Download as PDF, PPTX
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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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mappi
ing each
h nod
de list](https://image.slidesharecdn.com/graph-theoreticmodels-231023141248-0910bafd/75/graph-theoretic-Models-pdf-18-2048.jpg)
![%$3$%':
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
QKKKM N LT](https://image.slidesharecdn.com/graph-theoreticmodels-231023141248-0910bafd/75/graph-theoretic-Models-pdf-19-2048.jpg)
![$'%'%78
def DFS(graph, start, end, path, shortest, toPrint = False):
path = path + [start]
if toPrint:
print('Current DFS path:', printPath(path))
if start == end:
return path
for node in graph.childrenOf(start):
if node not in path: #avoid cycles
if shortest == None or len(path) len(shortest):
newPath = DFS(graph, node, end, path, shortest, toPrint)
if newPath != None:
shortest = newPath
elif toPrint:
print('Already visited', node)
return shortest
def shortestPath(graph, start, end, toPrint = False):
return DFS(graph, start, end, [], None, toPrint)
''.*( 0/.3./$*)/0.0,.*,.'7
5.,,.3)1*)=
shortestPath
QKKKM N MR](https://image.slidesharecdn.com/graph-theoreticmodels-231023141248-0910bafd/75/graph-theoretic-Models-pdf-27-2048.jpg)
![#%'!:4%'6%'%78
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
QKKKM N NN
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graph-theoretic Models.pdf
- 1. %$6'#%( # %%!# $%'!' '% % #!$,'% QKKKM N L
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- 8. / %$%#, *.'$/3''*)05*.//*).'1*)/#$,/ W *(,30.)05*./ W.)/,*.01*))05*./ W $))$')05*./ W 5.*.50.)05*./ W *'$1')05*./ W .$($)')05*./ W *$')05*./ W 0 QKKKM N S )'7/$/*@$8.*8A= C/$8*)*. 0/)3(.*/)/ $)5#$##.0./#./$'*3 C*'*.*'3/0./. 0/)03.' $)0.1*)/5$0##*0#.30)*0 *0#./ Wizard of Oz dialogue map © Mapr.com. All rights reserved. This content is excluded from our Creative Commons license. For more information, see https://ocw.mit.edu/help/faq-fair-use.
- 9. / %$%#, 5$''/0#0)*0*)'7*.,#/,03. .'1*)/#$,/$)*))0)05*./*'()0/0#7 '/*/3,,*.0$).)*)0#*//0.303./ W $)$)/-3)/*'$)/05)'()0/D$/0#. ,0#.*(0* W$)$)0#'/06,)/$4,0#05)'()0/E /#*.0/0,0#,.*'(F W .11*)$)0#.,#$)0*/0/**))0'()0/ E.,#,.11*),.*'(F W $)$)0#(*/0$)0570*/,.0/0/* *))0'()0/E0#($)C30B(6C *5,.*'(F QKKKM N T
- 10. %$#%/- !-%// QKKKM NLK 0DSLPDJH‹VRXUFHXQNQRZQ$OOULJKWVUHVHUYHG7KLVFRQWHQWLVH[FOXGHGIURPRXUUHDWLYH RPPRQVOLFHQVH)RUPRUHLQIRUPDWLRQVHHKWWSVRFZPLWHGXKHOSIDTIDLUXVH
- 11. *%'# *'.*/7/0(3/$)$.,# W */=,*$)0/5#..*/)*.(0 W/=*))1*)/05),*$)0/ W ##/5$#0 W 6,01(0*0.*(/*3.)*0*/1)1*))**.0#0 W $/0)05)/*3.)/1)1*))*/ W 4./,*0.4'05)/*3.)/1)1*))*/ *'4.,#*,1($81*),.*'( W #*.0/05$#0,0#05)(7#*3/)(7* LL QKKKM N ,PDJHV‹VRXUFHVXQNQRZQ$OOULJKWVUHVHUYHG7KLVFRQWHQWLVH[FOXGHGIURPRXU UHDWLYH RPPRQVOLFHQVH)RUPRUHLQIRUPDWLRQVHHKWWSVRFZPLWHGXKHOSIDTIDLUXVH
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- 13. #%, %5 # #$/'))* #.$)3)$.0 *'/0.0/57$..'4)00$'/ W $8*$/')/ W )0#*.$/ /0#.,0#0#0*)0$)/#60'7*); W QKKKM N LN
- 14. !$ !(,%$ 3$'$).,#/ W */ W/ W 10#$)0*0#.0*(.,#/ /$).,#/ W .#$)*.,0#/05))*/ W .#$)*.*,1(',0#/05))*/ QKKKM N LO
- 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 QKKKM N LP
- 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() QKKKM N LQ
- 17. #!!#$%'(##%$ $.,#$/$.0.,# W /,//$)*)$.1*)*)'7 %)7(0.$6 W *5/=/*3.)*/ W*'3()/=/1)1*))*/ W ''G/HUL$0#.$/).*(/0* UK*0#.5$/ W *00#0$)$.,#(0.$6$/ /7((0.$ %)7'$/0 W //*$05$0##)*'$/0*/1)1*))*/ QKKKM N LR
- 18. %$3$%'9 class Digraph(object): edges isa 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) QKKKM N LS mappi ing each h nod de list
- 19. %$3$%': def childrenOf(self, node): returnself.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 QKKKM N LT
- 20. %$ class Graph(Digraph): def addEdge(self,edge): Digraph.addEdge(self, edge) rev = Edge(edge.getDestination(), edge.getSource()) Digraph.addEdge(self, rev) .,#*/)*0#4$.1*)'$07//*$05$0#) W /''*5,//$)$0#.$.1*) #7$/.,#/3'//*$.,#; ((.0#/3/1031*).3'; W '$)0*5*./*..0'73/$))$)/0)*0# /3,.07,$0/#*3''/*5*.*..0'75#))$)/0)* 0#/307,$//3/1030*.0#$)/0)*0#/3,.07, )7,.*.(0#05*./5$0#$.,#5$'''/*5*.5$0# .,#E30)*0F QKKKM N MK
- 21. %$$(!0(#%# ! #*.0/0,0#.*()L0*)M W #*.0/0/-3)*//3#0#0 W*3.)**./0$/)L W /1)1*)*'/0$/)M W *./L)M$)0#/-3)$M*''*5/L$)0# /-3)0#/*3.*M$/0#/1)1*)*L #*.0/05$#0,0# W $)$($80#/3(*0#5$#0/*0#/$)0#,0# QKKKM N ML
- 22. #!#%'''%# ! $)$).*30.*(*)$070*)*0#. /$)$)*((3)$1*))05*./ $)$),0#*.(*'3'0#.*3##($' '7.$)0# ? QKKKM NMM ,PDJHV‹VRXUFHVXQNQRZQ$OOULJKWVUHVHUYHG7KLVFRQWHQWLVH[FOXGHGIURPRXUUHDWLYH RPPRQVOLFHQVH)RUPRUHLQIRUPDWLRQVHHKWWSVRFZPLWHGXKHOSIDTIDLUXVH
- 23. .!$ QKKKM NMN */0*) */0*) .*4$) .*4$) 5*. 5*. #$* #$* )4. )4. #*)$6 #*)$6 */)'/ */)'/ %)7 $/0 */0*)=.*4$)5*. .*4$)=*/0*)5*. 5*.=#$* #$*=)4.#*)$6 )4.=#*)$65*. */)'/=*/0*) #*)$6=
- 24. , ' %$ defbuildCityGraph(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'))) QKKKM N MO
- 25. '#%''' '*.$0#(L,0#C./0/.#EF $($'.0*'!C./0,0#C./0(0#**)3(.1) /.#0.E 03.MF $)$.)$/0#0.,#($#0#47'//*5 (3/0,0.*5#0)*/5#44$/$00*4*$ *$)$)$))$0'**,/ QKKKMN MP *00#05.3/$)$4$C)C*)-3.=$5)),0# .*(/*3.0*)$)0.($0)*),0#.*(0# $)0.($0)*0*0#/1)1*)0#*($)1*)$/,0# .*(/*3.0*/1)1*)
- 26.
- 27. $'%'%78 def DFS(graph, start,end, path, shortest, toPrint = False): path = path + [start] if toPrint: print('Current DFS path:', printPath(path)) if start == end: return path for node in graph.childrenOf(start): if node not in path: #avoid cycles if shortest == None or len(path) len(shortest): newPath = DFS(graph, node, end, path, shortest, toPrint) if newPath != None: shortest = newPath elif toPrint: print('Already visited', node) return shortest def shortestPath(graph, start, end, toPrint = False): return DFS(graph, start, end, [], None, toPrint) ''.*( 0/.3./$*)/0.0,.*,.'7 5.,,.3)1*)= shortestPath QKKKM N MR
- 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') QKKKM N MS
- 29. .!$ QKKKM NMT */0*) */0*) .*4$) .*4$) 5*. 5*. #$* #$* )4. )4. #*)$6 #*)$6 */)'/ */)'/ %)7 $/0 */0*)=.*4$)5*. .*4$)=*/0*)5*. 5*.=#$* #$*=)4.#*)$6 )4.=#*)$65*. */)'/=*/0*) #*)$6=
- 30. ,'$,'7#'##'#8 3..)0,0#=#$* 3..)0,0#=#$*CV)4. 3..)0,0#=#$*CV)4.CV#*)$6 3..)0,0#=#$*CV)4.CV5*. '.74$/$0#$* 3..)0,0#=#$*CV#*)$6 #.$/)*,0#.*(#$*0**/0*) QKKKM N NK */0*) */0*) .*4$) .*4$)5*. 5*. #$* #$* )4. )4. #*)$6 #*)$6 */)'/ */)'/
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- 33. #%'!:4%'6%'%78 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 QKKKM N NN ; 6,'*.'',0#/5$0#)#*,/*. 6,'*.$))7,0#5$0#(*.0#))#*,/
- 34.
- 35.
- 36.
- 37. $ .,#/.**' W /0570*.0(*'*()70#$)/ W ,03..'1*)/#$,/(*)*%0/ W)7$(,*.0)0,.*'(/),*//.,# *,1($81*),.*'(/5'.7)*5#*50*/*'4 ,0#C./0).0#C./0/.#.$(,*.0)0 '*.$0#(/ W )3/0*/*'4()7,.*'(/ QKKKM N NR
- 38. MIT OpenCourseWare https://ocw.mit.edu 6.0002 Introductionto Computational Thinking and Data Science Fall 2016 For information about citing these materials or our Terms of Use, visit: https://ocw.mit.edu/terms.