class DijkSP(object): def __init__(self, G, s, t = None): "find the shortest path tree (in a directed graph with non-negative weights) from s to every other vertex using Dijkstra's alg" self._G = G self._s = s self._distTo = [_INF for _ in range(G.V())] self._distTo[s] = 0 self._edgeTo = [_SENTINEL for _ in range(G.V())] # edgeTo[v]: last edge on shortest path from s to v self._pq = IndexMinPQ(G.V()) self._pq.insert(s, 0) while (not self._pq.isEmpty()): v = self._pq.delMin() # add closest vertex to source to Tree if t and v == t: return self._relaxVertix(v) def distTo(self, v): "distance from src to vertex v" return self._distTo[v] def hasPathTo(self, v): "checks whether path exists from src to vertex v" return self._edgeTo[v] != _SENTINEL def pathTo(self, v): "returns path from src to vertex v" if not self.hasPathTo(v): return path = [] e = self._edgeTo[v] # last edge of path while e.src() != self._s: path.append(e) e = self._edgeTo[e.src()] path.append(e) return path[::-1] def _relaxVertix(self, v): for e in self._G.adj(v): self._relaxEdge(e) # relaxEdge(e) updates the distTo and edgeTo data structures def _relaxEdge(self, edge): "relaxes an edge by updating data structures with that edge" v = edge.src() w = edge.sink() if self._distTo[w] > self._distTo[v] + edge.weight(): self._distTo[w] = self._distTo[v] + edge.weight() # distance to source self._edgeTo[w] = edge if not self._pq.contains(w): self._pq.insert(w, self._distTo[w]) else: self._pq.decreaseKey(w, self._distTo[w]) def __repr__(self): "print spt built by Digjkstra object" V = len(self._edgeTo) spt = GraphLib.EdgeWeightedDigraph(V) for i in range(V): if self._edgeTo[i] != _SENTINEL: spt.addEdge(self._edgeTo[i]) print str(spt.edges())
class DijkSP(object):
def __init__(self, G, s, t=None):
"find the shortest path tree (in a directed graph with non-negative weights) from s to every other vertex using Dijkstra's alg"
self._s = s
self._distTo = [_INF for _ in range(G.V())]
self._distTo[s] = 0
self._edgeTo = [_SENTINEL for _ in range(G.V())
] # edgeTo[v]: last edge on shortest path from s to v
self._pq = IndexMinPQ(G.V())
self._pq.insert(s, 0)
while (not self._pq.isEmpty()):
v = self._pq.delMin() # add closest vertex to source to Tree
if t and v == t: return
for e in G.adj(v):
self._relax(
e
) # relax(e) updates the distTo and edgeTo data structures
def distTo(self, v):
"distance from src to vertex v"
return self._distTo[v]
def hasPathTo(self, v):
"checks whether path exists from src to vertex v"
return self._edgeTo[v] != _SENTINEL
def pathTo(self, v):
"returns path from src to vertex v"
if not self.hasPathTo(v): return
path = []
e = self._edgeTo[v] # last edge of path
while e.src() != self._s:
path.append(e)
e = self._edgeTo[e.src()]
path.append(e)
return path[::-1]
def _relax(self, edge):
"relaxes an edge by updating data structures with that edge"
v = edge.src()
w = edge.sink()
if self._distTo[w] > self._distTo[v] + edge.weight():
self._distTo[w] = self._distTo[v] + edge.weight(
) # distance to source
self._edgeTo[w] = edge
if not self._pq.contains(w):
self._pq.insert(w, self._distTo[w])
else:
self._pq.decreaseKey(w, self._distTo[w])
def __repr__(self):
"print spt built by Digjkstra object"
V = len(self._edgeTo)
spt = GraphLib.EdgeWeightedDigraph(V)
for i in range(V):
if self._edgeTo[i] != _SENTINEL:
spt.addEdge(self._edgeTo[i])
print str(spt.edges())
class EagerPrimMST(object): ''' similar to LazyPrimMST except remove obsolete edges from PQ given a connected, undirected, weighted graph, finds an MST and its weight key = vertex; priority = weight of edge PQ has 1 entry per vertex ''' def __init__(self, EG): self._edgeTo = [-1 for _ in range(EG.V())] self._distTo = [_INF for _ in range(EG.V()) ] self._distTo[0] = 0 self._pq = IndexMinPQ(EG.V()) self._mst = [] # list of edges in MST self._weight = 0 self._marked = set() # set of vertices in MST self._pq.insert(0, 0) while (not self._pq.isEmpty() and len(self._mst) < EG.V() - 1): v = self._pq.delMin() if v > 0: self._mst.append(self._edgeTo[v]) self._weight += self._edgeTo[v].weight() self._visit(EG, v) def _visit(self, EG, v): ''' add v to Tree; add all non-tree vertices adjacent to v to PQ; update priority of edges connecting non-tree vertices to Tree ''' self._marked.add(v) for e in EG.adj(v): # e is edge connecting w (non-Tree vertex) to Tree w = e.other(v) if w not in self._marked: if self._distTo[w] > e.weight(): self._edgeTo[w] = e self._distTo[w] = e.weight() if not self._pq.contains(w): # w is not in PQ self._pq.insert(w, e.weight()) else: self._pq.decreaseKey(w, e.weight()) def mst(self): "returns edges in MST" return self._mst def weight(self): "returns weight of MST" return self._weight def __repr__(self): "Everything about MST" return "edges=%r wt=%r" % (self.mst(), self.weight())
class EagerPrimMST(object):
'''
similar to LazyPrimMST except remove obsolete edges from PQ
given a connected, undirected, weighted graph, finds an MST and its weight
key = vertex; priority = weight of edge
PQ has 1 entry per vertex
'''
def __init__(self, EG):
self._edgeTo = [-1 for _ in range(EG.V())]
self._distTo = [_INF for _ in range(EG.V())]
self._distTo[0] = 0
self._pq = IndexMinPQ(EG.V())
self._mst = [] # list of edges in MST
self._weight = 0
self._marked = set() # set of vertices in MST
self._pq.insert(0, 0)
while (not self._pq.isEmpty() and len(self._mst) < EG.V() - 1):
v = self._pq.delMin()
if v > 0:
self._mst.append(self._edgeTo[v])
self._weight += self._edgeTo[v].weight()
self._visit(EG, v)
def _visit(self, EG, v):
'''
add v to Tree; add all non-tree vertices adjacent to v to PQ;
update priority of edges connecting non-tree vertices to Tree
'''
self._marked.add(v)
for e in EG.adj(v):
# e is edge connecting w (non-Tree vertex) to Tree
w = e.other(v)
if w not in self._marked:
if self._distTo[w] > e.weight():
self._edgeTo[w] = e
self._distTo[w] = e.weight()
if not self._pq.contains(w):
# w is not in PQ
self._pq.insert(w, e.weight())
else:
self._pq.decreaseKey(w, e.weight())
def mst(self):
"returns edges in MST"
return self._mst
def weight(self):
"returns weight of MST"
return self._weight
def __repr__(self):
"Everything about MST"
return "edges=%r wt=%r" % (self.mst(), self.weight())
def __init__(self, EG):
self._edgeTo = [-1 for _ in range(EG.V())]
self._distTo = [_INF for _ in range(EG.V())]
self._distTo[0] = 0
self._pq = IndexMinPQ(EG.V())
self._mst = [] # list of edges in MST
self._weight = 0
self._marked = set() # set of vertices in MST
self._pq.insert(0, 0)
while (not self._pq.isEmpty() and len(self._mst) < EG.V() - 1):
v = self._pq.delMin()
if v > 0:
self._mst.append(self._edgeTo[v])
self._weight += self._edgeTo[v].weight()
self._visit(EG, v)
def __init__(self, G, s, t=None):
"find the shortest path tree (in a directed graph with non-negative weights) from s to every other vertex using Dijkstra's alg"
self._s = s
self._distTo = [_INF for _ in range(G.V())]
self._distTo[s] = 0
self._edgeTo = [_SENTINEL for _ in range(G.V())
] # edgeTo[v]: last edge on shortest path from s to v
self._pq = IndexMinPQ(G.V())
self._pq.insert(s, 0)
while (not self._pq.isEmpty()):
v = self._pq.delMin() # add closest vertex to source to Tree
if t and v == t: return
for e in G.adj(v):
self._relax(
e
) # relax(e) updates the distTo and edgeTo data structures
def __init__(self, G, s, t = None): "find the shortest path tree (in a directed graph with non-negative weights) from s to every other vertex using Dijkstra's alg" self._G = G self._s = s self._distTo = [_INF for _ in range(G.V())] self._distTo[s] = 0 self._edgeTo = [_SENTINEL for _ in range(G.V())] # edgeTo[v]: last edge on shortest path from s to v self._pq = IndexMinPQ(G.V()) self._pq.insert(s, 0) while (not self._pq.isEmpty()): v = self._pq.delMin() # add closest vertex to source to Tree if t and v == t: return self._relaxVertix(v)
def __init__(self, EG): self._edgeTo = [-1 for _ in range(EG.V())] self._distTo = [_INF for _ in range(EG.V()) ] self._distTo[0] = 0 self._pq = IndexMinPQ(EG.V()) self._mst = [] # list of edges in MST self._weight = 0 self._marked = set() # set of vertices in MST self._pq.insert(0, 0) while (not self._pq.isEmpty() and len(self._mst) < EG.V() - 1): v = self._pq.delMin() if v > 0: self._mst.append(self._edgeTo[v]) self._weight += self._edgeTo[v].weight() self._visit(EG, v)