"""
Is It A Tree? A Tree Finder.
This python script is for solving the ACM problem Q1308: Is It A Tree?
http://acm.pku.edu.cn/JudgeOnline/problem?id=1308
Copyright 2009 Shao-Chuan Wang <shaochuan.wang@gmail.com>
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
"""
__author__ = "Shao-Chuan Wang"
__email__ = "shaochuan.wang@gmail.com"
__version__ = "1.0"
__URL__ = "http://shao-chuan.appspot.com"
class DirectedGraph(object):
def __init__(self):
self.vertices = set()
self.adjs = {}
def add_vertex(self, v):
if v not in self.vertices:
self.vertices.add(v)
self.adjs[v] = {}
else:
print 'warning! try to add a existed vertex.'
def add_edge(self, u, v, w=1):
''' @ add an edge from u -> v.
'''
if u not in self.vertices:
self.add_vertex(u)
if v not in self.vertices:
self.add_vertex(v)
self.adjs[u][v] = w
def adjacents(self, u):
return self.adjs[u].keys()
class TreeFinder(object):
def __init__(self):
self.has_duplicate_edges = False
self.inv_g = DirectedGraph()
self.roots = set()
def add_edges(self, edges):
if len(edges) != len(set(edges)):
self.has_duplicate_edges = True
for u,v in edges:
self.inv_g.add_edge(v,u) # here, the most tricky part!!
def find_roots(self, v, visited):
''' @return: False, if failed to find the root,
starting with vertex 'v' and past path 'visited'
True, otherwise.
'''
adjs = self.inv_g.adjacents(v)
if not adjs:
self.roots.add(v)
return True
if len(adjs)>1:
return False # With bifurcation
else:
u = adjs[0]
visited[v] = True
if not visited.get(u, False):
return self.find_roots(u, visited)
else:
return False # With cycle
return True
def isTree(self):
if not self.inv_g.vertices:
return True
if self.has_duplicate_edges:
return False
isATree = True
for v in self.inv_g.vertices:
if not self.find_roots(v, {}):
isATree = False
if not isATree:
return False
if len(self.roots) != 1:
return False
return True
class Reader(object):
def __init__(self, fd):
self.fd = fd
def process_line(self, line):
it = iter(map(int, line.strip().split()))
return zip(it,it)
def gen_edges(self):
edges = []
while True:
try:
line = self.fd.next()
edges.extend( self.process_line(line) )
if edges[-1] == (0,0):
edges.pop()
yield edges
edges = []
elif edges[-1] == (-1,-1):
break
except StopIteration:
break
def __del__(self):
self.fd.close()
if __name__=='__main__':
import StringIO
import random
import time
def test(test_data):
fd = StringIO.StringIO()
fd.write(test_data)
fd.seek(0)
r = Reader(fd)
for case_id, edges in enumerate(r.gen_edges()):
tree_finder = TreeFinder()
tree_finder.add_edges(edges)
s = '' if tree_finder.isTree() else 'not '
print 'Case %d is %sa tree' % (case_id+1, s)
simple_test_data = '''8 1
7 3 6 2 8 9 7 5
7 4 7 8 7 6 0 0
6 8 5 3 5 2 6 4
5 6 0 0
3 8 6 8 6 4
5 3 5 6 5 2 0 0
0 0
1 2 0 0
1 2 1 3 4 5 0 0
1 1 0 0
1 2 2 1 0 0
1 2 1 2 0 0
1 2 2 3 3 1 4 5 0 0
-1 -1
'''
test(simple_test_data)
print '='*5,'my test data','='*5
long_path = ' '.join(
['%d %d' % (i, i+1) for i in xrange(1,300)]+['\n']
)
long_path_2 = ' '.join(
['%d %d' % (i, i+1) for i in xrange(301,400)]+['\n']
)
is_a_tree_test_data = ''.join([long_path, long_path_2, '32 301 0 0'])
start_time = time.time()
test(is_a_tree_test_data)
print 'time: %f' %(time.time()-start_time)
is_not_a_tree_test_data = ''.join([long_path, long_path_2, '32 305 0 0'])
start_time = time.time()
test(is_not_a_tree_test_data)
print 'time: %f' %(time.time()-start_time)
