Python图算法实例分析
作者：intergret
这篇文章主要介绍了Python图算法,结合实例形式详细分析了Python数据结构与算法中的图算法实现技巧,需要的朋友可以参考下
本文实例讲述了Python图算法。分享给大家供大家参考，具体如下：
#encoding=utf-8
import networkx,heapq,sys
from matplotlib import pyplot
from collections import defaultdict,OrderedDict
from numpy import array
# Data in graphdata.txt:
# a b 4
# a h 8
# b c 8
# b h 11
# h i 7
# h g 1
# g i 6
# g f 2
# c f 4
# c i 2
# c d 7
# d f 14
# d e 9
# f e 10
def Edge(): return defaultdict(Edge)
class Graph:
def __init__(self):
self.Link = Edge()
self.FileName = ''
self.Separator = ''
def MakeLink(self,filename,separator):
self.FileName = filename
self.Separator = separator
graphfile = open(filename,'r')
for line in graphfile:
items = line.split(separator)
self.Link[items[0]][items[1]] = int(items[2])
self.Link[items[1]][items[0]] = int(items[2])
graphfile.close()
def LocalClusteringCoefficient(self,node):
neighbors = self.Link[node]
if len(neighbors) <= 1: return 0
links = 0
for j in neighbors:
for k in neighbors:
if j in self.Link[k]:
links += 0.5
return 2.0*links/(len(neighbors)*(len(neighbors)-1))
def AverageClusteringCoefficient(self):
total = 0.0
for node in self.Link.keys():
total += self.LocalClusteringCoefficient(node)
return total/len(self.Link.keys())
def DeepFirstSearch(self,start):
visitedNodes = []
todoList = [start]
while todoList:
visit = todoList.pop(0)
if visit not in visitedNodes:
visitedNodes.append(visit)
todoList = self.Link[visit].keys() + todoList
return visitedNodes
def BreadthFirstSearch(self,start):
visitedNodes = []
todoList = [start]
while todoList:
visit = todoList.pop(0)
if visit not in visitedNodes:
visitedNodes.append(visit)
todoList = todoList + self.Link[visit].keys()
return visitedNodes
def ListAllComponent(self):
allComponent = []
visited = {}
for node in self.Link.iterkeys():
if node not in visited:
oneComponent = self.MakeComponent(node,visited)
allComponent.append(oneComponent)
return allComponent
def CheckConnection(self,node1,node2):
return True if node2 in self.MakeComponent(node1,{}) else False
def MakeComponent(self,node,visited):
visited[node] = True
component = [node]
for neighbor in self.Link[node]:
if neighbor not in visited:
component += self.MakeComponent(neighbor,visited)
return component
def MinimumSpanningTree_Kruskal(self,start):
graphEdges = [line.strip('\n').split(self.Separator) for line in open(self.FileName,'r')]
nodeSet = {}
for idx,node in enumerate(self.MakeComponent(start,{})):
nodeSet[node] = idx
edgeNumber = 0; totalEdgeNumber = len(nodeSet)-1
for oneEdge in sorted(graphEdges,key=lambda x:int(x[2]),reverse=False):
if edgeNumber == totalEdgeNumber: break
nodeA,nodeB,cost = oneEdge
if nodeA in nodeSet and nodeSet[nodeA] != nodeSet[nodeB]:
nodeBSet = nodeSet[nodeB]
for node in nodeSet.keys():
if nodeSet[node] == nodeBSet:
nodeSet[node] = nodeSet[nodeA]
print nodeA,nodeB,cost
edgeNumber += 1
def MinimumSpanningTree_Prim(self,start):
expandNode = set(self.MakeComponent(start,{}))
distFromTreeSoFar = {}.fromkeys(expandNode,sys.maxint); distFromTreeSoFar[start] = 0
linkToNode = {}.fromkeys(expandNode,'');linkToNode[start] = start
while expandNode:
# Find the closest dist node
closestNode = ''; shortestdistance = sys.maxint;
for node,dist in distFromTreeSoFar.iteritems():
if node in expandNode and dist < shortestdistance:
closestNode,shortestdistance = node,dist
expandNode.remove(closestNode)
print linkToNode[closestNode],closestNode,shortestdistance
for neighbor in self.Link[closestNode].iterkeys():
recomputedist = self.Link[closestNode][neighbor]
if recomputedist < distFromTreeSoFar[neighbor]:
distFromTreeSoFar[neighbor] = recomputedist
linkToNode[neighbor] = closestNode
def ShortestPathOne2One(self,start,end):
pathFromStart = {}
pathFromStart[start] = [start]
todoList = [start]
while todoList:
current = todoList.pop(0)
for neighbor in self.Link[current]:
if neighbor not in pathFromStart:
pathFromStart[neighbor] = pathFromStart[current] + [neighbor]
if neighbor == end:
return pathFromStart[end]
todoList.append(neighbor)
return []
def Centrality(self,node):
path2All = self.ShortestPathOne2All(node)
# The average of the distances of all the reachable nodes
return float(sum([len(path)-1 for path in path2All.itervalues()]))/len(path2All)
def SingleSourceShortestPath_Dijkstra(self,start):
expandNode = set(self.MakeComponent(start,{}))
distFromSourceSoFar = {}.fromkeys(expandNode,sys.maxint); distFromSourceSoFar[start] = 0
while expandNode:
# Find the closest dist node
closestNode = ''; shortestdistance = sys.maxint;
for node,dist in distFromSourceSoFar.iteritems():
if node in expandNode and dist < shortestdistance:
closestNode,shortestdistance = node,dist
expandNode.remove(closestNode)
for neighbor in self.Link[closestNode].iterkeys():
recomputedist = distFromSourceSoFar[closestNode] + self.Link[closestNode][neighbor]
if recomputedist < distFromSourceSoFar[neighbor]:
distFromSourceSoFar[neighbor] = recomputedist
for node in distFromSourceSoFar:
print start,node,distFromSourceSoFar[node]
def AllpairsShortestPaths_MatrixMultiplication(self,start):
nodeIdx = {}; idxNode = {};
for idx,node in enumerate(self.MakeComponent(start,{})):
nodeIdx[node] = idx; idxNode[idx] = node
matrixSize = len(nodeIdx)
MaxInt = 1000
nodeMatrix = array([[MaxInt]*matrixSize]*matrixSize)
for node in nodeIdx.iterkeys():
nodeMatrix[nodeIdx[node]][nodeIdx[node]] = 0
for line in open(self.FileName,'r'):
nodeA,nodeB,cost = line.strip('\n').split(self.Separator)
if nodeA in nodeIdx:
nodeMatrix[nodeIdx[nodeA]][nodeIdx[nodeB]] = int(cost)
nodeMatrix[nodeIdx[nodeB]][nodeIdx[nodeA]] = int(cost)
result = array([[0]*matrixSize]*matrixSize)
for i in xrange(matrixSize):
for j in xrange(matrixSize):
result[i][j] = nodeMatrix[i][j]
for itertime in xrange(2,matrixSize):
for i in xrange(matrixSize):
for j in xrange(matrixSize):
if i==j:
result[i][j] = 0
continue
result[i][j] = MaxInt
for k in xrange(matrixSize):
result[i][j] = min(result[i][j],result[i][k]+nodeMatrix[k][j])
for i in xrange(matrixSize):
for j in xrange(matrixSize):
if result[i][j] != MaxInt:
print idxNode[i],idxNode[j],result[i][j]
def ShortestPathOne2All(self,start):
pathFromStart = {}
pathFromStart[start] = [start]
todoList = [start]
while todoList:
current = todoList.pop(0)
for neighbor in self.Link[current]:
if neighbor not in pathFromStart:
pathFromStart[neighbor] = pathFromStart[current] + [neighbor]
todoList.append(neighbor)
return pathFromStart
def NDegreeNode(self,start,n):
pathFromStart = {}
pathFromStart[start] = [start]
pathLenFromStart = {}
pathLenFromStart[start] = 0
todoList = [start]
while todoList:
current = todoList.pop(0)
for neighbor in self.Link[current]:
if neighbor not in pathFromStart:
pathFromStart[neighbor] = pathFromStart[current] + [neighbor]
pathLenFromStart[neighbor] = pathLenFromStart[current] + 1
if pathLenFromStart[neighbor] <= n+1:
todoList.append(neighbor)
for node in pathFromStart.keys():
if len(pathFromStart[node]) != n+1:
del pathFromStart[node]
return pathFromStart
def Draw(self):
G = networkx.Graph()
nodes = self.Link.keys()
edges = [(node,neighbor) for node in nodes for neighbor in self.Link[node]]
G.add_edges_from(edges)
networkx.draw(G)
pyplot.show()
if __name__=='__main__':
separator = '\t'
filename = 'C:\\Users\\Administrator\\Desktop\\graphdata.txt'
resultfilename = 'C:\\Users\\Administrator\\Desktop\\result.txt'
myGraph = Graph()
myGraph.MakeLink(filename,separator)
print 'LocalClusteringCoefficient',myGraph.LocalClusteringCoefficient('a')
print 'AverageClusteringCoefficient',myGraph.AverageClusteringCoefficient()
print 'DeepFirstSearch',myGraph.DeepFirstSearch('a')
print 'BreadthFirstSearch',myGraph.BreadthFirstSearch('a')
print 'ShortestPathOne2One',myGraph.ShortestPathOne2One('a','d')
print 'ShortestPathOne2All',myGraph.ShortestPathOne2All('a')
print 'NDegreeNode',myGraph.NDegreeNode('a',3).keys()
print 'ListAllComponent',myGraph.ListAllComponent()
print 'CheckConnection',myGraph.CheckConnection('a','f')
print 'Centrality',myGraph.Centrality('c')
myGraph.MinimumSpanningTree_Kruskal('a')
myGraph.AllpairsShortestPaths_MatrixMultiplication('a')
myGraph.MinimumSpanningTree_Prim('a')
myGraph.SingleSourceShortestPath_Dijkstra('a')
# myGraph.Draw()
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