class BinaryTree:
def __init__(self, root):
self.root = root
self.leftChild = None
self.rightChild = None
def setRoot(self, root):
self.root = root
def getRoot(self):
return self.root
def getLeftChild(self):
return self.leftChild
def getRightChild(self):
return self.rightChild
def insertLeftChild(self, newNode):
if self.leftChild == None:
self.leftChild = BinaryTree(newNode)
else:
t = BinaryTree(newNode)
t.leftChild = self.leftChild
self.leftChild = t
def insertRightChild(self, newNode):
if self.rightChild == None:
self.rightChild = BinaryTree(newNode)
else:
t = BinaryTree(newNode)
t.rightChild = self.rightChild
self.rightChild = t
'''Recursive method for searching an element in a tree'''
def searchingElementRecursive(tree,element):
if tree == None:
return False
else:
if tree.root == element:
return True
else:
temp = searchingElementRecursive(tree.leftChild,element)
if temp != 0:
return temp
else:
return searchingElementRecursive(tree.rightChild,element)
'''Iterative method for searching an element in a tree'''
def searchingElementIterative(tree,element):
queue = []
# current = tree
queue.append(tree)
if tree == None:
return False
while (queue != []):
temp = queue.pop(0)
if temp.root == element:
return True
if temp.getLeftChild():
queue.append(temp.getLeftChild())
if temp.getRightChild():
queue.append(temp.getRightChild())
return False
if __name__ == "__main__":
r = BinaryTree(5)
r.insertLeftChild(6)
r.insertRightChild(7)
r.leftChild.insertLeftChild(12)
r.leftChild.insertRightChild(54)
r.rightChild.insertRightChild(63)
print "Search for element 63", searchingElementRecursive(r,63)
print "\n\n"
print "Search for element 36", searchingElementRecursive(r,36)
print "\n\n"
print "Search for element 63", searchingElementIterative(r,63)
print "\n\n"
print "Search for element 36", searchingElementIterative(r,36)
print "\n\n"
Category Archives: Data Structures and Algorithms
Maximum Element in A Binary Tree
class BinaryTree:
def __init__(self, root):
self.root = root
self.leftChild = None
self.rightChild = None
def setRoot(self, root):
self.root = root
def getRoot(self):
return self.root
def getLeftChild(self):
return self.leftChild
def getRightChild(self):
return self.rightChild
def insertLeftChild(self, newNode):
if self.leftChild == None:
self.leftChild = BinaryTree(newNode)
else:
t = BinaryTree(newNode)
t.leftChild = self.leftChild
self.leftChild = t
def insertRightChild(self, newNode):
if self.rightChild == None:
self.rightChild = BinaryTree(newNode)
else:
t = BinaryTree(newNode)
t.rightChild = self.rightChild
self.rightChild = t
'''recursive way to find the maximum element of a tree'''
def maximumElement(tree):
max = 0
if tree == None:
return
else:
rootValue = tree.root
left = maximumElement(tree.leftChild)
right = maximumElement(tree.rightChild)
if left > right:
max = left
else:
max = right
if rootValue > max:
max = rootValue
return max
'''iterative way to find the maximum element of a tree'''
def maximumElementIterative(tree):
queue = []
current = tree
max = 0
queue.append(tree)
if tree == None:
return 0
else:
while (queue != []):
temp = queue.pop(0)
if max <= temp.root:
max = temp.root
if temp.getLeftChild():
queue.append(temp.getLeftChild())
if temp.getRightChild():
queue.append(temp.getRightChild())
return max
if __name__ == "__main__":
r = BinaryTree(5)
r.insertLeftChild(6)
r.insertRightChild(7)
r.leftChild.insertLeftChild(12)
r.leftChild.insertRightChild(54)
r.rightChild.insertRightChild(63)
print "The maximum element in the tree recursively is:", maximumElement(r)
print "\n\n"
print "The maximum element in the tree iteratively is:", maximumElementIterative(r)
print "\n\n"
Breadth First and Depth First Traversal
Here is the graph that has to be traversed:
'''graph representation'''
graph = {1:[2,3], 2:[4,5], 3:[6], 4:None, 5:[7,8], 6:None, 7:None, 8:None}
def breadthFirstTraversal(graph,start):
visited = []
tobevisited = [start]
while len(tobevisited) > 0:
currentNode = tobevisited.pop(0)
if currentNode not in visited:
visited += [currentNode]
if graph[currentNode] is not None:
tobevisited = tobevisited + graph[currentNode]
return visited
print breadthFirstTraversal(graph,1)
'''Output: [1, 2, 3, 4, 5, 6, 7, 8]'''
def depthFirstTraversal(graph,start):
visited = []
tobevisited = [start]
while len(tobevisited) > 0:
currentNode = tobevisited.pop(0)
if currentNode not in visited:
visited += [currentNode]
if graph[currentNode] is not None:
tobevisited = graph[currentNode] + tobevisited
return visited
print depthFirstTraversal(graph,1)
'''Output: [1, 2, 4, 5, 7, 8, 3, 6]'''
Quick Sort
Have a look at this video and learn quick sort with Hungarian Folk Dance.
Here is another very good video that illustrates quick sort.
Here are some different ways of implementing quick sort in Python.
import random
from random import randrange
mylist = [3,0,1,8,7,2,5,4,9,6]
def qsort1(mylist):
if mylist == []:
return []
else:
pivot = mylist[0]
lesser = qsort1([x for x in mylist[1:] if x < pivot])
greater = qsort1([x for x in mylist[1:] if x >= pivot])
return lesser + [pivot] + greater
print qsort1(mylist)
def partition(mylist, l, e, g):
while mylist != []:
head = mylist.pop(0)
if head < e[0]:
l = [head] + l
if head > e[0]:
g = [head]+ g
if head == e[0]:
e = [head] + e
return (l,e,g)
def qsort2(mylist):
if mylist == []:
return []
else:
pivot = mylist[0]
lesser,equal,greater = partition(mylist[1:],[],list([pivot]),[])
return qsort2(lesser)+equal+qsort2(greater)
print qsort2(mylist)
This one works for any randomly chosen pivot element.
def qsort1a(list):
def qsort(list):
if list == []:
return []
else:
pivot = list.pop(randrange(len(list)))
lesser = qsort([l for l in list if l < pivot])
greater = qsort([l for l in list if l >= pivot])
return lesser + [pivot] + greater
return qsort(list[:])
print qsort1a(mylist)
Merge Sort
Learn Merge Sort with Transylvanian Saxon and German Folk dance:
The python code for Merge Sort is as follows:
mylist = [4,2,8,6,0,5,1,7,3,9]
def merge(left, right):
mergedList = []
i, j = 0, 0
while i < len(left) and j < len(right):
if left[i] <= right[j]:
mergedList.append(left[i])
i += 1
else:
mergedList.append(right[j])
j += 1
mergedList += left[i:]
mergedList += right[j:]
return mergedList
def mergesort(lst):
if len(lst) <=1:
return lst
else:
middle = int(len(lst)/2)
left = mergesort(lst[:middle])
right = mergesort(lst[middle:])
return merge(left,right)
print mergesort(mylist)
Insertion Sort and Shell Sort – the two brothers
A good explanation of insertion sort can be found over here:
I personally like this video a lot:
itemList = [4,28,56,3,89,90,126]
def insertion_sort(itemList):
for i in range(1,len(itemList)):
value = itemList[i]
j = i
while (j-1 >= 0 and value < itemList[j-1]):
itemList[j]=itemList[j-1]
j-=1
itemList[j] = value
return itemList
print insertion_sort(itemList)
You can find a similar video for shell sort:
def shell_sort(itemList):
gap = len(itemList)//2
while (gap > 0):
for i in range(gap,len(itemList)):
value = itemList[i]
j = i
while (j-gap >= 0 and value < itemList[j-gap]):
itemList[j] = itemList[j-gap]
j -= gap
itemList[j] = value
gap //= 2
return itemList
print shell_sort(itemList)
Count Sort
A very good explanation of Count Sort is provided by Saurabh over here:
I tried to implement it in the simplest possible way in python.
arr = [1,2,4,5,7,7,8,9,11,13,11,9,14,15,6,5,4,3,2,1,1,0,0,1]
def countSort(arr):
maxValue = max(arr)+1
print maxValue
count = [0]*maxValue
for entries in arr:
count[entries] += 1
sortedarray = []
for i in range(len(count)):
sortedarray += [i]*count[i]
return sortedarray
Preorder Traversal of Binary Tree
Here is the code for iterative preorder traversal of binary trees.
'''class implementing binary tree'''
'''Binary Tree Class and its methods'''
class BinaryTree:
def __init__(self, root):
self.root = root #root node
self.leftChild = None #left child
self.rightChild = None #right child
#set root node
def setRoot(self, root):
self.root = root
#get root node
def getRoot(self):
return self.root
#get left child of a node
def getLeftChild(self):
return self.leftChild
#get right child of a node
def getRightChild(self):
return self.rightChild
#insert a left child of a node
def insertLeftChild(self, newNode):
if self.leftChild == None:
self.leftChild = BinaryTree(newNode)
else:
t = BinaryTree(newNode)
t.leftChild = self.leftChild
self.leftChild = t
#insert a right child of a node
def insertRightChild(self, newNode):
if self.rightChild == None:
self.rightChild = BinaryTree(newNode)
else:
t = BinaryTree(newNode)
t.rightChild = self.rightChild
self.rightChild = t
#recursive function for inorder traversal of binary tree
def preOrderTraversalRecursive(tree):
if tree == None:
return
else:
print tree.root
preOrderTraversal(tree.leftChild)
preOrderTraversal(tree.rightChild)
#iterative function for inorder traversal of binary tree
def preOrderTraversalIterative(tree)
stack = []
if tree == None:
return
stack.append(tree)
while(stack != []):
node = stack.pop()
print node.root
if node.getRightChild():
stack.append(node.getRightChild())
if node.getLeftChild():
stack.append(node.getLeftChild())
if __name__ == "__main__":
r = BinaryTree(5)
r.insertLeftChild(6)
r.insertRightChild(7)
r.leftChild.insertLeftChild(12)
r.leftChild.insertRightChild(54)
r.rightChild.insertRightChild(63)
print "Preorder traversal of tree recursively is:", preOrderTraversalRecursive(r)
print "\n\n"
print "Preorder traversal of the tree iteratively is:", preOrderTraversalIterative(r)
print "\n\n"
Inorder Traversal Of Binary Tree
Although recursion is a very easy way of traversing through Binary Tree but it can easily cause memory problems. The iterative solution can be handy in such cases. A very good explanation of iterative inorder traversal of Binary Tree can be found in the following video produced by Saurabh.
I have implemented using python.
'''Binary Tree Class and its methods'''
class BinaryTree:
def __init__(self, root):
self.root = root #root node
self.leftChild = None #left child
self.rightChild = None #right child
#set root node
def setRoot(self, root):
self.root = root
#get root node
def getRoot(self):
return self.root
#get left child of a node
def getLeftChild(self):
return self.leftChild
#get right child of a node
def getRightChild(self):
return self.rightChild
#insert a left child of a node
def insertLeftChild(self, newNode):
if self.leftChild == None:
self.leftChild = BinaryTree(newNode)
else:
t = BinaryTree(newNode)
t.leftChild = self.leftChild
self.leftChild = t
#insert a right child of a node
def insertRightChild(self, newNode):
if self.rightChild == None:
self.rightChild = BinaryTree(newNode)
else:
t = BinaryTree(newNode)
t.rightChild = self.rightChild
self.rightChild = t
#recursive function for inorder traversal of binary tree
def inOrderTraversalRecursive(tree):
if tree == None:
return
else:
inOrderTraversal(tree.leftChild)
print tree.root
inOrderTraversal(tree.rightChild
#iterative function for inorder traversal of binary tree
def inOrderTraversalIterative(tree)
current = tree
stack = []
done = True
while(done):
if current:
stack.append(current)
current = current.getLeftChild()
else:
if stack == []:
done = True
else:
current = stack.pop()
print current.root
current = current.getRightChild()
if __name__ == "__main__":
r = BinaryTree(5)
r.insertLeftChild(6)
r.insertRightChild(7)
r.leftChild.insertLeftChild(12)
r.leftChild.insertRightChild(54)
r.rightChild.insertRightChild(63)
print "Inorder traversal of tree recursively is:", inOrderTraversalRecursive(r)
print "\n\n"
print "Inorder traversal of the tree iteratively is:", inOrderTraversalIterative(r)
print "\n\n"
Detecting Cycles in Linked List (Hare and Tortoise)
The problem is as follows:
Check whether the given linked list is NULL terminated or ends in a cycle.
Sample Input: 1->2->3->4->5->6->7->8->3
where the numbers 1,2… are the positions in the linked list instead of actual entries.
The node at the 8th position again points to the node at the 3rd position forming a cycle.
Sample Output: True
A very good discussion of how the cycles are detected can be found in wikipedia over here:http://en.wikipedia.org/wiki/Cycle_detection
The Floyds’ algorithm commonly referred as tortoise and hare method is often used for detecting cycles. It could be an interesting read.
We can think of a hare and a tortoise running on a track. The faster running hare will catch up with the tortoise if they are running in a loop.
The basic algorithm is as follows:
Step 1. Start Tortoise and Hare at the first node of the List.
Step 2. If Hare reaches end of the List, return as there is no loop in the list.
Else move Hare one step forward.
Step 3. If Hare reaches end of the List, return as there is no loop in the list.
Else move Hare and Tortoise one step forward.
Step 4. If Hare and Tortoise pointing to same Node return, we found loop in the List.
Else start with STEP-2.
'''Complexity
Space : O(n) Time: O(1)'''
class Node:
def __init__(self,data):
self.data = data
self.next = None
def setData(self,data):
self.data = data
def getData(self):
return self.data
def setNext(self, next):
self.next = next
def getNext(self):
return self.next
class LinkedList:
def __init__(self):
self.head = None
def isEmpty(self):
return self.head == None
def insertAtBeg(self,item):
node = Node(item)
node.setNext(self.head)
self.head = node
def length(self):
current = self.head
count = 0
while current != None:
count += 1
current = current.getNext()
return count
def search(self,item):
found = False
current = self.head
while current != None and not found:
if current.getData() == item:
found = True
else:
current = current.getNext()
return found
def insertAtEnd(self,item):
current = self.head
while current.getNext() != None:
current = current.getNext()
node = Node(item)
current.setNext(node)
def insertBeforeItem(self,inItem,item):
current = self.head
previous = None
found = False
stop = False
while current != None and not found and not stop:
if current.getData() == item:
found = True
stop = True
else:
previous = current
current = current.getNext()
node = Node(inItem)
previous.setNext(node)
node.setNext(current)
def insertAfterItem(self,inItem,item):
current = self.head
found = False
stop = False
while current != None and not found and not stop:
if current.getData() == item:
found = True
stop = True
else:
# previous = current
current = current.getNext()
successor = current.getNext()
node = Node(inItem)
current.setNext(node)
node.setNext(successor)
def printList(self):
current = self.head
while current != None:
print current.getData()
current = current.getNext()
def remove(self,item):
found = False
current = self.head
previous = None
while current.getNext() != None and not found:
if current.getData() == item:
print current.getData()
print previous.getData()
found = True
previous.setNext(current.next)
else:
previous = current
current = current.getNext()
def induceCycle(self,end,start):
current = self.head
stop = False
endnodeFound = False
endnodePointer = None
count = 0
while current!= None and not stop:
count += 1
if count == end:
endnodeFound = True
endnodePointer = current.getNext()
else:
if count == start:
stop = True
else:
current = current.getNext()
current.setNext(endnodePointer)
def detectCycle(self):
hare = self.head
tortoise = self.head
while (hare and tortoise):
hare = hare.getNext()
if (hare == tortoise):
return True
if hare == None:
return False
hare = hare.getNext()
if (hare == tortoise):
return True
tortoise = tortoise.getNext()
if __name__ == "__main__":
ll = LinkedList()
ll.insertAtBeg(1)
ll.insertAtBeg(2)
ll.insertAtEnd(3)
ll.insertBeforeItem(4, 3)
ll.insertAfterItem(5, 1)
ll.insertAtEnd(6)
ll.insertAtEnd(8)
ll.insertAtEnd(7)
ll.printList()
ll.induceCycle(2, 8)
print ll.detectCycle()
codeatsociallywired 