"""
Copyright 2011 Shao-Chuan Wang <shaochuan.wang AT 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.
"""
import heapq
def dijkstra(adj, costs, s, t):
''' Return predecessors and min distance if there exists a shortest path
from s to t; Otherwise, return None '''
Q = [] # priority queue of items; note item is mutable.
d = {s: 0} # vertex -> minimal distance
Qd = {} # vertex -> [d[v], parent_v, v]
p = {} # predecessor
visited_set = set([s])
for v in adj.get(s, []):
d[v] = costs[s, v]
item = [d[v], s, v]
heapq.heappush(Q, item)
Qd[v] = item
while Q:
print Q
cost, parent, u = heapq.heappop(Q)
if u not in visited_set:
print 'visit:', u
p[u]= parent
visited_set.add(u)
if u == t:
return p, d[u]
for v in adj.get(u, []):
if d.get(v):
if d[v] > costs[u, v] + d[u]:
d[v] = costs[u, v] + d[u]
Qd[v][0] = d[v] # decrease key
Qd[v][1] = u # update predecessor
heapq._siftdown(Q, 0, Q.index(Qd[v]))
else:
d[v] = costs[u, v] + d[u]
item = [d[v], u, v]
heapq.heappush(Q, item)
Qd[v] = item
return None
def make_undirected(cost):
ucost = {}
for k, w in cost.iteritems():
ucost[k] = w
ucost[(k[1],k[0])] = w
return ucost
if __name__=='__main__':
# adjacent list
adj = { 1: [2,3,6],
2: [1,3,4],
3: [1,2,4,6],
4: [2,3,5,7],
5: [4,6,7],
6: [1,3,5,7],
7: [4,5,6]}
# edge costs
cost = { (1,2):7,
(1,3):9,
(1,6):14,
(2,3):10,
(2,4):15,
(3,4):11,
(3,6):2,
(4,5):6,
(5,6):9,
(4,7):2,
(5,7):1,
(6,7):12}
cost = make_undirected(cost)
s, t = 1, 7
predecessors, min_cost = dijkstra(adj, cost, s, t)
c = t
path = [c]
print 'min cost:', min_cost
while predecessors.get(c):
path.insert(0, predecessors[c])
c = predecessors[c]
print 'shortest path:', path
