Dijkstra shortest path algorithm.
Python, 113 lines
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# http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm
# FB - 201110296
from heapq import heappush, heappop # for priority queue
pq = []
class node:
label = ''
# adjacency list of the node
neighbors = [] # list of nodes
distances = [] # distances to neighbors
# for Dijkstra
prevNode = None
totalDistance = float('Inf')
visited = False
# constructor
def __init__(self, label):
self.label = label
self.neighbors = []
self.distances = []
self.prevNode = None
self.totalDistance = float('Inf')
self.visited = False
# find the shortest paths to all nodes recursively
def dijkstra(node):
# visit all neighbors and update them if necessary
for i in range(len(node.neighbors)):
n = node.neighbors[i]
d = node.distances[i]
if n.totalDistance > d + node.totalDistance:
n.prevNode = node
n.totalDistance = d + node.totalDistance
heappush(pq, (n.totalDistance, n))
node.visited = True
(d, ne) = heappop(pq)
if not ne.visited:
dijkstra(ne)
# get the shortest path to the given node
def route(endNode):
node = endNode
labels = [endNode.label]
# distances = []
while node.label != node.prevNode.label:
# distances.append(node.totalDistance - node.prevNode.totalDistance)
node = node.prevNode
labels.append(node.label)
labels.reverse()
return labels
# distances.reverse()
# return (labels, distances)
# create a graph
a = node('a')
b = node('b')
c = node('c')
d = node('d')
e = node('e')
f = node('f')
graph = (a, b, c, d, e, f)
# create bidirectional edges of the graph
edges = []
edges.append((b, c, 3))
edges.append((d, e, 1))
edges.append((b, d, 2))
edges.append((c, e, 1))
edges.append((a, b, 1))
edges.append((a, d, 1))
edges.append((c, f, 1))
edges.append((e, f, 3))
# create adjaceny list of neighbors for each node
for edge in edges:
edge[0].neighbors.append(edge[1])
edge[0].distances.append(edge[2])
edge[1].neighbors.append(edge[0])
edge[1].distances.append(edge[2])
# print the graph
print 'The graph:'
print
for n in graph:
print 'Node: ', n.label
print 'Neighbors:'
for i in range(len(n.neighbors)):
print n.neighbors[i].label, n.distances[i]
print
# find the shortest paths to all neighbors starting w/ the given node
startNode = a
print 'Route start node:', startNode.label
startNode.prevNode = startNode
startNode.totalDistance = 0
dijkstra(startNode)
##print
##print 'The graph after Dijkstra:'
##print
##for n in graph:
## print 'Node:', n.label
## print 'totalDistance:', n.totalDistance
## print 'prevNode:', n.prevNode.label
## print
# print the shortest path to the given node
endNode = f
print 'Route end node:', endNode.label
print 'Route:', route(endNode)
print 'Total distance:', endNode.totalDistance
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Something is flawed in the code. At least if I understand it correctly.
As an example, if you replace lines 56-64 with:
The output of the code is:
Clearly the shortest route is: ['a','d','e','c','f'] with total distance:4
I'm not sure if there is an elegant fix to this problem. It seems that once the code uses an edge and saves a total distance to that node, it does not have the ability to adjust the total distance if the total distance to the previous node decreases.
Thanks for letting me know. I changed the algorithm to use a priority queue. Now it outputs the correct route (it is not exactly same w/ your answer but still correct):
Route start node: a
Route end node: f
Route: ['a', 'd', 'e', 'c', 'f']
Total distance: 4