C++实现及理论https://www.cnblogs.com/polly333/category/720001.html
https://github.com/liuyubobobo/Play-with-Algorithms
python实现https://github.com/ShiveryMoon/Imooc-Algorithm-PythonEdition
图的表达方式：邻接矩阵（适合表示稠密图（边的个数））、邻接表（适合表示稀疏图（边的个数远远小于所能拥有的最大的边的个数））
邻接表实现：
# -*- coding: utf-8 -*- import sys #由于python的面向对象特性，将定义一个Vertex类，所有与节点有关的属性都储存在vertex类中，比如节点id，节点邻居，节点的前继节点，节点是否被遍历过等等 #注意，此时我们定义的邻接表已经可以存储权重了，也就是说，这个邻接表已经适用于有权无权有向无向图，所以第八章将不会再新实现一个邻接表。 class Vertex(object): def __init__(self,key): self.id = key self.connectedTo = {} #key是vertex对象，value是两个对象之间的边的权重 self.ccid = 0 #Connected Components id，即该节点所属的连通分量的id self.dist = sys.maxsize self.pred = None #当前节点的前继节点 self.isvisited = False def addNeighbor(self,nbr,weight=0): self.connectedTo[nbr] = weight def __str__(self): return str(self.id) + ' connectedTo: ' + str([x.id for x in self.connectedTo]) def getConnections(self): return self.connectedTo.keys() def getConnectionsId(self): idList=[] for k in self.connectedTo.keys(): idList.append(k.getId()) return sorted(idList) def getConnectionsIdAndWeight(self): idList = [] for k in self.connectedTo.keys(): idList.append(k.getId()) weightList=list(self.connectedTo.values()) return {idList[i]:weightList[i] for i in range(len(idList))} def getWeight(self,nbr): return self.connectedTo[nbr] def getId(self): return self.id def getCCID(self): return self.ccid def setCCID(self,ccid): self.ccid=ccid def getPred(self): return self.pred def setPred(self,pred): self.pred=pred def visited(self): return self.isvisited def setVisited(self,bool): self.isvisited=bool def getDistance(self): return self.dist def setDistance(self, dist): self.dist = dist class SparseGraph(object): def __init__(self,directed=False,weighted=False): self.vertDict = {} #key是vertex的id，value是vertex self.numVertices = 0 self.directed=directed self.weighted=weighted self.ccount=0 #一个图有多少个连通分量应当属于图的属性 def addVertex(self,key): self.numVertices = self.numVertices + 1 newVertex = Vertex(key) self.vertDict[key] = newVertex return newVertex def getVertex(self,n): if n in self.vertDict: return self.vertDict[n] else: return None def __contains__(self,n): return n in self.vertDict def addEdge(self,f,t,weight=0): if f not in self.vertDict: self.addVertex(f) if t not in self.vertDict: self.addVertex(t) self.vertDict[f].addNeighbor(self.vertDict[t], weight) if self.directed is False: self.vertDict[t].addNeighbor(self.vertDict[f], weight) def getVertices(self): return list(self.vertDict.keys()) def getVertNum(self): return self.numVertices def __iter__(self): return iter(self.vertDict.values()) def getAllInfo(self): verticesList=[int(x) for x in list(self.getVertices())] verticesList.sort() if self.weighted: for i in range(len(verticesList)): print('vertex %s : %s' % (i, self.getVertex(i).getConnectionsIdAndWeight())) else: for i in range(len(verticesList)): print('vertex %s : %s' %(i,self.getVertex(i).getConnectionsId())) def isConnected(self,p,q): return self.vertDict[p].getCCID() == self.vertDict[q].getCCID() def getCcount(self): return self.ccount def setCcount(self,ccount): self.ccount=ccount连通分量与连通分量之间没有边相连
文章来源: 算法与数据结构――图论