Postorder Traversal of Binary Tree
Postorder traversal is defined as a type of tree traversal which follows the Left-Right-Root policy such that for each node:
- The left subtree is traversed first
- Then the right subtree is traversed
- Finally, the root node of the subtree is traversed
Algorithm for Postorder Traversal of Binary Tree:
The algorithm for postorder traversal is shown as follows:
- Follow step 2 to 4 until root != NULL
- Postorder (root -> left)
- Postorder (root -> right)
- Write root -> data
- End loop
How does Postorder Traversal of Binary Tree Work?
Consider the following tree:
If we perform a postorder traversal in this binary tree, then the traversal will be as follows:
Step 1: The traversal will go from 1 to its left subtree i.e., 2, then from 2 to its left subtree root, i.e., 4. Now 4 has no subtree, so it will be visited.
Step 2: As the left subtree of 2 is visited completely, now it will traverse the right subtree of 2 i.e., it will move to 5. As there is no subtree of 5, it will be visited.
Step 3: Now both the left and right subtrees of node 2 are visited. So now visit node 2 itself.
Step 4: As the left subtree of node 1 is traversed, it will now move to the right subtree root, i.e., 3. Node 3 does not have any left subtree, so it will traverse the right subtree i.e., 6. Node 6 has no subtree and so it is visited.
Step 5: All the subtrees of node 3 are traversed. So now node 3 is visited.
Step 6: As all the subtrees of node 1 are traversed, now it is time for node 1 to be visited and the traversal ends after that as the whole tree is traversed.
So the order of traversal of nodes is 4 -> 5 -> 2 -> 6 -> 3 -> 1.
Program to implement Postorder Traversal of Binary Tree
Below is the code implementation of the postorder traversal:
Postorder traversal of binary tree is: 4 5 2 6 3 1
Time Complexity: O(N) where N is the total number of nodes. Because it traverses all the nodes at least once.
Auxiliary Space: O(1) if no recursion stack space is considered. Otherwise, O(h) where h is the height of the tree
- In the worst case, h can be the same as N (when the tree is a skewed tree)
- In the best case, h can be the same as logN (when the tree is a complete tree)
Use cases of Postorder Traversal:
Some use cases of postorder traversal are:
- This is used for tree deletion.
- It is also useful to get the postfix expression from an expression tree.
- Types of Tree traversals
- Iterative Postorder traversal (using two stacks)
- Iterative Postorder traversal (using one stack)
- Postorder of Binary Tree without recursion and without stack
- Find Postorder traversal of BST from preorder traversal
- Morris traversal for Postorder
- Print postorder traversal from preoreder and inorder traversal
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