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# determine if two trees are identical
# binary tree node has data, pointer to left child and a pointer to right child
class Node:
# Constructor to create a new node
def __init__(self, data):
self.data = data
self.left = None
self.right = None
def identicalTrees(a, b):
# 1. Both empty
if a is None and b is None:
return True
# 2. Both non-empty -> Compare them
if a is not None and b is not None:
return ((a.data == b.data) and
identicalTrees(a.left, b.left)and
identicalTrees(a.right, b.right))
# 3. one empty, one not -- false
return False
# Driver program to test identicalTress function
root1 = Node(1)
root2 = Node(1)
root1.left = Node(2)
root1.right = Node(3)
root1.left.left = Node(4)
root1.left.right = Node(5)
root2.left = Node(2)
root2.right = Node(3)
root2.left.left = Node(4)
root2.left.right = Node(5)
if identicalTrees(root1, root2):
print "Both trees are identical"
else:
print "Trees are not identical"
### Check if binary tree is binary search tree
# --------------------------------------------
class TreeNode:
def __init__(self, value):
self.value = value
self.left = None
self.right = None
def is_binary_search_tree(root):
def in_order_traversal(node, prev):
if node is None:
return True
# Recursively check the left subtree
if not in_order_traversal(node.left, prev):
return False
# Check if the current node's value is greater than the previous node's value
if node.value <= prev[0]:
return False
prev[0] = node.value # Update the previous value
# Recursively check the right subtree
return in_order_traversal(node.right, prev)
prev = [float('-inf')] # Initialize the previous value to negative infinity
return in_order_traversal(root, prev)
# Example usage
if __name__ == "__main__":
root = TreeNode(2)
root.left = TreeNode(1)
root.right = TreeNode(3)
if is_binary_search_tree(root):
print("The binary tree is a Binary Search Tree (BST).")
else:
print("The binary tree is not a BST.")
### Post order without recursion using 2 stacks
# ---------------------------------------------
class TreeNode:
def __init__(self, value):
self.value = value
self.left = None
self.right = None
def post_order_traversal(root):
if root is None:
return []
result = []
stack1 = [root]
stack2 = []
while stack1:
node = stack1.pop()
stack2.append(node)
if node.left:
stack1.append(node.left)
if node.right:
stack1.append(node.right)
while stack2:
node = stack2.pop()
result.append(node.value)
return result
# Example usage
if __name__ == "__main__":
root = TreeNode(1)
root.left = TreeNode(2)
root.right = TreeNode(3)
root.left.left = TreeNode(4)
root.left.right = TreeNode(5)
result = post_order_traversal(root)
print("Post-order traversal:", result)
### In order traversal without recursion using stack
# ---------------------------------------------------
class TreeNode:
def __init__(self, value):
self.value = value
self.left = None
self.right = None
def in_order_traversal(root):
if root is None:
return []
result = []
stack = []
current = root
while stack or current:
if current:
stack.append(current)
current = current.left
else:
current = stack.pop()
result.append(current.value)
current = current.right
return result
# Example usage
if __name__ == "__main__":
root = TreeNode(1)
root.left = TreeNode(2)
root.right = TreeNode(3)
root.left.left = TreeNode(4)
root.left.right = TreeNode(5)
result = in_order_traversal(root)
print("In-order traversal:", result)
### Preorder traversal without recursion - using stack
#-----------------------------------------------------
class TreeNode:
def __init__(self, value):
self.value = value
self.left = None
self.right = None
def depth_first_traversal(root):
if root is None:
return []
result = []
stack = [root]
while stack:
node = stack.pop()
result.append(node.value)
# Push the right child first to ensure left child is processed first (LIFO)
if node.right:
stack.append(node.right)
if node.left:
stack.append(node.left)
return result
# Example usage
if __name__ == "__main__":
root = TreeNode(1)
root.left = TreeNode(2)
root.right = TreeNode(3)
root.left.left = TreeNode(4)
root.left.right = TreeNode(5)
result = depth_first_traversal(root)
print("Depth-first traversal (pre-order):", result)
### Breadth first (LeVeL order) without recursion using queue
# -----------------------------------------------------------
class TreeNode:
def __init__(self, value):
self.value = value
self.left = None
self.right = None
def level_order_traversal(root):
if root is None:
return []
result = []
queue = [root]
while queue:
node = queue.pop(0)
result.append(node.value)
if node.left:
queue.append(node.left)
if node.right:
queue.append(node.right)
return result
# Example usage
if __name__ == "__main__":
root = TreeNode(1)
root.left = TreeNode(2)
root.right = TreeNode(3)
root.left.left = TreeNode(4)
root.left.right = TreeNode(5)
result = level_order_traversal(root)
print("Level-order traversal:", result)
########################
### Diameter of binary tree
#----------------------------
class TreeNode:
def __init__(self, value):
self.value = value
self.left = None
self.right = None
class Result:
def __init__(self):
self.diameter = 0
def tree_diameter(root, result):
if root is None:
return 0
left_height = tree_diameter(root.left, result)
right_height = tree_diameter(root.right, result)
# Calculate the diameter passing through the current node
diameter_through_node = left_height + right_height
# Update the maximum diameter found so far
result.diameter = max(result.diameter, diameter_through_node)
# Return the height of the subtree rooted at the current node
return 1 + max(left_height, right_height)
def tree_max_diameter(root):
result = Result()
tree_diameter(root, result)
return result.diameter
# Example usage
if __name__ == "__main__":
root = TreeNode(1)
root.left = TreeNode(2)
root.right = TreeNode(3)
root.left.left = TreeNode(4)
root.left.right = TreeNode(5)
max_diameter = tree_max_diameter(root)
print("Maximum distance between any two nodes (diameter) of the binary tree is:", max_diameter)
### Height of binary tree
class TreeNode:
def __init__(self, value):
self.value = value
self.left = None
self.right = None
def tree_height(root):
if root is None:
return -1 # Height of an empty tree is -1
left_height = tree_height(root.left)
right_height = tree_height(root.right)
return 1 + max(left_height, right_height)
# Example usage
if __name__ == "__main__":
root = TreeNode(1)
root.left = TreeNode(2)
root.right = TreeNode(3)
root.left.left = TreeNode(4)
root.left.right = TreeNode(5)
height = tree_height(root)
print("Height of the binary tree is:", height)
## Least common accessor of 2 nodes (p,q) in binary tree
class TreeNode:
def __init__(self, val):
self.val = val
self.left = None
self.right = None
def findLCA(root, p, q):
if root is None:
return None
if root.val == p or root.val == q:
return root
left_lca = findLCA(root.left, p, q)
right_lca = findLCA(root.right, p, q)
if left_lca and right_lca:
return root
return left_lca if left_lca else right_lca
# Helper function to check if a node with a given value exists in the tree
def nodeExists(root, value):
if root is None:
return False
if root.val == value:
return True
return nodeExists(root.left, value) or nodeExists(root.right, value)
# Example usage
if __name__ == "__main__":
root = TreeNode(3)
root.left = TreeNode(5)
root.right = TreeNode(1)
root.left.left = TreeNode(6)
root.left.right = TreeNode(2)
root.right.left = TreeNode(0)
root.right.right = TreeNode(8)
root.left.right.left = TreeNode(7)
root.left.right.right = TreeNode(4)
p = 5
q = 1
if nodeExists(root, p) and nodeExists(root, q):
lca = findLCA(root, p, q)
print("Least Common Ancestor of {} and {} is {}".format(p, q, lca.val))
else:
print("Nodes {} and/or {} do not exist in the tree.".format(p, q))