s) - edge[0]
if ll > 1: sa.append(len(self.s)-ll)
else:
stack.append((edge[2], iter(sorted(edge[2].out.items())), edge[1]-edge[0]))
l += edge[1] - edge[0]
return sa
# Represent the entire Suffix Tree as a string (for debugging)
def string(self, i):
stack = [(self.root, 0)]
n = 1
s = ""
while len(stack) > 0:
node, node_id = stack.pop()
s += "%s:" % node_id
for k, e in node.out.items():
if e[2] != None:
s += " (%s)\'%s\'[%s:%s]->%s" % (k, self.s[e[0]:e[1]],e[0],e[1], n)
stack.append((e[2], n))
n += 1
else:
s += " (%s)\'%s\'[%s:%s]->leaf" % (k, self.s[e[0]:i],e[0],i)
s += "\n"
return s
def __str__(self): return self.string(None)
def _string_test():
import random
A = "abcdefghijklmnopqrstuvwxyz"
def StringGenerator(length, alphabet):
s = [0]*length
while 1:
yield "".join([alphabet[x] for x in s])
p = length - 1
while p >= 0 and s[p] == len(alphabet) - 1:
s[p] = 0
p -= 1
if p == -1: return
s[p] += 1
def ZFunctionSlow(s):
z = []
for i in range(0,len(s)):
l = 0
while i+l < len(s) and s[l] == s[i+l]: l += 1
z.append(l)
return z
def PrefixFunctionSlow(s):
p = [0] if len(s) > 0 else []
for i in range(1, len(s)):
l = 0
for t in range(0,i):
if s[0:t+1] == s[i-t:i+1]: l = t+1
p.append(l)
return p
def test_ZFunction_PrefixFunction():
for l in range(0,7):
for s in StringGenerator(l, A[0:l]):
assert(PrefixFunctionSlow(s) == PrefixFunction(s))
assert(ZFunctionSlow(s) == ZFunction(s))
assert(ZFunction2PrefixFunction(ZFunction(s)) == PrefixFunction(s))
assert(ZFunction(s) == PrefixFunction2ZFunction(PrefixFunction(s)))
print("Test ZFunction_PrefixFunction Passed")
def SuffixArraySlow(s):
suff = []
for i in range(len(s)):
suff.append(s[i:])
sa = []
for i in sorted(suff):
sa.append(len(s) - len(i))
return sa
def test_SuffixTree():
assert "aba" not in SuffixTree("aabba")
line = "".join([A[random.randrange(len(A))] for i in range(100000)])
t = SuffixTree(line)
for i in range(len(line)): assert line[i:] in t
for s in t: assert line.endswith(s)
print("Test Suffix Tree Passed")
def test_SuffixArray():
line = "".join([A[random.randrange(len(A))] for i in range(100000)])
assert(SuffixArraySlow(line) == SuffixTree(line).SA())
print("Test Suffix Array Passed")
test_ZFunction_PrefixFunction()
test_SuffixTree()
test_SuffixArray()
if __name__ == "__main__": _string_test()