def DFS (G, start = unspecified):
'''
This is a generator that yields vertices from the vertex set of graph
$G$ in the order they are encountered in a depth-first search of $G$
starting from the vertex \code{start} (if specified) or from some
arbitrary vertex in \code {G.vertices} if \code {start} is not
specified.
'''
if start is unspecified:
start = arbitraryElementOf (G.vertices)
neighbors = graph.adjacencyLists (G)
yield start
visited = set ([start])
stack = neighbors [start]
while stack:
w = stack.pop()
if w not in visited:
yield w
visited.add (w)
stack.extend (neighbors [w])
def Prim (G, root = unspecified):
'''
Returns the edges of a minimum-weight spanning tree of $G$,
starting from the vertex \code {root} (if specified).
'''
if root is unspecified:
root = arbitraryElementOf(G.vertices)
key = {}
Pi = {}
adj = graph.adjacencyLists(G)
for u in G.vertices:
key [u] = Infinity
Pi [u] = None
key [root] = 0
Q = PriorityQueue (G.vertices)
while Q:
u = Q.extract_min()
for v in adj[u]:
if v in Q and G.weight ( (u, v) ) < key [v]:
Pi [v] = u
key[v] = G.weight ( (u, v) )
return [(v, Pi[v]) for v in G.vertices if v is not root]
def BFS (G, start = unspecified):
'''
This is a generator that yields the vertices of $G$ in the order
they are encountered during a breadth-first search of $G$ starting at the
vertex \code {start} (if specified), or starting at some arbitrary vertex
in \code {G.vertices} if not specified.
'''
if start is unspecified:
start = arbitraryElementOf (G.vertices)
neighbors = graph.adjacencyLists (G)
reached = Queue([])
searched = set ([])
reached.add (start)
while not reached.empty():
v = reached.remove()
yield v
for w in neighbors [v]:
if w not in searched and w not in reached:
reached.add (w)
searched.add (v)
