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from collections import defaultdict
class DiGraph(object):
"""Implementation of directed graph"""
def __init__(self):
self._nodes = set()
self._edges = []
# N -> Nodes N2 with a edge (N -> N2)
self._nodes_succ = {}
# N -> Nodes N2 with a edge (N2 -> N)
self._nodes_pred = {}
def __repr__(self):
out = []
for n in self._nodes:
out.append(str(n))
for a, b in self._edges:
out.append("%s -> %s" % (a, b))
return '\n'.join(out)
def nodes(self):
return self._nodes
def edges(self):
return self._edges
def add_node(self, n):
if n in self._nodes:
return
self._nodes.add(n)
self._nodes_succ[n] = []
self._nodes_pred[n] = []
def del_node(self, node):
"""Delete the @node of the graph; Also delete every edge to/from this
@node"""
if node in self._nodes:
self._nodes.remove(node)
for pred in self.predecessors(node):
self.del_edge(pred, node)
for succ in self.successors(node):
self.del_edge(node, succ)
def add_edge(self, a, b):
if not a in self._nodes:
self.add_node(a)
if not b in self._nodes:
self.add_node(b)
self._edges.append((a, b))
self._nodes_succ[a].append((a, b))
self._nodes_pred[b].append((a, b))
def add_uniq_edge(self, a, b):
if (a, b) in self._edges:
return
else:
self.add_edge(a, b)
def del_edge(self, a, b):
self._edges.remove((a, b))
self._nodes_succ[a].remove((a, b))
self._nodes_pred[b].remove((a, b))
def predecessors_iter(self, n):
if not n in self._nodes_pred:
raise StopIteration
for a, _ in self._nodes_pred[n]:
yield a
def predecessors(self, n):
return [x for x in self.predecessors_iter(n)]
def successors_iter(self, n):
if not n in self._nodes_succ:
raise StopIteration
for _, b in self._nodes_succ[n]:
yield b
def successors(self, n):
return [x for x in self.successors_iter(n)]
def leaves_iter(self):
for n in self._nodes:
if len(self._nodes_succ[n]) == 0:
yield n
def leaves(self):
return [x for x in self.leaves_iter()]
def heads_iter(self):
for node in self._nodes:
if len(self._nodes_pred[node]) == 0:
yield node
def heads(self):
return [node for node in self.heads_iter()]
def roots_iter(self):
for n in self._nodes:
if len(self._nodes_pred[n]) == 0:
yield n
def roots(self):
return [x for x in self.roots_iter()]
def find_path(self, a, b, cycles_count=0, done=None):
if done is None:
done = {}
if b in done and done[b] > cycles_count:
return [[]]
if a == b:
return [[a]]
out = []
for n in self.predecessors(b):
done_n = dict(done)
done_n[b] = done_n.get(b, 0) + 1
for path in self.find_path(a, n, cycles_count, done_n):
if path and path[0] == a:
out.append(path + [b])
return out
def node2str(self, n):
return str(n)
def edge2str(self, a, b):
return ""
def dot(self):
out = """
digraph asm_graph {
graph [
splines=polyline,
];
node [
fontsize = "16",
shape = "box"
];
"""
for n in self.nodes():
out += '%s [label="%s"];\n' % (
hash(n) & 0xFFFFFFFFFFFFFFFF, self.node2str(n))
for a, b in self.edges():
out += '%s -> %s [label="%s"]\n' % (hash(a) & 0xFFFFFFFFFFFFFFFF,
hash(b) & 0xFFFFFFFFFFFFFFFF,
self.edge2str(a, b))
out += "}"
return out
def _reachable_nodes(self, head, next_cb):
"""Generic algorithm to compute every nodes reachable from/to node
@head"""
todo = set([head])
reachable = set()
while todo:
node = todo.pop()
if node in reachable:
continue
reachable.add(node)
yield node
for next_node in next_cb(node):
todo.add(next_node)
def reachable_sons(self, head):
"""Compute every nodes reachable from node @head"""
return self._reachable_nodes(head, self.successors_iter)
def reachable_parents(self, leaf):
"""Compute every parents of node @leaf"""
return self._reachable_nodes(leaf, self.predecessors_iter)
def _compute_generic_dominators(self, head, reachable_cb, prev_cb, next_cb):
"""Generic algorithm to compute either the dominators or postdominators
of the graph.
@head: the head/leaf of the graph
@reachable_cb: sons/parents of the head/leaf
@prev_cb: return predecessors/succesors of a node
@next_cb: return succesors/predecessors of a node
"""
nodes = set(reachable_cb(head))
dominators = {}
for node in nodes:
dominators[node] = set(nodes)
dominators[head] = set([head])
modified = True
todo = set(nodes)
while todo:
node = todo.pop()
# Heads state must not be changed
if node == head:
continue
# Compute intersection of all predecessors'dominators
new_dom = None
for pred in prev_cb(node):
if not pred in nodes:
continue
if new_dom is None:
new_dom = set(dominators[pred])
new_dom.intersection_update(dominators[pred])
# We are not a head to we have at least one dominator
assert(new_dom is not None)
new_dom.update(set([node]))
# If intersection has changed, add sons to the todo list
if new_dom == dominators[node]:
continue
dominators[node] = new_dom
for succ in next_cb(node):
todo.add(succ)
return dominators
def compute_dominators(self, head):
"""Compute the dominators of the graph"""
return self._compute_generic_dominators(head,
self.reachable_sons,
self.predecessors_iter,
self.successors_iter)
def compute_postdominators(self, leaf):
"""Compute the postdominators of the graph"""
return self._compute_generic_dominators(leaf,
self.reachable_parents,
self.successors_iter,
self.predecessors_iter)
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