# Problem 3
def printexp(tree):
sVal = ""
if tree:
sVal = '(' + printexp(tree.getLeftChild())
sVal = sVal + str(tree.getRootVal())
sVal = sVal + printexp(tree.getRightChild())+')'
return sVal
#### Functions and classes to help with Homework 6
#### You should not make any changes to the functions and
classes in this file,
#### but you should understand what they do and how they work.
import sys
### This function will be re-defined in hw6.py. However, it is
needed for ExpTree,
### so it is redefined here as well. Do not modify this function,
modify the
### one in hw6.py!
def printexp(tree):
sVal = ""
if tree:
sVal = '(' + printexp(tree.getLeftChild())
sVal = sVal + str(tree.getRootVal())
sVal = sVal + printexp(tree.getRightChild())+')'
return sVal
class ExpTree:
def __init__(self,key):
self.key = key
self.leftChild = None
self.rightChild = None
def setRightChild(self, child):
self.rightChild = child
def setLeftChild(self, child):
self.leftChild = child
def getRightChild(self):
return self.rightChild
def getLeftChild(self):
return self.leftChild
def setRootVal(self,obj):
self.key = obj
def getRootVal(self):
return self.key
def __str__(self):
sVal = printexp(self)
return sVal
class Graph:
def __init__(self):
self.vertices = {}
self.numVertices = 0
def addVertex(self,key):
self.numVertices = self.numVertices + 1
newVertex = Vertex(key)
self.vertices[key] = newVertex
return newVertex
def getVertex(self,n):
if n in self.vertices:
return self.vertices[n]
else:
return None
def __contains__(self,n):
return n in self.vertices
def addEdge(self,f,t,cost=0):
if f not in self.vertices:
nv = self.addVertex(f)
if t not in self.vertices:
nv = self.addVertex(t)
self.vertices[f].addNeighbor(self.vertices[t],cost)
def getVertices(self):
return list(self.vertices.keys())
def __iter__(self):
return iter(self.vertices.values())
class Vertex:
def __init__(self,num):
self.id = num
self.connectedTo = {}
self.color = 'white'
self.dist = sys.maxsize
self.pred = None
self.disc = 0
self.fin = 0
# def __lt__(self,o):
# return self.id < o.id
def addNeighbor(self,nbr,weight=0):
self.connectedTo[nbr] = weight
def setColor(self,color):
self.color = color
def setDistance(self,d):
self.dist = d
def setPred(self,p):
self.pred = p
def setDiscovery(self,dtime):
self.disc = dtime
def setFinish(self,ftime):
self.fin = ftime
def getFinish(self):
return self.fin
def getDiscovery(self):
return self.disc
def getPred(self):
return self.pred
def getDistance(self):
return self.dist
def getColor(self):
return self.color
def getConnections(self):
return self.connectedTo.keys()
def getWeight(self,nbr):
return self.connectedTo[nbr]
def __str__(self):
return str(self.id) + ":color " + self.color + ":disc " +
str(self.disc) + ":fin " + str(self.fin) + ":dist " +
str(self.dist) + ":pred \n\t[" + str(self.pred)+ "]\n"
def getId(self):
return self.id
class PriorityQueue:
def __init__(self):
self.heapArray = [(0,0)]
self.currentSize = 0
def buildHeap(self,alist):
self.currentSize = len(alist)
self.heapArray = [(0,0)]
for i in alist:
self.heapArray.append(i)
i = len(alist) // 2
while (i > 0):
self.percDown(i)
i = i - 1
def percDown(self,i):
while (i * 2) <= self.currentSize:
mc = self.minChild(i)
if self.heapArray[i][0] > self.heapArray[mc][0]:
tmp = self.heapArray[i]
self.heapArray[i] = self.heapArray[mc]
self.heapArray[mc] = tmp
i = mc
def minChild(self,i):
if i*2 > self.currentSize:
return -1
else:
if i*2 + 1 > self.currentSize:
return i*2
else:
if self.heapArray[i*2][0] < self.heapArray[i*2+1][0]:
return i*2
else:
return i*2+1
def percUp(self,i):
while i // 2 > 0:
if self.heapArray[i][0] < self.heapArray[i//2][0]:
tmp = self.heapArray[i//2]
self.heapArray[i//2] = self.heapArray[i]
self.heapArray[i] = tmp
i = i//2
def add(self,k):
self.heapArray.append(k)
self.currentSize = self.currentSize + 1
self.percUp(self.currentSize)
def delMin(self):
retval = self.heapArray[1][1]
self.heapArray[1] = self.heapArray[self.currentSize]
self.currentSize = self.currentSize - 1
self.heapArray.pop()
self.percDown(1)
return retval
def isEmpty(self):
if self.currentSize == 0:
return True
else:
return False
def decreaseKey(self,val,amt):
# this is a little wierd, but we need to find the heap thing to
decrease by
# looking at its value
done = False
i = 1
myKey = 0
while not done and i <= self.currentSize:
if self.heapArray[i][1] == val:
done = True
myKey = i
else:
i = i + 1
if myKey > 0:
self.heapArray[myKey] = (amt,self.heapArray[myKey][1])
self.percUp(myKey)
def __contains__(self,vtx):
for pair in self.heapArray:
if pair[1] == vtx:
return True
return False
def dijkstra(aGraph,start):
pq = PriorityQueue()
start.setDistance(0)
pq.buildHeap([(v.getDistance(),v) for v in aGraph])
while not pq.isEmpty():
currentVert = pq.delMin()
for nextVert in currentVert.getConnections():
newDist = currentVert.getDistance() \
+ currentVert.getWeight(nextVert)
if newDist < nextVert.getDistance():
nextVert.setDistance( newDist )
nextVert.setPred(currentVert)
pq.decreaseKey(nextVert,newDist)
Explanation in code comment :
rest of the code is same, only the printexp is modified as asked
CODE :
# Problem 3
"""
def printexp(tree):
sVal = ""
if tree:
sVal = '(' + printexp(tree.getLeftChild())
sVal = sVal + str(tree.getRootVal())
sVal = sVal + printexp(tree.getRightChild())+')'
return sVal
"""
#### Functions and classes to help with Homework 6
#### You should not make any changes to the functions and classes
in this file,
#### but you should understand what they do and how they work.
import sys
### This function will be re-defined in hw6.py. However, it is
needed for ExpTree,
### so it is redefined here as well. Do not modify this function,
modify the
### one in hw6.py!
"""
EXPLANATION : Instead of adding braces whenever each node is
calculated , we only need to add braces
whenever an expression is being evaluated and after traversal of
left and right child
Hence by addding the condition of adding braces before and after
the evaulted expression
for a given tree only when non numeric data is encountered solves
the problem
EX : Simplify the tree for one root and 2 child nodes
*
/ \
2 5
the output would be (2*5)
Hence first left child call is made - sVal = 2
then again left and right call for node 2 are made and
returned
Then node data is added - sVal = 2*
then right child call is made - sVal = 2*5
then again left and right call for node 5 are made and
returned
then we add braces before and after sVal - (sVal) = (2*5)
"""
def printexp(tree):
sVal = ""
if tree:
sVal = printexp(tree.getLeftChild())
sVal = sVal + str(tree.getRootVal())
sVal = sVal + printexp(tree.getRightChild())
if not str(tree.getRootVal()).isnumeric():
sVal = '(' + sVal + ')'
return sVal
class ExpTree:
def __init__(self,key):
self.key = key
self.leftChild = None
self.rightChild = None
def setRightChild(self, child):
self.rightChild = child
def setLeftChild(self, child):
self.leftChild = child
def getRightChild(self):
return self.rightChild
def getLeftChild(self):
return self.leftChild
def setRootVal(self,obj):
self.key = obj
def getRootVal(self):
return self.key
def __str__(self):
sVal = printexp(self)
return sVal
class Graph:
def __init__(self):
self.vertices = {}
self.numVertices = 0
def addVertex(self,key):
self.numVertices = self.numVertices + 1
newVertex = Vertex(key)
self.vertices[key] = newVertex
return newVertex
def getVertex(self,n):
if n in self.vertices:
return self.vertices[n]
else:
return None
def __contains__(self,n):
return n in self.vertices
def addEdge(self,f,t,cost=0):
if f not in self.vertices:
nv = self.addVertex(f)
if t not in self.vertices:
nv = self.addVertex(t)
self.vertices[f].addNeighbor(self.vertices[t],cost)
def getVertices(self):
return list(self.vertices.keys())
def __iter__(self):
return iter(self.vertices.values())
class Vertex:
def __init__(self,num):
self.id = num
self.connectedTo = {}
self.color = 'white'
self.dist = sys.maxsize
self.pred = None
self.disc = 0
self.fin = 0
# def __lt__(self,o):
# return self.id < o.id
def addNeighbor(self,nbr,weight=0):
self.connectedTo[nbr] = weight
def setColor(self,color):
self.color = color
def setDistance(self,d):
self.dist = d
def setPred(self,p):
self.pred = p
def setDiscovery(self,dtime):
self.disc = dtime
def setFinish(self,ftime):
self.fin = ftime
def getFinish(self):
return self.fin
def getDiscovery(self):
return self.disc
def getPred(self):
return self.pred
def getDistance(self):
return self.dist
def getColor(self):
return self.color
def getConnections(self):
return self.connectedTo.keys()
def getWeight(self,nbr):
return self.connectedTo[nbr]
def __str__(self):
return str(self.id) + ":color " + self.color + ":disc " +
str(self.disc) + ":fin " + str(self.fin) + ":dist " +
str(self.dist) + ":pred \n\t[" + str(self.pred)+ "]\n"
def getId(self):
return self.id
class PriorityQueue:
def __init__(self):
self.heapArray = [(0,0)]
self.currentSize = 0
def buildHeap(self,alist):
self.currentSize = len(alist)
self.heapArray = [(0,0)]
for i in alist:
self.heapArray.append(i)
i = len(alist) // 2
while (i > 0):
self.percDown(i)
i = i - 1
def percDown(self,i):
while (i * 2) <= self.currentSize:
mc = self.minChild(i)
if self.heapArray[i][0] > self.heapArray[mc][0]:
tmp = self.heapArray[i]
self.heapArray[i] = self.heapArray[mc]
self.heapArray[mc] = tmp
i = mc
def minChild(self,i):
if i*2 > self.currentSize:
return -1
else:
if i*2 + 1 > self.currentSize:
return i*2
else:
if self.heapArray[i*2][0] < self.heapArray[i*2+1][0]:
return i*2
else:
return i*2+1
def percUp(self,i):
while i // 2 > 0:
if self.heapArray[i][0] < self.heapArray[i//2][0]:
tmp = self.heapArray[i//2]
self.heapArray[i//2] = self.heapArray[i]
self.heapArray[i] = tmp
i = i//2
def add(self,k):
self.heapArray.append(k)
self.currentSize = self.currentSize + 1
self.percUp(self.currentSize)
def delMin(self):
retval = self.heapArray[1][1]
self.heapArray[1] = self.heapArray[self.currentSize]
self.currentSize = self.currentSize - 1
self.heapArray.pop()
self.percDown(1)
return retval
def isEmpty(self):
if self.currentSize == 0:
return True
else:
return False
def decreaseKey(self,val,amt):
# this is a little wierd, but we need to find the heap thing to
decrease by
# looking at its value
done = False
i = 1
myKey = 0
while not done and i <= self.currentSize:
if self.heapArray[i][1] == val:
done = True
myKey = i
else:
i = i + 1
if myKey > 0:
self.heapArray[myKey] = (amt,self.heapArray[myKey][1])
self.percUp(myKey)
def __contains__(self,vtx):
for pair in self.heapArray:
if pair[1] == vtx:
return True
return False
def dijkstra(aGraph,start):
pq = PriorityQueue()
start.setDistance(0)
pq.buildHeap([(v.getDistance(),v) for v in aGraph])
while not pq.isEmpty():
currentVert = pq.delMin()
for nextVert in currentVert.getConnections():
newDist = currentVert.getDistance() \
+ currentVert.getWeight(nextVert)
if newDist < nextVert.getDistance():
nextVert.setDistance( newDist )
nextVert.setPred(currentVert)
pq.decreaseKey(nextVert,newDist)
rl2 = ExpTree(5)
rr2 = ExpTree(2)
rr1 = ExpTree('-')
ll3 = ExpTree(1)
lr3 = ExpTree(2)
lr2 = ExpTree('/')
ll2 = ExpTree(3)
ll1 = ExpTree('+')
r = ExpTree('*')
r.setLeftChild(ll1)
r.setRightChild(rr1)
ll1.setLeftChild(ll2)
ll1.setRightChild(lr2)
lr2.setLeftChild(ll3)
lr2.setRightChild(lr3)
rr1.setLeftChild(rl2)
rr1.setRightChild(rr2)
print(str(r))
# Problem 3 def printexp(tree): sVal = "" if tree: sVal = '(' + printexp(tree.getLeftChild()) sVal = sV...
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