图算法|Dijkstra算法python实现
01
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Dijkstra算法的理论部分
关于Dijkstra算法的原理部分，请参考之前的推送：
Dijkstra算法总结如下：
1. 此算法是计算从入度为0的起始点开始的单源最短路径算法，它能计算从源点到图中任何一点的最短路径，假定起始点为A
2. 选取一个中心点center，是S集合中的最后一个元素，注意起始点到这个点的最短距离已经计算出来，并存储在dist字典中了。
3. 因为已经求出了从A->center的最短路径，所以每次迭代只需要找出center->{有关系的节点nodei}的最短距离，如果两者的和小于dist(A->nodei)，则找到一条更短的路径。
02
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代码实现
"""
Dijkstra algorithm
graphdict={"A":[("B",6),("C",3)], "B":[("C",2),("D",5)],"C":[("B",2),("D",3),("E",4)],\
"D":[("B",5),("C",3),("E",2),("F",3)],"E":[("C",4),("D",2),("F",5)],"F":[("D",3),"(E",5)]})
assert: start node must be zero in-degree
"""
def Dijkstra(startNode, endNode, graphdict=None):
S=[startNode]
V=[]
for node in graphdict.keys():
if node !=startNode:
V.append(node)
#distance dict from startNode
dist={}
for node in V:
dist[node]=float('Inf')
while len(V)>0:
center = S[-1] # get final node for S as the new center node
minval = ("None",float("Inf"))
for node,d in graphdict[center]:
if node not in V:
continue
#following is the key logic.If S length is bigger than 1,need to get the final ele of S, which is the center point in current
#iterator, and distance between start node and center node is startToCenterDist; d is distance between node
# among out-degree for center point; dist[node] is previous distance to start node, possibly Inf or a updated value
# so if startToCenterDist+d is less than dist[node], then it shows we find a shorter distance.
if len(S)==1:
dist[node] = d
else:
startToCenterDist = dist[center]
if startToCenterDist + d < dist[node]:
dist[node] = startToCenterDist + d
#this is the method to find a new center node and
# it's the minimum distance among out-degree nodes for center node
if d < minval[1]:
minval = (node,d)
V.remove(minval[0])
S.append(minval[0]) # append node with min val
return dist
03
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测试
求出以上图中，从A到各个节点的最短路径：
shortestRoad = Dijkstra("A","F",graphdict={"A":[("B",6),("C",3)], "B":[("C",2),("D",5)],\
"C":[("B",2),("D",3),("E",4)],\
"D":[("B",5),("C",3),("E",2),("F",3)],\
"E":[("C",4),("D",2),("F",5)],"F":[("D",3),("E",5)]})
mystr = "shortest distance from A begins to "
for key,shortest in shortestRoad.items():
print(mystr+ str(key) +" is: " + str(shortest) )
打印结果如下：
shortest distance from A begins to B is: 5
shortest distance from A begins to C is: 3
shortest distance from A begins to D is: 6
shortest distance from A begins to E is: 7
shortest distance from A begins to F is: 9
点击阅读原文，去我的github库下载代码。