"""
A Minimum Cut Solver
This python script is for solving the ACM problem Q2914: Minimum Cut.
http://acm.pku.edu.cn/JudgeOnline/problem?id=2914
Instead of using Ford-Fulkerson method, I use Stoer and Wagner's Min cut Algorithm.
http://www.cs.dartmouth.edu/~ac/Teach/CS105-Winter05/Handouts/stoerwagner-mincut.pdf
However I also include the max flow method (from wiki) for benchmark.
The code can be found at: http://en.wikipedia.org/wiki/Ford-Fulkerson_algorithm
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"
g_TryFlowNetwork = False
class FlowNetwork(object):
''' This class is copied from wiki for benchmark.
'''
def __init__(self):
self.adj, self.flow, = {},{}
self.src, self.sink = None, None
def add_vertex(self, vertex):
self.adj[vertex] = []
def add_vertices(self, vertices):
map(self.add_vertex, vertices)
def get_edges(self, v):
return self.adj[v]
def add_edge(self, u,v,w=0):
self.adj[u].append((v,w))
self.adj[v].append((u,0))
self.flow[(u,v)] = self.flow[(v,u)] = 0
def find_path(self, source, sink, path):
if source == sink:
return path
for vertex, capacity in self.get_edges(source):
residual = capacity - self.flow[(source,vertex)]
edge = (source,vertex,residual)
if residual > 0 and not edge in path:
result = self.find_path(vertex, sink, path + [edge])
if result != None:
return result
def max_flow(self, source, sink):
path = self.find_path(source, sink, [])
while path != None:
flow = min(r for u,v,r in path)
for u,v,_ in path:
self.flow[(u,v)] += flow
self.flow[(v,u)] -= flow
path = self.find_path(source, sink, [])
return sum(self.flow[(source, vertex)] for vertex, capacity in self.get_edges(source))
class UndirectedGraph(object):
def __init__(self):
self.vertices = []
self.edges = {}
def add_vertex(self, v):
self.vertices.append(v)
self.edges[(v,v)] = 0
def add_vertices(self, v_s):
self.vertices.extend(v_s)
for v in v_s:
self.edges[(v,v)] = 0
def add_edge(self, u, v, w=0):
self.edges[(u,v)] = w
self.edges[(v,u)] = w
def adjacents(self, u):
li = []
for v in self.vertices:
w = self.edges.get((u,v),0)
if w:
li.append((v,w))
return li
def merge(self, u, v):
''' merge u to v, where v is in the graph
'''
u_adjs = self.adjacents(u)
for z,w in u_adjs:
self.edges.pop((u,z))
self.edges.pop((z,u))
self.vertices.remove(u)
v_adjs = dict(self.adjacents(v))
for n, w in u_adjs:
if n == v:
continue
v_adjs[n] = v_adjs.get(n,0) + w
for n, w in v_adjs.iteritems():
self.edges[(v,n)] = w
self.edges[(n,v)] = w
def w(g, A, y):
assert y not in A
return sum(w for v, w in g.adjacents(y) if v in A)
def min_cut_phase(g, a):
A = set([a])
V = set(g.vertices)
order = [a]
while A != V:
w_candidates = [(w(g, A, v), v) for v in V-A] #: candidates for most tightly connected
_, x = max(w_candidates)
A.add(x)
order.append(x)
t, s = order[-1], order[-2]
min_cut = sum(w for v, w in g.adjacents(t))
g.merge(t, s)
return min_cut
def minimum_cut(g, a):
min_cut = sum(w for v, w in g.adjacents(a))
while len(g.vertices) > 1:
min_cut_candidate = min_cut_phase(g, a)
if min_cut_candidate < min_cut:
min_cut = min_cut_candidate
return min_cut
class Reader(object):
''' A file reader: read the formated input data provided by Q2914: Minimum Cut
'''
def __init__(self, fd):
''' @param fd: an opened file-like object, and its contents are the input data.
'''
self.fd = fd
def gen_graph(self):
''' a generator that yield graphs in order
'''
while True:
try:
line = self.fd.next()
nVertices, nEdges = map(int, line.split())
if g_TryFlowNetwork:
g = FlowNetwork()
g.add_vertices(xrange(nVertices))
for i in xrange(nEdges):
u,v,w = map(int, self.fd.next().split())
if u < v:
g.add_edge(u, v, w)
else:
g.add_edge(v, u, w)
g.src, g.sink = 0, nVertices-1
else:
g = UndirectedGraph()
g.add_vertices(xrange(nVertices))
for i in xrange(nEdges):
u,v,w = map(int, self.fd.next().split())
g.add_edge(u, v, w)
yield g
except StopIteration:
break
def __del__(self):
self.fd.close()
if __name__=='__main__':
import time
from StringIO import StringIO
test_input = '''3 3
0 1 1
1 2 1
2 0 1
4 3
0 1 1
1 2 1
2 3 1
8 14
0 1 1
0 2 1
0 3 1
1 2 1
1 3 1
2 3 1
4 5 1
4 6 1
4 7 1
5 6 1
5 7 1
6 7 1
4 0 1
7 3 1
8 12
0 1 2
0 4 3
1 4 2
4 5 3
1 2 3
1 5 2
5 6 1
2 6 2
2 3 4
3 6 2
3 7 2
6 7 3
5 10
0 1 1
0 2 1
0 3 1
0 4 1
1 2 1
1 3 1
1 4 1
2 3 1
2 4 1
3 4 1
20 190
0 1 1
0 2 1
0 3 1
0 4 1
0 5 1
0 6 1
0 7 1
0 8 1
0 9 1
0 10 1
0 11 1
0 12 1
0 13 1
0 14 1
0 15 1
0 16 1
0 17 1
0 18 1
0 19 1
1 2 1
1 3 1
1 4 1
1 5 1
1 6 1
1 7 1
1 8 1
1 9 1
1 10 1
1 11 1
1 12 1
1 13 1
1 14 1
1 15 1
1 16 1
1 17 1
1 18 1
1 19 1
2 3 1
2 4 1
2 5 1
2 6 1
2 7 1
2 8 1
2 9 1
2 10 1
2 11 1
2 12 1
2 13 1
2 14 1
2 15 1
2 16 1
2 17 1
2 18 1
2 19 1
3 4 1
3 5 1
3 6 1
3 7 1
3 8 1
3 9 1
3 10 1
3 11 1
3 12 1
3 13 1
3 14 1
3 15 1
3 16 1
3 17 1
3 18 1
3 19 1
4 5 1
4 6 1
4 7 1
4 8 1
4 9 1
4 10 1
4 11 1
4 12 1
4 13 1
4 14 1
4 15 1
4 16 1
4 17 1
4 18 1
4 19 1
5 6 1
5 7 1
5 8 1
5 9 1
5 10 1
5 11 1
5 12 1
5 13 1
5 14 1
5 15 1
5 16 1
5 17 1
5 18 1
5 19 1
6 7 1
6 8 1
6 9 1
6 10 1
6 11 1
6 12 1
6 13 1
6 14 1
6 15 1
6 16 1
6 17 1
6 18 1
6 19 1
7 8 1
7 9 1
7 10 1
7 11 1
7 12 1
7 13 1
7 14 1
7 15 1
7 16 1
7 17 1
7 18 1
7 19 1
8 9 1
8 10 1
8 11 1
8 12 1
8 13 1
8 14 1
8 15 1
8 16 1
8 17 1
8 18 1
8 19 1
9 10 1
9 11 1
9 12 1
9 13 1
9 14 1
9 15 1
9 16 1
9 17 1
9 18 1
9 19 1
10 11 1
10 12 1
10 13 1
10 14 1
10 15 1
10 16 1
10 17 1
10 18 1
10 19 1
11 12 1
11 13 1
11 14 1
11 15 1
11 16 1
11 17 1
11 18 1
11 19 1
12 13 1
12 14 1
12 15 1
12 16 1
12 17 1
12 18 1
12 19 1
13 14 1
13 15 1
13 16 1
13 17 1
13 18 1
13 19 1
14 15 1
14 16 1
14 17 1
14 18 1
14 19 1
15 16 1
15 17 1
15 18 1
15 19 1
16 17 1
16 18 1
16 19 1
17 18 1
17 19 1
18 19 1
50 1225
0 1 1
0 2 1
0 3 1
0 4 1
0 5 1
0 6 1
0 7 1
0 8 1
0 9 1
0 10 1
0 11 1
0 12 1
0 13 1
0 14 1
0 15 1
0 16 1
0 17 1
0 18 1
0 19 1
0 20 1
0 21 1
0 22 1
0 23 1
0 24 1
0 25 1
0 26 1
0 27 1
0 28 1
0 29 1
0 30 1
0 31 1
0 32 1
0 33 1
0 34 1
0 35 1
0 36 1
0 37 1
0 38 1
0 39 1
0 40 1
0 41 1
0 42 1
0 43 1
0 44 1
0 45 1
0 46 1
0 47 1
0 48 1
0 49 1
1 2 1
1 3 1
1 4 1
1 5 1
1 6 1
1 7 1
1 8 1
1 9 1
1 10 1
1 11 1
1 12 1
1 13 1
1 14 1
1 15 1
1 16 1
1 17 1
1 18 1
1 19 1
1 20 1
1 21 1
1 22 1
1 23 1
1 24 1
1 25 1
1 26 1
1 27 1
1 28 1
1 29 1
1 30 1
1 31 1
1 32 1
1 33 1
1 34 1
1 35 1
1 36 1
1 37 1
1 38 1
1 39 1
1 40 1
1 41 1
1 42 1
1 43 1
1 44 1
1 45 1
1 46 1
1 47 1
1 48 1
1 49 1
2 3 1
2 4 1
2 5 1
2 6 1
2 7 1
2 8 1
2 9 1
2 10 1
2 11 1
2 12 1
2 13 1
2 14 1
2 15 1
2 16 1
2 17 1
2 18 1
2 19 1
2 20 1
2 21 1
2 22 1
2 23 1
2 24 1
2 25 1
2 26 1
2 27 1
2 28 1
2 29 1
2 30 1
2 31 1
2 32 1
2 33 1
2 34 1
2 35 1
2 36 1
2 37 1
2 38 1
2 39 1
2 40 1
2 41 1
2 42 1
2 43 1
2 44 1
2 45 1
2 46 1
2 47 1
2 48 1
2 49 1
3 4 1
3 5 1
3 6 1
3 7 1
3 8 1
3 9 1
3 10 1
3 11 1
3 12 1
3 13 1
3 14 1
3 15 1
3 16 1
3 17 1
3 18 1
3 19 1
3 20 1
3 21 1
3 22 1
3 23 1
3 24 1
3 25 1
3 26 1
3 27 1
3 28 1
3 29 1
3 30 1
3 31 1
3 32 1
3 33 1
3 34 1
3 35 1
3 36 1
3 37 1
3 38 1
3 39 1
3 40 1
3 41 1
3 42 1
3 43 1
3 44 1
3 45 1
3 46 1
3 47 1
3 48 1
3 49 1
4 5 1
4 6 1
4 7 1
4 8 1
4 9 1
4 10 1
4 11 1
4 12 1
4 13 1
4 14 1
4 15 1
4 16 1
4 17 1
4 18 1
4 19 1
4 20 1
4 21 1
4 22 1
4 23 1
4 24 1
4 25 1
4 26 1
4 27 1
4 28 1
4 29 1
4 30 1
4 31 1
4 32 1
4 33 1
4 34 1
4 35 1
4 36 1
4 37 1
4 38 1
4 39 1
4 40 1
4 41 1
4 42 1
4 43 1
4 44 1
4 45 1
4 46 1
4 47 1
4 48 1
4 49 1
5 6 1
5 7 1
5 8 1
5 9 1
5 10 1
5 11 1
5 12 1
5 13 1
5 14 1
5 15 1
5 16 1
5 17 1
5 18 1
5 19 1
5 20 1
5 21 1
5 22 1
5 23 1
5 24 1
5 25 1
5 26 1
5 27 1
5 28 1
5 29 1
5 30 1
5 31 1
5 32 1
5 33 1
5 34 1
5 35 1
5 36 1
5 37 1
5 38 1
5 39 1
5 40 1
5 41 1
5 42 1
5 43 1
5 44 1
5 45 1
5 46 1
5 47 1
5 48 1
5 49 1
6 7 1
6 8 1
6 9 1
6 10 1
6 11 1
6 12 1
6 13 1
6 14 1
6 15 1
6 16 1
6 17 1
6 18 1
6 19 1
6 20 1
6 21 1
6 22 1
6 23 1
6 24 1
6 25 1
6 26 1
6 27 1
6 28 1
6 29 1
6 30 1
6 31 1
6 32 1
6 33 1
6 34 1
6 35 1
6 36 1
6 37 1
6 38 1
6 39 1
6 40 1
6 41 1
6 42 1
6 43 1
6 44 1
6 45 1
6 46 1
6 47 1
6 48 1
6 49 1
7 8 1
7 9 1
7 10 1
7 11 1
7 12 1
7 13 1
7 14 1
7 15 1
7 16 1
7 17 1
7 18 1
7 19 1
7 20 1
7 21 1
7 22 1
7 23 1
7 24 1
7 25 1
7 26 1
7 27 1
7 28 1
7 29 1
7 30 1
7 31 1
7 32 1
7 33 1
7 34 1
7 35 1
7 36 1
7 37 1
7 38 1
7 39 1
7 40 1
7 41 1
7 42 1
7 43 1
7 44 1
7 45 1
7 46 1
7 47 1
7 48 1
7 49 1
8 9 1
8 10 1
8 11 1
8 12 1
8 13 1
8 14 1
8 15 1
8 16 1
8 17 1
8 18 1
8 19 1
8 20 1
8 21 1
8 22 1
8 23 1
8 24 1
8 25 1
8 26 1
8 27 1
8 28 1
8 29 1
8 30 1
8 31 1
8 32 1
8 33 1
8 34 1
8 35 1
8 36 1
8 37 1
8 38 1
8 39 1
8 40 1
8 41 1
8 42 1
8 43 1
8 44 1
8 45 1
8 46 1
8 47 1
8 48 1
8 49 1
9 10 1
9 11 1
9 12 1
9 13 1
9 14 1
9 15 1
9 16 1
9 17 1
9 18 1
9 19 1
9 20 1
9 21 1
9 22 1
9 23 1
9 24 1
9 25 1
9 26 1
9 27 1
9 28 1
9 29 1
9 30 1
9 31 1
9 32 1
9 33 1
9 34 1
9 35 1
9 36 1
9 37 1
9 38 1
9 39 1
9 40 1
9 41 1
9 42 1
9 43 1
9 44 1
9 45 1
9 46 1
9 47 1
9 48 1
9 49 1
10 11 1
10 12 1
10 13 1
10 14 1
10 15 1
10 16 1
10 17 1
10 18 1
10 19 1
10 20 1
10 21 1
10 22 1
10 23 1
10 24 1
10 25 1
10 26 1
10 27 1
10 28 1
10 29 1
10 30 1
10 31 1
10 32 1
10 33 1
10 34 1
10 35 1
10 36 1
10 37 1
10 38 1
10 39 1
10 40 1
10 41 1
10 42 1
10 43 1
10 44 1
10 45 1
10 46 1
10 47 1
10 48 1
10 49 1
11 12 1
11 13 1
11 14 1
11 15 1
11 16 1
11 17 1
11 18 1
11 19 1
11 20 1
11 21 1
11 22 1
11 23 1
11 24 1
11 25 1
11 26 1
11 27 1
11 28 1
11 29 1
11 30 1
11 31 1
11 32 1
11 33 1
11 34 1
11 35 1
11 36 1
11 37 1
11 38 1
11 39 1
11 40 1
11 41 1
11 42 1
11 43 1
11 44 1
11 45 1
11 46 1
11 47 1
11 48 1
11 49 1
12 13 1
12 14 1
12 15 1
12 16 1
12 17 1
12 18 1
12 19 1
12 20 1
12 21 1
12 22 1
12 23 1
12 24 1
12 25 1
12 26 1
12 27 1
12 28 1
12 29 1
12 30 1
12 31 1
12 32 1
12 33 1
12 34 1
12 35 1
12 36 1
12 37 1
12 38 1
12 39 1
12 40 1
12 41 1
12 42 1
12 43 1
12 44 1
12 45 1
12 46 1
12 47 1
12 48 1
12 49 1
13 14 1
13 15 1
13 16 1
13 17 1
13 18 1
13 19 1
13 20 1
13 21 1
13 22 1
13 23 1
13 24 1
13 25 1
13 26 1
13 27 1
13 28 1
13 29 1
13 30 1
13 31 1
13 32 1
13 33 1
13 34 1
13 35 1
13 36 1
13 37 1
13 38 1
13 39 1
13 40 1
13 41 1
13 42 1
13 43 1
13 44 1
13 45 1
13 46 1
13 47 1
13 48 1
13 49 1
14 15 1
14 16 1
14 17 1
14 18 1
14 19 1
14 20 1
14 21 1
14 22 1
14 23 1
14 24 1
14 25 1
14 26 1
14 27 1
14 28 1
14 29 1
14 30 1
14 31 1
14 32 1
14 33 1
14 34 1
14 35 1
14 36 1
14 37 1
14 38 1
14 39 1
14 40 1
14 41 1
14 42 1
14 43 1
14 44 1
14 45 1
14 46 1
14 47 1
14 48 1
14 49 1
15 16 1
15 17 1
15 18 1
15 19 1
15 20 1
15 21 1
15 22 1
15 23 1
15 24 1
15 25 1
15 26 1
15 27 1
15 28 1
15 29 1
15 30 1
15 31 1
15 32 1
15 33 1
15 34 1
15 35 1
15 36 1
15 37 1
15 38 1
15 39 1
15 40 1
15 41 1
15 42 1
15 43 1
15 44 1
15 45 1
15 46 1
15 47 1
15 48 1
15 49 1
16 17 1
16 18 1
16 19 1
16 20 1
16 21 1
16 22 1
16 23 1
16 24 1
16 25 1
16 26 1
16 27 1
16 28 1
16 29 1
16 30 1
16 31 1
16 32 1
16 33 1
16 34 1
16 35 1
16 36 1
16 37 1
16 38 1
16 39 1
16 40 1
16 41 1
16 42 1
16 43 1
16 44 1
16 45 1
16 46 1
16 47 1
16 48 1
16 49 1
17 18 1
17 19 1
17 20 1
17 21 1
17 22 1
17 23 1
17 24 1
17 25 1
17 26 1
17 27 1
17 28 1
17 29 1
17 30 1
17 31 1
17 32 1
17 33 1
17 34 1
17 35 1
17 36 1
17 37 1
17 38 1
17 39 1
17 40 1
17 41 1
17 42 1
17 43 1
17 44 1
17 45 1
17 46 1
17 47 1
17 48 1
17 49 1
18 19 1
18 20 1
18 21 1
18 22 1
18 23 1
18 24 1
18 25 1
18 26 1
18 27 1
18 28 1
18 29 1
18 30 1
18 31 1
18 32 1
18 33 1
18 34 1
18 35 1
18 36 1
18 37 1
18 38 1
18 39 1
18 40 1
18 41 1
18 42 1
18 43 1
18 44 1
18 45 1
18 46 1
18 47 1
18 48 1
18 49 1
19 20 1
19 21 1
19 22 1
19 23 1
19 24 1
19 25 1
19 26 1
19 27 1
19 28 1
19 29 1
19 30 1
19 31 1
19 32 1
19 33 1
19 34 1
19 35 1
19 36 1
19 37 1
19 38 1
19 39 1
19 40 1
19 41 1
19 42 1
19 43 1
19 44 1
19 45 1
19 46 1
19 47 1
19 48 1
19 49 1
20 21 1
20 22 1
20 23 1
20 24 1
20 25 1
20 26 1
20 27 1
20 28 1
20 29 1
20 30 1
20 31 1
20 32 1
20 33 1
20 34 1
20 35 1
20 36 1
20 37 1
20 38 1
20 39 1
20 40 1
20 41 1
20 42 1
20 43 1
20 44 1
20 45 1
20 46 1
20 47 1
20 48 1
20 49 1
21 22 1
21 23 1
21 24 1
21 25 1
21 26 1
21 27 1
21 28 1
21 29 1
21 30 1
21 31 1
21 32 1
21 33 1
21 34 1
21 35 1
21 36 1
21 37 1
21 38 1
21 39 1
21 40 1
21 41 1
21 42 1
21 43 1
21 44 1
21 45 1
21 46 1
21 47 1
21 48 1
21 49 1
22 23 1
22 24 1
22 25 1
22 26 1
22 27 1
22 28 1
22 29 1
22 30 1
22 31 1
22 32 1
22 33 1
22 34 1
22 35 1
22 36 1
22 37 1
22 38 1
22 39 1
22 40 1
22 41 1
22 42 1
22 43 1
22 44 1
22 45 1
22 46 1
22 47 1
22 48 1
22 49 1
23 24 1
23 25 1
23 26 1
23 27 1
23 28 1
23 29 1
23 30 1
23 31 1
23 32 1
23 33 1
23 34 1
23 35 1
23 36 1
23 37 1
23 38 1
23 39 1
23 40 1
23 41 1
23 42 1
23 43 1
23 44 1
23 45 1
23 46 1
23 47 1
23 48 1
23 49 1
24 25 1
24 26 1
24 27 1
24 28 1
24 29 1
24 30 1
24 31 1
24 32 1
24 33 1
24 34 1
24 35 1
24 36 1
24 37 1
24 38 1
24 39 1
24 40 1
24 41 1
24 42 1
24 43 1
24 44 1
24 45 1
24 46 1
24 47 1
24 48 1
24 49 1
25 26 1
25 27 1
25 28 1
25 29 1
25 30 1
25 31 1
25 32 1
25 33 1
25 34 1
25 35 1
25 36 1
25 37 1
25 38 1
25 39 1
25 40 1
25 41 1
25 42 1
25 43 1
25 44 1
25 45 1
25 46 1
25 47 1
25 48 1
25 49 1
26 27 1
26 28 1
26 29 1
26 30 1
26 31 1
26 32 1
26 33 1
26 34 1
26 35 1
26 36 1
26 37 1
26 38 1
26 39 1
26 40 1
26 41 1
26 42 1
26 43 1
26 44 1
26 45 1
26 46 1
26 47 1
26 48 1
26 49 1
27 28 1
27 29 1
27 30 1
27 31 1
27 32 1
27 33 1
27 34 1
27 35 1
27 36 1
27 37 1
27 38 1
27 39 1
27 40 1
27 41 1
27 42 1
27 43 1
27 44 1
27 45 1
27 46 1
27 47 1
27 48 1
27 49 1
28 29 1
28 30 1
28 31 1
28 32 1
28 33 1
28 34 1
28 35 1
28 36 1
28 37 1
28 38 1
28 39 1
28 40 1
28 41 1
28 42 1
28 43 1
28 44 1
28 45 1
28 46 1
28 47 1
28 48 1
28 49 1
29 30 1
29 31 1
29 32 1
29 33 1
29 34 1
29 35 1
29 36 1
29 37 1
29 38 1
29 39 1
29 40 1
29 41 1
29 42 1
29 43 1
29 44 1
29 45 1
29 46 1
29 47 1
29 48 1
29 49 1
30 31 1
30 32 1
30 33 1
30 34 1
30 35 1
30 36 1
30 37 1
30 38 1
30 39 1
30 40 1
30 41 1
30 42 1
30 43 1
30 44 1
30 45 1
30 46 1
30 47 1
30 48 1
30 49 1
31 32 1
31 33 1
31 34 1
31 35 1
31 36 1
31 37 1
31 38 1
31 39 1
31 40 1
31 41 1
31 42 1
31 43 1
31 44 1
31 45 1
31 46 1
31 47 1
31 48 1
31 49 1
32 33 1
32 34 1
32 35 1
32 36 1
32 37 1
32 38 1
32 39 1
32 40 1
32 41 1
32 42 1
32 43 1
32 44 1
32 45 1
32 46 1
32 47 1
32 48 1
32 49 1
33 34 1
33 35 1
33 36 1
33 37 1
33 38 1
33 39 1
33 40 1
33 41 1
33 42 1
33 43 1
33 44 1
33 45 1
33 46 1
33 47 1
33 48 1
33 49 1
34 35 1
34 36 1
34 37 1
34 38 1
34 39 1
34 40 1
34 41 1
34 42 1
34 43 1
34 44 1
34 45 1
34 46 1
34 47 1
34 48 1
34 49 1
35 36 1
35 37 1
35 38 1
35 39 1
35 40 1
35 41 1
35 42 1
35 43 1
35 44 1
35 45 1
35 46 1
35 47 1
35 48 1
35 49 1
36 37 1
36 38 1
36 39 1
36 40 1
36 41 1
36 42 1
36 43 1
36 44 1
36 45 1
36 46 1
36 47 1
36 48 1
36 49 1
37 38 1
37 39 1
37 40 1
37 41 1
37 42 1
37 43 1
37 44 1
37 45 1
37 46 1
37 47 1
37 48 1
37 49 1
38 39 1
38 40 1
38 41 1
38 42 1
38 43 1
38 44 1
38 45 1
38 46 1
38 47 1
38 48 1
38 49 1
39 40 1
39 41 1
39 42 1
39 43 1
39 44 1
39 45 1
39 46 1
39 47 1
39 48 1
39 49 1
40 41 1
40 42 1
40 43 1
40 44 1
40 45 1
40 46 1
40 47 1
40 48 1
40 49 1
41 42 1
41 43 1
41 44 1
41 45 1
41 46 1
41 47 1
41 48 1
41 49 1
42 43 1
42 44 1
42 45 1
42 46 1
42 47 1
42 48 1
42 49 1
43 44 1
43 45 1
43 46 1
43 47 1
43 48 1
43 49 1
44 45 1
44 46 1
44 47 1
44 48 1
44 49 1
45 46 1
45 47 1
45 48 1
45 49 1
46 47 1
46 48 1
46 49 1
47 48 1
47 49 1
48 49 1
'''
global g_TryFlowNetwork
g_TryFlowNetwork = False #: when this variable is True, use FlowNetwork to find the min cut.
fd = StringIO()
fd.write(test_input)
fd.seek(0)
r = Reader(fd)
for g in r.gen_graph():
start_time = time.time()
if g_TryFlowNetwork:
print g.max_flow(g.src, g.sink)
else:
print minimum_cut(g, 1)
print time.time() - start_time
