Python 数据结构 —— 图

1. 图的存储方式

1.1 图的存储数据结构

图可以用 邻接矩阵 和 邻接表 （Adjacency List）来表示，当边数不多的时候，使用邻接表存储效率更高

如存储下面的图：

对应的邻接表为：

1.2 字典实现邻接表

采用字典实现邻接表很方便：

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2 顶点 Vertex

每一个顶点中存储了 顶点信息 + 相邻顶点信息，具有 addNeighbor(), getId(), getWeright() 等方法：

class Vertex:
	def __init__(self, id):
		self.id = id
		self.adjacency = {}

	def getId(self):
		return self.id

	def getNeighbors(self):
		return self.adjacency.keys()

	def addNeighbor(self, neighbor, weight):
		self.adjacency[neighbor] = weight

	def delNeighbor(self, neighbor):
		if neighbor in adjacency.keys():
			del self.adjacency[neighbor]

	def getWeight(self, neighbor):
		if neighbor in self.adjacency.keys():
			return self.adjacency[neighbor]
		return -1

	def __str__(self):
		res = str(self.id) + \
			'\tadjacency: ' + str([(k, v) for (k, v) in self.adjacency.items()])
		return res

if __name__ == '__main__':
	v = Vertex(5)
	v.addNeighbor(2, 6)
	v.addNeighbor(3, 5)
	print(v)

测试打印结果为：

5	adjacency: [(2, 6), (3, 5)]

符合预期要求

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3. 图 Gragh

图的属性和方法如下：

from Vertex import Vertex

class Gragh:
	def __init__(self):
		self.numEdge = 0
		self.numVertex = 0
		# (key, value) = (id, Vertex(id)) 
		self.vertexList = {}

	def getNumEgde(self):
		pass

	def getNumVertex(self):
		pass

	def addVertex(self, id):
		pass

	def cost(self, fromVertex, toVertex):
		pass

	def getVertex(self, id):
		pass

	def addEdge(self, fromVertex, toVertex, weight):
		pass

	def delEdge(self, fromVertex, toVertex):
		pass

	def __str__(self):
		pass

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属性

初始化时存储了边的数量 numEdge 和顶点的数量 numVertex

其中 vertexList 是一个字典，字典的 key 为顶点的 id，字典的 value 为顶点（Vertex 类型，具有 id 和 adjacency 属性）

为了方便理解，利用 Gragh 创建图存储先前的图，内存中存储的数据如下：

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方法

具体的方法定义如下：

from Vertex import Vertex

class Gragh:
	def __init__(self):
		self.vertexList = {}
		self.numVertex = 0
		self.numEdge = 0

	def getNumEgde(self):
		return self.numEdge

	def getNumVertex(self):
		return self.numVertex

	def addVertex(self, id):
		self.numVertex += 1
		self.vertexList[id] = Vertex(id)

	def getVertex(self, id):
		if id in self.vertexList:
			return self.vertexList[id]
		else:
			return None

	def addEdge(self, fromVertex, toVertex, weight):
		if fromVertex not in self.vertexList:
			self.addVertex(fromVertex)
		if toVertex not in self.vertexList:
			self.addVertex(toVertex)
		self.vertexList[fromVertex].addNeighbor(toVertex, weight)
		self.numEdge += 1

	def delEdge(self, fromVertex, toVertex):
		if fromVertex in self.vertexList and toVertex in self.vertexList:
			self.vertexList[fromVertex].delNeighbor(toVertex)
			self.numEdge -= 1

	def cost(self, fromVertex, toVertex):
		if fromVertex in self.vertexList:
			if toVertex in self.vertexList[fromVertex].getNeighbors():
				return self.vertexList[fromVertex].getWeight(toVertex)
		return -1

	def __str__(self):
		res = 'numEdge = ' + str(self.numEdge) + '\n' + \
			'numVertex = ' + str(self.numVertex) + '\n'
		for v in self.vertexList.values():
			res += str(v) + '\n'
		return res

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测试

我们测试一下定义好的数据结构：

if __name__ == '__main__':
	g = Gragh()
	for i in ['V0', 'V1', 'V2', 'V3', 'V4', 'V5']:
		g.addVertex(i)
	print(g)

	g.addEdge('V0', 'V1', 5)
	g.addEdge('V0', 'V5', 2)
	g.addEdge('V1', 'V2', 4)
	g.addEdge('V2', 'V3', 9)
	g.addEdge('V3', 'V4', 7)
	g.addEdge('V3', 'V5', 3)
	g.addEdge('V4', 'V0', 1)
	g.addEdge('V5', 'V4', 1)
	g.addEdge('V5', 'V5', 8)
	print(g)

打印结果为：

numEdge = 0
numVertex = 6
V0	adjacency: []
V1	adjacency: []
V2	adjacency: []
V3	adjacency: []
V4	adjacency: []
V5	adjacency: []

numEdge = 9
numVertex = 6
V0	adjacency: [('V1', 5), ('V5', 2)]
V1	adjacency: [('V2', 4)]
V2	adjacency: [('V3', 9)]
V3	adjacency: [('V4', 7), ('V5', 3)]
V4	adjacency: [('V0', 1)]
V5	adjacency: [('V4', 1), ('V5', 8)]

结果正确

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完结