The document discusses graph theory concepts like nodes, edges, and graph optimization problems. It provides code definitions for a Node class and Edge class to represent graph elements. It also gives examples of graph models like maps of roads and bridges between islands. The summary discusses how graphs can capture relationships between entities and how graph algorithms can find optimal paths between nodes.

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15. #
class Node(object):
def __init__(self, name):
Assumes name is a string
self.name = name
def getName(self):
return self.name
def __str__(self):
return self.name
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16. class Edge(object):
def __init__(self, src, dest):
Assumes src and dest are nodes
self.src = src
self.dest = dest
def getSource(self):
return self.src
def getDestination(self):
return self.dest
def __str__(self):
return self.src.getName() + '-’
+ self.dest.getName()
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18. %$3$%'9
class Digraph(object):
edges is a dict mapping each node to a list of
its children”
def __init__(self):
self.edges = {}
def addNode(self, node):
if node in self.edges:
raise ValueError('Duplicate node')
else:
self.edges[node] = []
def addEdge(self, edge):
src = edge.getSource()
dest = edge.getDestination()
if not (src in self.edges and dest in self.edges):
raise ValueError('Node not in graph')
self.edges[src].append(dest)
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19. %$3$%':
def childrenOf(self, node):
return self.edges[node]
def hasNode(self, node):
return node in self.edges
def getNode(self, name):
for n in self.edges:
if n.getName() == name:
return n
raise NameError(name)
def __str__(self):
result = ''
for src in self.edges:
for dest in self.edges[src]:
result = result + src.getName() + '-'
+ dest.getName() + 'n'
return result[:-1] #omit final newline
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20. %$
class Graph(Digraph):
def addEdge(self, edge):
Digraph.addEdge(self, edge)
rev = Edge(edge.getDestination(), edge.getSource())
Digraph.addEdge(self, rev)
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def buildCityGraph(graphType):
g = graphType()
for name in ('Boston', 'Providence', 'New York', 'Chicago',
'Denver', 'Phoenix', 'Los Angeles'): #Create 7 nodes
g.addNode(Node(name))
g.addEdge(Edge(g.getNode('Boston'), g.getNode('Providence')))
g.addEdge(Edge(g.getNode('Boston'), g.getNode('New York')))
g.addEdge(Edge(g.getNode('Providence'), g.getNode('Boston')))
g.addEdge(Edge(g.getNode('Providence'), g.getNode('New York')))
g.addEdge(Edge(g.getNode('New York'), g.getNode('Chicago')))
g.addEdge(Edge(g.getNode('Chicago'), g.getNode('Denver')))
g.addEdge(Edge(g.getNode('Chicago'), g.getNode('Phoenix')))
g.addEdge(Edge(g.getNode('Denver'), g.getNode('Phoenix')))
g.addEdge(Edge(g.getNode('Denver'), g.getNode(’New York')))
g.addEdge(Edge(g.getNode('Los Angeles'), g.getNode('Boston')))
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def DFS(graph, start, end, path, shortest, toPrint = False):
path = path + [start]
if toPrint:
print('Current DFS path:', printPath(path))
if start == end:
return path
for node in graph.childrenOf(start):
if node not in path: #avoid cycles
if shortest == None or len(path) len(shortest):
newPath = DFS(graph, node, end, path, shortest, toPrint)
if newPath != None:
shortest = newPath
elif toPrint:
print('Already visited', node)
return shortest
def shortestPath(graph, start, end, toPrint = False):
return DFS(graph, start, end, [], None, toPrint)
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28. '
def testSP(source, destination):
g = buildCityGraph(DiGraph)
sp = shortestPath(g, g.getNode(source), g.getNode(destination)
toPrint = True)
if sp != None:
print('Shortest path from', source, 'to',
destination, 'is', printPath(sp))
else:
print('There is no path from', source, 'to', destination)
testSP('Boston', ’Chicago')
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def BFS(graph, start, end, toPrint = False):
initPath = [start]
pathQueue = [initPath]
while len(pathQueue) != 0:
#Get and remove oldest element in pathQueue
tmpPath = pathQueue.pop(0)
if toPrint:
print('Current BFS path:', printPath(tmpPath))
lastNode = tmpPath[-1]
if lastNode == end:
return tmpPath
for nextNode in graph.childrenOf(lastNode):
if nextNode not in tmpPath:
newPath = tmpPath + [nextNode]
pathQueue.append(newPath)
return None
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38. MIT OpenCourseWare
https://ocw.mit.edu
6.0002 Introduction to Computational Thinking and Data Science
Fall 2016
For information about citing these materials or our Terms of Use, visit: https://ocw.mit.edu/terms.