从邻接表制作无向图

Question

我正在尝试从邻接表中创建一个无向图来练习 Karger 的 Min Cut 算法。以下是我的代码

class Vertex(object):
    '''Represents a vertex, with the indices of edges
       incident on it'''
    def __init__(self,name,edgeIndices=[]):
        self.name = name
        self.edgeIndices = edgeIndices
    def getName(self):
        return self.name
    def addEdge(self,ind):
        self.edgeIndices.append(ind)
    def getEdges(self):
        return self.edgeIndices
    def __eq__(self,other):
        return self.name == other.name

class Edge(object):
    '''Represents an edge with the indices of its endpoints''' 
    def __init__(self,ends):
        self.ends = ends
    def getEnds(self):
        return self.ends
    def __eq__(self,other):
        return (self.ends == other.ends)\
               or ((self.ends[1],self.ends[0]) == other.ends)

class Graph(object):
    def __init__(self,vertices,edges):
        self.edges = edges
        self.vertices = vertices

def createGraph(filename):
    '''Input: Adjacency list
       Output: Graph object'''
    vertices = []
    edges = []
    with open(filename) as f:
        for line in f:
            elements = line.split()
            newVert = Vertex(elements[0])
            if newVert not in vertices:
                vertices.append(newVert)

            for verts in elements[1:]:
                otherVert = Vertex(verts)
                if otherVert not in vertices:
                    vertices.append(otherVert)
                end1 = vertices.index(newVert)
                end2 = vertices.index(otherVert)
                newEdge = Edge((end1,end2))
                if newEdge not in edges:
                    edges.append(newEdge)
                newVert.addEdge(edges.index(newEdge))
    return Graph(vertices,edges)

假设邻接表如下，顶点用整数表示

1 -> 2,3,4
2 -> 1,3
3 -> 1,2,4
4 -> 1,3

该图总共有 5 条边，因此包含与顶点关联的边的索引的列表长度不能超过 5 条。

例如，我希望顶点“2”只有两条边的索引，即顶点 1 和 3 的边。相反，我得到的是[0, 1, 2, 3, 0, 2, 1, 3]。 我需要帮助找出问题所在。

Answer 1

第一个错误来自 Vertex init。当传递一个列表作为默认参数时，Python 将它实例化一次，并与所有未来的 Vertex 实例共享这个实例。 传递 None，如果没有给出列表，则使用本地列表。

class Vertex(object):
    def __init__(self,name,edgeIndices=None):
        self.name = name
        self.edgeIndices = edgeIndices if edgeIndices else []

在createGraph方法中，当顶点已经存在于图中时，需要使用它。请参阅添加的else: newVert = ... 您似乎也有关于木质分裂的问题。查看elements[2].split(',') 的迭代。

def createGraph(filename):
    '''Input: Adjacency list
       Output: Graph object'''
    vertices = []
    edges = []
    with open(filename) as f:
        for line in f:
            elements = line.split()
            newVert = Vertex(elements[0])
            if newVert not in vertices:
                vertices.append(newVert)
            else:
                newVert = vertices[vertices.index(newVert)]

            for verts in elements[2].split(','):
                otherVert = Vertex(verts)
                if otherVert not in vertices:
                    vertices.append(otherVert)
                end1 = vertices.index(newVert)
                end2 = vertices.index(otherVert)
                newEdge = Edge((end1,end2))
                if newEdge not in edges:
                    edges.append(newEdge)
                newVert.addEdge(edges.index(newEdge))
    return Graph(vertices,edges)

作为旁注，我会尝试使用 dict 来存储顶点（和边）并进行查找。 List.index 用的比较多，你可能会白白创建很多对象。

Answer 2

我建议看一下基于 Dict、OrderedDict、Linked List 的图形实现。比基于列表和索引更有效。 为了让您的代码工作，您可以执行以下操作：

更改顶点以避免上一个答案中描述的问题：

class Vertex(object):
    def __init__(self,name, edgeIndices=None):
        self.name = name
        self.edgeIndices = edgeIndices or []     

让图表做一些工作：

class Graph(object):
    def __init__(self):
        self.edges = []
        self.vertices = []

    def add_vertex(self, name):
        vertex = Vertex(name)
        if vertex not in self.vertices:
            self.vertices.append(vertex)

    def add_edge(self, *names):
        self._add_vertices(names)
        edge = self._add_edge(names)
        self._update_vertices_links(edge, names)

    def get_vertex_index(self, name):
        vertex = Vertex(name)
        return self.vertices.index(vertex)

    def get_vertex(self, name):
        return self.vertices[self.get_vertex_index(name)]

    def _update_vertices_links(self, edge, names):
        for name in names:
            vertex = self.get_vertex(name)
            vertex.addEdge(self.edges.index(edge))

    def _add_edge(self, names):
        edge = Edge((self.get_vertex_index(names[0]), self.get_vertex_index(names[1])))
        if edge not in self.edges:
            self.edges.append(edge)
        return edge

    def _add_vertices(self, names):
        for name in names:
            self.add_vertex(name)

    def __repr__(self):
        return "Vertices: %s\nEdges: %s" % (self.vertices, self.edges)

创建图表：

def createGraph(filename):
    with open(filename) as f:
        graph = Graph()
        for line in f:
            elements = line.strip().split()
            graph.add_vertex(elements[0])
            for element in elements[2].split(","):
                graph.add_edge(elements[0], element)
    return graph

运行它：

graph = createGraph('input.txt')
print graph

输入的输出：

Vertices: [<Name:1 Edges:[0, 1, 2]>, <Name:2 Edges:[0, 3]>, <Name:3 Edges:[1, 3, 4]>, <Name:4 Edges:[2, 4]>]
Edges: [(0, 1), (0, 2), (0, 3), (1, 2), (2, 3)]