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from collections import defaultdict | |
from heapq import * | |
def dijkstra(edges, f, t): | |
g = defaultdict(list) | |
for l,r,c in edges: | |
g[l].append((c,r)) | |
q, seen, mins = [(0,f,())], set(), {f: 0} | |
while q: | |
(cost,v1,path) = heappop(q) | |
if v1 not in seen: | |
seen.add(v1) | |
path = (v1, path) | |
if v1 == t: return (cost, path) | |
for c, v2 in g.get(v1, ()): | |
if v2 in seen: continue | |
prev = mins.get(v2, None) | |
next = cost + c | |
if prev is None or next < prev: | |
mins[v2] = next | |
heappush(q, (next, v2, path)) | |
return float("inf"), None | |
if __name__ == "__main__": | |
edges = [ | |
("A", "B", 7), | |
("A", "D", 5), | |
("B", "C", 8), | |
("B", "D", 9), | |
("B", "E", 7), | |
("C", "E", 5), | |
("D", "E", 15), | |
("D", "F", 6), | |
("E", "F", 8), | |
("E", "G", 9), | |
("F", "G", 11) | |
] | |
print "=== Dijkstra ===" | |
print edges | |
print "A -> E:" | |
print dijkstra(edges, "A", "E") | |
print "F -> G:" | |
print dijkstra(edges, "F", "G") |
This is a slightly simpler approach, following the wikipedia definition closely:
http://rebrained.com/?p=392
import sys
def shortestpath(graph,start,end,visited=[],distances={},predecessors={}):
"""Find the shortest path btw start & end nodes in a graph"""
# detect if first time through, set current distance to zero
if not visited: distances[start]=0
# if we've found our end node, find the path to it, and return
if start==end:
path=[]
while end != None:
path.append(end)
end=predecessors.get(end,None)
return distances[start], path[::-1]
# process neighbors as per algorithm, keep track of predecessors
for neighbor in graph[start]:
if neighbor not in visited:
neighbordist = distances.get(neighbor,sys.maxint)
tentativedist = distances[start] + graph[start][neighbor]
if tentativedist < neighbordist:
distances[neighbor] = tentativedist
predecessors[neighbor]=start
# neighbors processed, now mark the current node as visited
visited.append(start)
# finds the closest unvisited node to the start
unvisiteds = dict((k, distances.get(k,sys.maxint)) for k in graph if k not in visited)
closestnode = min(unvisiteds, key=unvisiteds.get)
# now take the closest node and recurse, making it current
return shortestpath(graph,closestnode,end,visited,distances,predecessors)
if name == "main":
graph = {'a': {'w': 14, 'x': 7, 'y': 9},
'b': {'w': 9, 'z': 6},
'w': {'a': 14, 'b': 9, 'y': 2},
'x': {'a': 7, 'y': 10, 'z': 15},
'y': {'a': 9, 'w': 2, 'x': 10, 'z': 11},
'z': {'b': 6, 'x': 15, 'y': 11}}
print shortestpath(graph,'a','a')
print shortestpath(graph,'a','b')
"""
Expected Result:
(0, ['a'])
(20, ['a', 'y', 'w', 'b'])
"""
Flatten path version:
from collections import defaultdict
from heapq import *
def dijkstra(edges, f, t):
g = defaultdict(list)
for l, r, c in edges:
g[l].append((c, r))
q, seen, mins = [(0, f, [])], set(), {f: 0}
while q:
(cost, v1, path) = heappop(q)
if v1 not in seen:
seen.add(v1)
path = [v1] + path
if v1 == t:
return (cost, path)
for c, v2 in g.get(v1, ()):
if v2 in seen:
continue
prev = mins.get(v2, None)
next = cost + c
if prev is None or next < prev:
mins[v2] = next
heappush(q, (next, v2, path))
return (float("inf"), [])
if __name__ == "__main__":
edges = [
("A", "B", 7),
("A", "D", 5),
("B", "C", 8),
("B", "D", 9),
("B", "E", 7),
("C", "E", 5),
("D", "E", 15),
("D", "F", 6),
("E", "F", 8),
("E", "G", 9),
("F", "G", 11)
]
print("=== Dijkstra ===")
print(edges)
print("A -> E: ", end="")
print(dijkstra(edges, "A", "E"))
print("F -> G: ", end="")
print(dijkstra(edges, "F", "G"))
=== Dijkstra ===
[('A', 'B', 7), ('A', 'D', 5), ('B', 'C', 8), ('B', 'D', 9), ('B', 'E', 7), ('C', 'E', 5), ('D', 'E', 15), ('D', 'F', 6), ('E', 'F', 8), ('E', 'G', 9), ('F', 'G', 11)]
A -> E: (14, ['E', 'B', 'A'])
F -> G: (11, ['G', 'F'])
Hi, I think I made a bit cleaner (subjectively :)) implementation in Python that uses RBTree as a priority queue with tests there
https://github.com/ehborisov/algorithms/blob/master/8.Graphs/dijkstra.py
Unless I am missing something here, this is a BFS with a min-heap, not a Dijkstra's algorithm.
@JixinSiND Dijkstra's algorithm is essentially a weighted version of BFS.
Just leaving a comment to let the author know that his code has been inappropriately taken and re-used as material for teaching at a University master in London. The authorship has been modified to report the lecturer's one instead.
https://www.dcs.bbk.ac.uk/~ale/pwd/2019-20/pwd-8/src/pwd-ex-dijkstra+heap.py
@alelom Thanks a lot for letting me know, such a kind of you! This is not the first time this code was copy-pasted into lecture materials and/or projects codebases. Honestly, if it helped students to learn - I would be glad and proud. I care less about authorship or any sort of attribution. On the one hand, I wouldn't want to encourage disrespectful actions, on the other hand, I don't have reliable way to prevent this from happening. So, choosing between spread of knowledge or nurturing morality, I would always vote for the former. Thanks again for letting me know!
I just care for what is right. If I were the lecturer, I'd quote the real author and the source – an action that does not diminish the teaching potential, and encourages sharing of good code lawfully.
Thank you so much for this gift, very clean and clever solution 😄
If anyone just wonders how to easily receive as output only the value of the solution remove the cost from the return at line 15:
if v1 == t: return cost
instead of
if v1 == t: return (cost, path)
Nice and clean
Thank you very much for this beautiful algorithm.
pretty sure this is not Dijkstra; you're doing heappush(q, (next, v2, path))
at the very end, but in True dijkstra it would need a call to "decrease_key", which in python is heap._siftdown
@xdavidliu I was confused by this until I saw https://stackoverflow.com/a/31123108. I think Dijkstra's algorithm is a higher level concept, so either implementation is valid.
More concise with path reconstruction. The node IDs are represented as integers while the edge weights as floats
from typing import *
from heapq import *
class Dijkstra:
def __init__(self,
graph: Dict[int, Dict[int, float]],
origin: int):
self.graph = graph
self.edge_to: Dict[int, int] = {}
self.distances: Dict[int, float] = {vertex: float('inf') for vertex in self.graph}
self.origin = origin
self._find(self.origin)
def _find(self, node: int):
self.distances[node] = 0
# Priority queue which stores tuples from distance to node id
# Distance is the first in the tuple order since it needs to have
# priority when entries are inserted into the priority queue
priority_queue: List[(float, int)] = [(node, 0)]
while priority_queue:
current_node, current_distance = heappop(priority_queue)
# If the distance currently recorded at the distances dict is
# bigger than the one pushed to the pq then we do not need to
# process this entry
if current_distance > self.distances[current_node]:
continue
for n, weight in self.graph[current_node].items():
updated_distance = current_distance + weight
if updated_distance < self.distances[n]:
self.distances[n] = updated_distance
self.edge_to[n] = current_node
heappush(priority_queue, (n, updated_distance))
def reconstruct_path(self, destination: int) -> List[int]:
node: int = destination
path: List[int] = []
while node != self.origin:
path.append(node)
node = self.edge_to[node]
path.reverse()
return path
if __name__ == '__main__':
graph = {
1: {2: 1, 3: 4},
2: {1: 1, 3: 2, 4: 5},
3: {1: 4, 2: 2, 4: 1},
4: {2: 5, 3: 1}
}
dijkstra: Dijkstra = Dijkstra(graph, 1)
print(dijkstra.distances)
print(dijkstra.reconstruct_path(4))
print(dijkstra.reconstruct_path(2))
print(dijkstra.reconstruct_path(3))
friends don't let friends import *
😄
Wildcard imports (from module import *) should be avoided, as they make it unclear which names are present in the namespace, confusing both readers and many automated tools. There is one defensible use case for a wildcard import, which is to republish an internal interface as part of a public API (for example, overwriting a pure Python implementation of an interface with the definitions from an optional accelerator module and exactly which definitions will be overwritten isn’t known in advance).
When republishing names this way, the guidelines below regarding public and internal interfaces still apply.
Thanks for your code very much. But I want to make some expansion on this basis. The situation is that our map is a matrix, and there are more than one shortest path to reach the destination, if I want to find all the road not just the one, how to modify the code to achieve this? Thanks again.