1. 实验目的
理解图的十字链表这一存储结构，并掌握有向图的基本操作。
2. 实验介绍
掌握图的基本概念及相关术语和性质，掌握图的邻接矩阵和邻接表表示法，了解实际问题的求解效率与采用何种存储结构和算法有密切联系。熟练掌握图的两种搜索路径的遍历：深度优先搜索和广度优先搜索的算法。掌握构造最小生成树的两种算法及拓扑排序算法的思想，掌握迪杰斯特拉算法。了解关键路径的概念和求解方法，了解弗洛伊德算法。
3.实验内容
创建名为 ex060901_01.py 的文件，在文件中定义 3 个类，第一个是顶点的结点类，
第二个是弧的结点类，第三个是图类，该类包含存储有向图的十字链表及有向图的基本
操作。请按以下步骤设计实现代码并验证之。
（1） 创建一个图 6-1（主教材 P317 图 6-45）所示的有向图，并使用十字链表存
储。
（2）计算图中顶点的总数和弧的总数。
（3）计算每一个顶点的入度、出度和度。
（4）添加一条弧<D,C>。
（5）获取顶点 D 邻接到的第一个顶点，并将其值输出
4. 实验步骤与代码
class CircularSequenceQueue:
def __init__(self):
self.MaxQueueSize=4
self.s=[None for x in range(0,self.MaxQueueSize)]
self.front=0
self.rear=0
def InitQueue(self,Max):
self.MaxQueueSize=Max
self.s=[None for x in range(0,self.MaxQueueSize)]
self.front=0
self.rear=0
def QueueVisit(self,element):
print(element,end=' ')
def IsEmptyQueue(self):
if self.front==self.rear:
iQueue=True
else:
iQueue=False
return iQueue
def EnQueue(self,x):
if (self.rear+1)%self.MaxQueueSize!=self.front:
self.rear=(self.rear+1)%self.MaxQueueSize
self.s[self.rear]=x
else:
print("队列已满，无法入队")
return
def DeQueue(self):
if self.IsEmptyQueue():
print("队列为空，无法出队")
return
else:
self.front=(self.front+1)%self.MaxQueueSize
return self.s[self.front]
def QueueTraverse(self):
if self.IsEmptyQueue():
print("队列为空，队列无元素可以访问")
return
else:
if self.front<self.rear:
i=self.front+1
while i<self.rear:
self.QueueVisit(self.s[i])
i=i+1
self.QueueVisit(self.s[self.rear])
else:
i=self.front+1
while i<self.MaxQueueSize:
self.QueueVisit(self.s[i])
i=i+1
i=0
while i<=self.rear:
self.QueueVisit(self.s[i])
i=i+1
def GetHead(self):
if self.IsEmptyQueue():
print("队列为空，无法输出队首元素")
return
else:
return self.s[(self.front+1)%self.MaxQueueSize]
def GetQueueLength(self):
if self.IsEmptyQueue():
print("队列为空，队列长度为零")
return
else:
return (self.rear-self.front+self.MaxQueueSize)%self.MaxQueueSize
class Vertex(object):
def __init__(self,data):
self.data = data
self.FirstArc = None
class Arc(object):
def __init__(self,adjacent):
self.adjacent = adjacent
self.info = None
self.NextArc = None
class Graph(object):
def __init__(self,kind):
self.kind = kind
self.VertexNum = 0
self.ArcNum = 0
self.Vertices = []
self.indegree = {}
self.outdegree = {}
def CreateGraph(self):
print('请依次输入图中各顶点的值，每个顶点值以回车间隔，并以#作为输入结束符：')
data = input('->')
while data is not '#':
vertex = Vertex(data)
self.Vertices.append(vertex)
self.indegree[data] = 0
self.outdegree[data] = 0
self.VertexNum = self.VertexNum + 1
data = input('->')
print('请依次输入图中每条边的两个顶点值，两个顶点值以空格作为间隔，每输入一组后进行换行，最终以#结束输入：')
arc = input('->')
while arc is not '#':
TailVertex = arc.split()[0]
HeadVertex = arc.split()[1]
self.indegree[TailVertex] = self.indegree[TailVertex] + 1
self.outdegree[HeadVertex] = self.outdegree[HeadVertex] + 1
TailIndex = self.LocateVertex(TailVertex)
HeadIndex = self.LocateVertex(HeadVertex)
self.InsertArc(TailIndex,HeadIndex)
self.ArcNum = self.ArcNum + 1
arc = input('->')
print('创建成功!')
def LocateVertex(self,Vertex):
index = 0
while self.Vertices[index].data != Vertex and index < len(self.Vertices):
index = index + 1
return index
def InsertArc(self,TailIndex,HeadIndex):
if self.kind is 0:
TailArc = Arc(TailIndex)
HeadArc = Arc(HeadIndex)
HeadArc.NextArc = self.Vertices[TailIndex].FirstArc
self.Vertices[TailIndex].FirstArc = HeadArc
TailArc.NextArc = self.Vertices[HeadIndex].FirstArc
self.Vertices[HeadIndex].FirstArc = TailArc
elif self.kind is 2:
HeadArc = Arc(HeadIndex)
HeadArc.NextArc = self.Vertices[TailIndex].FirstArc
self.Vertices[TailIndex].FirstArc = HeadArc
def GetFirstAdjacentVertex(self,Vertex):
FirstArc = self.Vertices[Vertex].FirstArc
if FirstArc is not None:
return FirstArc.adjacent
def GetNextAdjacentVertex(self,Vertex,Adjacent):
ArcLink = self.Vertices[Vertex].FirstArc
while ArcLink is not None:
if ArcLink.adjacent is Adjacent:
if ArcLink.NextArc is not None:
return ArcLink.NextArc.adjacent
else:
return None
else:
ArcLink = ArcLink.NextArc
def VisitVertex(self,Vertex):
print(self.Vertices[Vertex].data,end='')
def BFSTraverse(self):
visited=[]
index = 0
Queue=CircularSequenceQueue()
Queue.InitQueue(10)
while index < self.VertexNum:
visited.append('False')
index = index + 1
index = 0
while index < self.VertexNum:
if visited[index] is 'False':
visited[index] = 'True'
self.VisitVertex(index)
Queue.EnQueue(index)
while Queue.IsEmptyQueue() is False:
tVertex = Queue.DeQueue()
NextAdjacent = self.GetFirstAdjacentVertex(tVertex)
while NextAdjacent is not None:
if visited[NextAdjacent] is 'False':
visited[NextAdjacent] = 'True'
self.VisitVertex(NextAdjacent)
Queue.EnQueue(NextAdjacent)
NextAdjacent = self.GetNextAdjacentVertex(tVertex,NextAdjacent)
index = index + 1
if __name__ =='__main__':
graph = Graph(2)
print('要构建如下图所示的图：')
print('A → B')
print('↓↘ ↗ ↓')
print('↓ E ↓')
print('↓↙ ↘ ↓')
print('C D')
graph.CreateGraph()
print('该图顶点数为',graph.VertexNum,'个','弧数为',graph.ArcNum,'个')
print(' ',end='')
for i in range(len(graph.indegree)):
print(list(graph.indegree.keys())[i],end=' ')
print()
print('入度',end=' ')
for i in range(len(graph.indegree)):
print(graph.indegree[list(graph.indegree.keys())[i]],end=' ')
print()
print('出度',end=' ')
for i in range(len(graph.indegree)):
print(graph.outdegree[list(graph.indegree.keys())[i]],end=' ')
print()
print(' 度',end=' ')
for i in range(len(graph.indegree)):
print(graph.indegree[list(graph.indegree.keys())[i]] + graph.outdegree[list(graph.indegree.keys())[i]],end=' ')
print()
print('插入弧<D,C>')
graph.InsertArc(3,2)
print('将D邻接的第一个顶点为：',end=' ')
print(chr(graph.GetFirstAdjacentVertex(3)+64))
print('广度优先遍历图的结果如下:',end=' ')
graph.BFSTraverse()
5.实验结果
