Postorder Traversal: Definition, Example, and Use Cases

Postorder traversal is a way to visit all nodes in a tree where you first visit the left subtree, then the right subtree, and finally the root node. It is commonly used in tree algorithms to process children before their parent nodes.

How It Works

Postorder traversal is like cleaning up a room by first putting away all the items on the left side, then the right side, and finally closing the door. In a tree, this means you visit the left child nodes first, then the right child nodes, and only after that do you visit the parent node.

This order ensures that you handle all the descendants of a node before the node itself. It is useful when you need to process or delete nodes starting from the bottom of the tree going upwards.

Example

This example shows postorder traversal on a simple binary tree using Python.

python

class Node:
    def __init__(self, value):
        self.value = value
        self.left = None
        self.right = None

def postorder_traversal(node):
    if node is None:
        return []
    return postorder_traversal(node.left) + postorder_traversal(node.right) + [node.value]

# Create tree:
#     1
#    / \
#   2   3
#  / \
# 4   5

root = Node(1)
root.left = Node(2)
root.right = Node(3)
root.left.left = Node(4)
root.left.right = Node(5)

result = postorder_traversal(root)
print(result)

Output

[4, 5, 2, 3, 1]

When to Use

Postorder traversal is useful when you need to process child nodes before their parent. For example, it is used in deleting trees because you remove children before the parent to avoid losing access. It is also used in expression trees to evaluate operations where operands come before the operator.

In real life, think of assembling or disassembling something where you must handle parts in a specific order, starting from the smallest pieces up to the whole.

Key Points

• Visits left subtree, then right subtree, then root node.
• Processes children before their parent.
• Commonly used in tree deletion and expression evaluation.
• Ensures bottom-up processing of nodes.

Key Takeaways

Postorder traversal visits left and right children before the parent node.

It is ideal for tasks that require processing or deleting child nodes first.

Common use cases include tree deletion and evaluating expression trees.

The traversal order is left subtree, right subtree, then root node.