# Searching an 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 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"
```

# 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}

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

'''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 != []:

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.

```'''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

def __init__(self):

def isEmpty(self):

def insertAtBeg(self,item):
node = Node(item)

def length(self):
count = 0
while current != None:
count += 1
current = current.getNext()
return count

def search(self,item):
found = False
if current.getData() == item:
found = True
else:
current = current.getNext()

return found

def insertAtEnd(self,item):

while current.getNext() != None:
current = current.getNext()

node = Node(item)
current.setNext(node)

def insertBeforeItem(self,inItem,item):
previous = None
found = False
stop = False

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):

found = False
stop = False

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):

while current != None:
print current.getData()
current = current.getNext()

def remove(self,item):
found = False
previous = None

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):
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):

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.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()
```