### Learn How to Construct Binary Trees with Postorder and Inorder

Table of Contents:

- Introduction
- Understanding Post Order Traversal
- Understanding In Order Traversal
- Finding the Root of the Binary Tree
- Constructing the Left Subtree
- Constructing the Right Subtree
- Verifying the Binary Tree
- Conclusion

Article:

# Understanding Post Order Traversal

Post order traversal is a method used to traverse a binary tree where the root node is visited after its left and right subtrees have been visited. The traversal is done in a "left-right-root" order. This means that for a given node, its left subtree is visited first, followed by its right subtree, and finally the node itself.

# Understanding In Order Traversal

In order traversal, on the other hand, is a method used to traverse a binary tree where the root node is visited between its left and right subtrees. The traversal is done in a "left-root-right" order. This means that for a given node, its left subtree is visited first, followed by the node itself, and finally its right subtree.

# Finding the Root of the Binary Tree

To construct a binary tree from its post order and in order traversals, we first need to find the root of the tree. From the post order traversal, we can easily identify the root as it is always the last element in the traversal.

# Constructing the Left Subtree

Once we have identified the root, we can use the in order traversal to find the elements in the left subtree. To do this, we locate the root element in the in order traversal and all elements to its left will belong to the left subtree. We then use the post order traversal to determine the root of the left subtree, which is the first element encountered when scanning the traversal from right to left.

# Constructing the Right Subtree

Similarly, we can use the in order traversal to find the elements in the right subtree. We locate the root element in the in order traversal and all elements to its right will belong to the right subtree. Again, we use the post order traversal to determine the root of the right subtree, which is the first element encountered when scanning the traversal from right to left.

# Verifying the Binary Tree

To verify if the constructed binary tree is correct, we can compare its post order and in order traversals with the given traversals. If the traversals match, then we can conclude that the binary tree has been correctly constructed.

# Conclusion

In conclusion, constructing a binary tree from its post order and in order traversals involves finding the root and then constructing the left and right subtrees. By using the post order and in order traversals, we can accurately build the binary tree. Verification can be done by comparing the traversals of the constructed binary tree with the given traversals.

Pros:

- Allows for the reconstruction of a binary tree from its traversals
- Helps understand the relationship between post order and in order traversals
- Useful in various applications such as binary tree analysis and manipulation

Cons:

- Requires both post order and in order traversals of the binary tree
- May be complex for larger binary trees with many nodes

Highlights:

- Understanding post order and in order traversals in binary trees
- Finding the root and constructing the left and right subtrees
- Verifying the constructed binary tree with the given traversals

FAQ:

Q: Can any binary tree be reconstructed from its post order and in order traversals?
A: Yes, any binary tree can be reconstructed using these traversals as long as the traversals are valid and accurately represent the tree structure.

Q: What happens if the post order and in order traversals do not match?
A: If the traversals do not match, it indicates that there is an error in the reconstruction of the binary tree or that the given traversals are incorrect.

Q: Are there any limitations to using post order and in order traversals for constructing binary trees?
A: One limitation is that both traversals must be available. Additionally, reconstructing larger binary trees with many nodes may be complex and time-consuming.