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"""
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Problem Statement: Given a binary perform an postorder traversal using Morris Postorder
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traversal algorithm. (Iterative version of Postorder traversal of tree)
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https://www.geeksforgeeks.org/morris-traversal-for-postorder/
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"""
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class TreeNode:
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"""
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Class representing a node in a binary tree.
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Attributes:
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-----------
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value : int
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The value stored at the node.
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left : TreeNode
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Pointer to the left child node (default is None).
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right : TreeNode
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Pointer to the right child node (default is None).
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"""
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def __init__(self, value: int) -> None:
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self.value = value
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self.left: TreeNode | None = None
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self.right: TreeNode | None = None
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class BinaryTree:
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"""
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Class representing a binary tree.
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Methods:
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--------
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insert(value: int) -> None:
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Insert a value into the binary tree following binary search tree (BST) rules.
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morris_postorder_traversal() -> List[int]:
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Perform postorder traversal and return list of node values.
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>>> bt = BinaryTree()
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>>> bt.insert(9)
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>>> bt.insert(6)
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>>> bt.insert(10)
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>>> bt.insert(3)
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>>> bt.insert(7)
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>>> bt.insert(12)
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>>> bt.insert(2)
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>>> bt.insert(5)
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>>> bt.insert(4)
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>>> bt.morris_postorder_traversal()
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[2, 4, 5, 3, 7, 6, 12, 10, 9]
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"""
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def __init__(self) -> None:
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self.root: TreeNode | None = None
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def insert(self, value: int) -> None:
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"""
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Insert a value into the binary tree.
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Parameters:
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-----------
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value : int
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The value to be inserted into the binary tree.
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"""
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if self.root is None:
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self.root = TreeNode(value)
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else:
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self._insert_recursive(self.root, value)
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def _insert_recursive(self, node: TreeNode, value: int) -> None:
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"""
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Helper function to insert a value recursively into the tree.
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Parameters:
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-----------
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node : TreeNode
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The current node in the binary tree.
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value : int
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The value to be inserted.
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"""
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if value < node.value:
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if node.left is None:
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node.left = TreeNode(value)
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else:
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self._insert_recursive(node.left, value)
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elif node.right is None:
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node.right = TreeNode(value)
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else:
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self._insert_recursive(node.right, value)
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def _successor(self, node: TreeNode) -> TreeNode:
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"""
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Helper Function to return successor of the given node in a binary tree
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Parameters:
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-----------
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node : TreeNode
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A node in the binary tree.
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Returns:
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--------
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TreeNode:
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The successor of the node passed in the parameter
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"""
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temp_node = node.right
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while temp_node and temp_node.left and temp_node.left != node:
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temp_node = temp_node.left
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assert temp_node is not None, "Successor should not be None"
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return temp_node
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def morris_postorder_traversal(self) -> list[int]:
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"""
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Function for postorder traversal using morris postorder traversal.
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Algorithm :
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------------
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First set current node as root node.
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while current node is not empty
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If the current node has no right child.
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push the current node to temp.
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point the current node to its left child
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else.
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find successor node of the current node.
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if successor left child points to current node,
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remove the link of the left child of successor node.
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point the current node to its left child.
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else,
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push the current node to temp.
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make the current node as the left child of the successor node.
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point current node to its right child.
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Reverse the temp array to get postorder traversaol.
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Returns:
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--------
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List[int]:
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A list of integers representing the postorder traversal.
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"""
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postorder_traversal = []
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current_node = self.root
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while current_node:
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if current_node.right is None:
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postorder_traversal.append(current_node.value)
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current_node = current_node.left
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else:
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successor_node = self._successor(current_node)
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if successor_node.left == current_node:
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successor_node.left = current_node
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current_node = current_node.left
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else:
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postorder_traversal.append(current_node.value)
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successor_node.left = current_node
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current_node = current_node.right
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return postorder_traversal[::-1]
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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