def testGeneralGraph(self):
g = {
0: [],
1: [0, 4],
2: [1, 5],
3: [1],
4: [1],
5: [2],
6: [4, 7],
7: [5, 9],
8: [6],
9: [8]
}
cc = scc.scc(g)
# 0 itself forms a cc.
# 3 itself forms a cc.
# 1 and 4 form a cc.
# 2 and 5 form a cc.
# 6, 7, 8, and 9 form a cc.
self.assertEqual(cc[1], cc[4])
self.assertEqual(cc[2], cc[5])
self.assertEqual(cc[6], cc[7])
self.assertEqual(cc[6], cc[8])
self.assertEqual(cc[6], cc[9])
# Check different cc are numbered differently.
self.assertNotEqual(cc[0], cc[1])
self.assertNotEqual(cc[0], cc[2])
self.assertNotEqual(cc[0], cc[3])
self.assertNotEqual(cc[0], cc[6])
self.assertNotEqual(cc[1], cc[2])
self.assertNotEqual(cc[1], cc[3])
self.assertNotEqual(cc[1], cc[6])
self.assertNotEqual(cc[2], cc[3])
self.assertNotEqual(cc[2], cc[6])
self.assertNotEqual(cc[3], cc[6])
def testGeneralGraph(self):
g = {0:[],
1:[0,4],
2:[1,5],
3:[1],
4:[1],
5:[2],
6:[4,7],
7:[5,9],
8:[6],
9:[8]}
cc = scc.scc(g)
# 0 itself forms a cc.
# 3 itself forms a cc.
# 1 and 4 form a cc.
# 2 and 5 form a cc.
# 6, 7, 8, and 9 form a cc.
self.assertEqual(cc[1], cc[4])
self.assertEqual(cc[2], cc[5])
self.assertEqual(cc[6], cc[7])
self.assertEqual(cc[6], cc[8])
self.assertEqual(cc[6], cc[9])
# Check different cc are numbered differently.
self.assertNotEqual(cc[0], cc[1])
self.assertNotEqual(cc[0], cc[2])
self.assertNotEqual(cc[0], cc[3])
self.assertNotEqual(cc[0], cc[6])
self.assertNotEqual(cc[1], cc[2])
self.assertNotEqual(cc[1], cc[3])
self.assertNotEqual(cc[1], cc[6])
self.assertNotEqual(cc[2], cc[3])
self.assertNotEqual(cc[2], cc[6])
self.assertNotEqual(cc[3], cc[6])
def testNoEdgeGraph(self):
g = {0: [], 1: [], 2: [], 3: [], 4: []}
cc = scc.scc(g)
self.assertNotEqual(cc[0], cc[1])
self.assertNotEqual(cc[0], cc[2])
self.assertNotEqual(cc[0], cc[3])
self.assertNotEqual(cc[0], cc[4])
self.assertNotEqual(cc[1], cc[2])
self.assertNotEqual(cc[3], cc[4])
def testTreeGraph(self):
g = {0: [1, 2], 1: [3, 4], 2: [5], 3: [], 4: [], 5: []}
cc = scc.scc(g)
self.assertNotEqual(cc[0], cc[1])
self.assertNotEqual(cc[0], cc[2])
self.assertNotEqual(cc[0], cc[3])
self.assertNotEqual(cc[0], cc[4])
self.assertNotEqual(cc[0], cc[5])
self.assertNotEqual(cc[1], cc[2])
self.assertNotEqual(cc[3], cc[4])
def find_cycles(self):
self.init()
self.g = Graph(self.graph, self.nodes)
self.list_scc = scc(self.g)
self.list_scc = [scc for scc in self.list_scc
if len(scc) > 1] # remove single node scc
if len(self.list_scc) == 0:
return False
else:
# print(self.list_scc)
return True
def getRanking(results, names, pvalues):
#print(results)
l = len(results)
edges, vertices = getEdges(results, True, pvalues)
#print(edges)
#strip edges
edgesXY = []
for e in edges:
edgesXY.append((e[0], e[1]))
sccs = scc.scc(edgesXY)
#print(sccs)
ranking = getBest(results, sccs, names)
return ranking
def testNoEdgeGraph(self):
g = {0:[],
1:[],
2:[],
3:[],
4:[]}
cc = scc.scc(g)
self.assertNotEqual(cc[0], cc[1])
self.assertNotEqual(cc[0], cc[2])
self.assertNotEqual(cc[0], cc[3])
self.assertNotEqual(cc[0], cc[4])
self.assertNotEqual(cc[1], cc[2])
self.assertNotEqual(cc[3], cc[4])
def main():
print '%s: reading input' % (datetime.datetime.now())
g = read_input('SCC.txt')
nodes = set()
for s in sorted(g.keys()):
nodes.add(s)
for t in g[s]:
nodes.add(t)
print '%s: Sloving' % (datetime.datetime.now())
groups = scc(g)
print '%s: Done Sloving' % (datetime.datetime.now())
print 'total_nodes in groups: %s' % sum(count_len(groups))
print 'total_nodes in graph: %s' % len(list(nodes))
print '%s: sorting to get output' % (datetime.datetime.now())
print count_len(groups)[:20]
def testTreeGraph(self):
g = {0:[1,2],
1:[3,4],
2:[5],
3:[],
4:[],
5:[]}
cc = scc.scc(g)
self.assertNotEqual(cc[0], cc[1])
self.assertNotEqual(cc[0], cc[2])
self.assertNotEqual(cc[0], cc[3])
self.assertNotEqual(cc[0], cc[4])
self.assertNotEqual(cc[0], cc[5])
self.assertNotEqual(cc[1], cc[2])
self.assertNotEqual(cc[3], cc[4])
def two_sat(graph):
"""
Given a 2SAT problem represented by a directed graph in forms of
{tail:[head_list], ...}, compute the satisfiability.
Below symbol 'v' means 'or', '^' means 'and', '<=>' means 'equivalent to',
'-' means 'negate', and '->' means material implication.
A 2SAT problem in CNF, which is (x1 v x2)^(x1 v x3)^(x2 v x3)..., can be
represented by an implication graph by replacing each of its disjunctions
by a pair of material implications. It is satisfiable if and only if no
vertex and its negation belong to the same SCC (strongly connected component)
of the implication graph. SCC can be computed in linear time O(m + n), where
m is the number of the edges of the graph and n is the number of nodes.
Equivalence between boolean clause and material implication:
(x1 v x2) <=> (-x1 -> x2) <=> (-x2 -> x1)
An implication graph is constructed by adding edges (-x1, x2) and (-x2, x1)
for each disjunction (x1 v x2). Despite the equivalence between the boolean
clause and EACH material implication, BOTH edges must be added to the graph
in order for the edges to be able to represent the relation of vertices.
If x and -x are both in the same SCC, which implies (-x -> x) ^ (x -> -x),
then a contradiction is concluded as below:
(-x -> x) <=> (x v x) <=> x
(x -> -x) <=> (-x v -x) <=> -x
thus, (-x v x) ^ (x -> -x) <=> (x ^ -x) <=> False
https://class.coursera.org/algo2-002/forum/thread?thread_id=428#post-1573
https://class.coursera.org/algo2-002/forum/thread?thread_id=428#comment-1584
"""
groups = scc.scc(graph)
for group in groups.values():
group = set(group)
for node in group:
if -node in group:
return 0
return 1
def scc_2sat(size, m):
"""
AvB = True as: (not A => B) or (not B => A) as graph edges
"""
graph = {k:[] for k in range(-size, size+1)}
graph.pop(0)
for a,b in m:
graph[-a].append(b)
graph[-b].append(a)
# determine scc, if in single scc both a and not a -> return false
components = scc(graph)
# check in each component a and not a
for comp in components:
vertices = set(comp)
for v in vertices:
if -v in vertices:
return False
return True
def test_sample_1(self):
graph = parse_file("sample-1.txt")
result = scc(graph)
answer = [3, 3, 3]
self.assertEqual(result, answer)
def test_sample_5(self):
graph = parse_file("sample-5.txt")
result = scc(graph)
answer = [6, 3, 2, 1]
self.assertEqual(result, answer)
if not options.bb_file:
print('No BIOS/BASIC ROM selected (e.g. msxbiosbasic.rom)')
sys.exit(1)
# bb == bios/basic
bb = rom(options.bb_file, debug, 0x0000)
put_page(0, 0, 0, bb)
put_page(0, 0, 1, bb)
snd = sound(debug)
if options.scc_rom:
for o in options.scc_rom:
parts = o.split(':')
scc_obj = scc(parts[2], snd, debug)
scc_slot = int(parts[0])
scc_subslot = int(parts[1])
put_page(scc_slot, scc_subslot, 1, scc_obj)
put_page(scc_slot, scc_subslot, 2, scc_obj)
if options.disk_rom:
for o in options.disk_rom:
parts = o.split(':')
disk_slot = int(parts[0])
disk_subslot = int(parts[1])
disk_obj = disk(parts[2], debug, parts[3])
put_page(disk_slot, disk_subslot, 1, disk_obj)
if options.rom:
for o in options.rom:
from scc import scc
from reverse import reverse
bookfigure3point7 = { 'A': ['B', 'C', 'F'],
'B': ['E'],
'C': ['D'],
'D': ['A', 'H'],
'E': ['F', 'G', 'H'],
'F': ['B', 'G'],
'G': [],
'H': ['G']
}
print "\nscc for textbook figure 3.7:"
scc(bookfigure3point7)
bookfigure3point8 = { 'A': ['C'],
'B': ['A', 'D'],
'C': ['E', 'F'],
'D': ['C'],
'E': [],
'F': []
}
print "\nscc for textbook figure 3.8:"
scc(bookfigure3point8)
bookfigure3point9 = { 'A': ['B'],
'B': ['C','D','E'],
'C': ['F'],
'D': [],
