使用邻接表的方法构造带权图,并利用Dijkstra算法寻找从某个源点到其他所有顶点的最短路径,要求: (1)写出完整的带权图的实现程序,不能直接import pythonds中的Graph和Vertex模块; (2)允许使用pythonds中的PriorityQueue模块辅助实现Dijkstra算法; (3)测试代码
时间: 2024-03-15 11:44:18 浏览: 55
好的,我理解你的问题了。下面是一个完整的实现程序,包括带权图的构造和使用Dijkstra算法寻找最短路径的代码:
```python
from pythonds3.priorityQueue import PriorityQueue
class Vertex:
def __init__(self, key):
self.id = key
self.connectedTo = {}
self.distance = float('inf')
self.visited = False
self.previous = None
def addNeighbor(self, nbr, weight=0):
self.connectedTo[nbr] = weight
def getConnections(self):
return self.connectedTo.keys()
def getId(self):
return self.id
def getWeight(self, nbr):
return self.connectedTo[nbr]
def setDistance(self, dist):
self.distance = dist
def getDistance(self):
return self.distance
def setVisited(self):
self.visited = True
def getVisited(self):
return self.visited
def setPrevious(self, prev):
self.previous = prev
def getPrevious(self):
return self.previous
class Graph:
def __init__(self):
self.vertices = {}
self.numVertices = 0
def addVertex(self, key):
self.numVertices += 1
newVertex = Vertex(key)
self.vertices[key] = newVertex
return newVertex
def getVertex(self, key):
if key in self.vertices:
return self.vertices[key]
else:
return None
def addEdge(self, fromVert, toVert, weight=0):
if fromVert not in self.vertices:
self.addVertex(fromVert)
if toVert not in self.vertices:
self.addVertex(toVert)
self.vertices[fromVert].addNeighbor(self.vertices[toVert], weight)
def getVertices(self):
return self.vertices.keys()
def __iter__(self):
return iter(self.vertices.values())
def dijkstra(aGraph, start):
pq = PriorityQueue()
start.setDistance(0)
pq.buildHeap([(v.getDistance(), v) for v in aGraph])
while not pq.isEmpty():
currentVert = pq.delMin()
for nextVert in currentVert.getConnections():
newDist = currentVert.getDistance() \
+ currentVert.getWeight(nextVert)
if newDist < nextVert.getDistance():
nextVert.setDistance(newDist)
nextVert.setPrevious(currentVert)
pq.decreaseKey(nextVert, newDist)
def shortest(v, path):
if v.getPrevious():
path.append(v.getPrevious().getId())
shortest(v.getPrevious(), path)
return
g = Graph()
g.addEdge('A', 'B', 2)
g.addEdge('A', 'C', 3)
g.addEdge('B', 'C', 1)
g.addEdge('B', 'D', 1)
g.addEdge('C', 'D', 4)
g.addEdge('D', 'E', 3)
start = g.getVertex('A')
dijkstra(g, start)
for v in g:
path = [v.getId()]
shortest(v, path)
print('The shortest path for vertex', v.getId(), 'is', path[::-1], 'with a distance of', v.getDistance())
```
这个实现程序中,我们首先定义了Vertex类来表示每个顶点,并将每个顶点存储在一个字典中。在Vertex类中,我们存储了每个顶点的邻接点、权重、距离、是否访问过以及前一个顶点。然后,我们定义了Graph类来管理所有的顶点和边。在Graph类中,我们可以添加新的顶点和边,获取所有的顶点以及实现__iter__方法来迭代所有的顶点。最后,我们使用Dijkstra算法来寻找从某个源点到其他所有顶点的最短路径,并输出结果。
希望这个实现程序能够帮助到你!
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