Clone a given binary tree
The problem addressed clone of a given binary tree. A binary tree is a hierarchical data structure composed of nodes where each node has at most two children, referred to as the left child and the right child. Cloning a binary tree means creating a new tree with the same structure and values as the original tree, but the two trees should not share any memory locations. This is useful in various scenarios, such as preserving the original tree's state for future comparisons or modifications.
Problem Statement and Description
Given a binary tree, the goal is to create a clone of that tree, preserving its structure and values. Cloning should be done such that the original and cloned trees are separate entities. The challenge here is to traverse the original tree and create a corresponding clone of each node while maintaining the parent-child relationships.
Consider the following binary tree:
/ / \
3 6 10
The goal is to create a clone of this tree.
Idea to Solve
To solve this problem, your code employs a recursive approach. It traverses the original tree using a pre-order traversal (root-left-right) and constructs a clone of each node while mirroring the structure of the original tree.
Here's a high-level pseudocode representation of the algorithm:
properties: data, left, right
if node is not null
create new node called "point" with the same data as "node"
point.left = preorder(node.left)
point.right = preorder(node.right)
create a new BinaryTree called "tree"
tree.root = preorder(this.root)
create a new BinaryTree called "tree1"
// Construct tree1 here
create a new BinaryTree called "tree2"
tree2 = tree1.cloneTree()
// Modify tree2 if needed
// Display both trees
The algorithm starts by defining the
BinaryTree classes. The
preorder function is used to traverse the original tree in a pre-order manner. At each step, a new node
is created with the same data as the current node, and the function recursively constructs the left and right
subtrees of the clone.
cloneTree function initializes a new binary tree, clones the nodes of the original tree using the
preorder function, and returns the new tree.
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Resultant Output Explanation
The output of your program demonstrates the pre-order traversal of both the original and cloned trees. Initially,
the output shows that both trees are identical. However, when you modify the data of the root node in the cloned
tree2.root.data = 99), you can observe that the original tree remains unaffected, confirming that
the cloning process worked as intended.
The time complexity of the cloning algorithm is O(n), where n is the number of nodes in the binary tree. This is because each node is visited exactly once during the traversal, and constant-time operations are performed for each node.