Trees/Postorder

Postorder traversal in trees

Postorder traversal is a depth-first recursive tree traversal algorithm that can be defined and applied recursively to Trees, very similar to Trees/Preorder (preorder traversal). Postorder is a bottom-up traversal, where the visit action is performed as the recursive functions return off the stack.

Recursive definition

As with any recursive method, this must be split into a base case and a recursive case. The base case is, we've reached an external node - no children. The recursive case is, we call preorder on each child. In this case we don't need an explicit base case and recursive case.

The postorder traversal is the patient, wait-and-see heuristic.

Here is an example of a postorder traversal pseudocode:

define public function postorder( tree )
    postorder_subtree( tree, root, 0 )

define private function postorder_subtree( tree, position, depth)
    for child in position.children():
        postorder_subtree(tree, child, depth+1)
    perform visit action on position

Because this is an intransitive recursive function - nothing is returned - the base case can remain implicit (if position is an external node, position.children is empty, and the for loop is not run, and an instance of the void recursive method returns).

Implementation

The implementation of postorder traversal is implemented in the linked binary tree class Binary Trees/LinkedBinTree using the following methods:

• A public method that takes no parameters, postorder(), returning an iterator over each node in postorder traversal order: https://git.charlesreid1.com/cs/java/src/master/trees/LinkedBinTree.java#L397
• A private method that takes two parameters, one position and one Collections object (a list) to store a list of items for the iterator to return back: https://git.charlesreid1.com/cs/java/src/master/trees/LinkedBinTree.java#L404

All the work is done by the second method. It is a recursive method that iterates over each child, recursively calling itself on each child, then adds the current node to the list when finished running on each child.

	/** Utility method for post-order tree traversal.  */
	private void postorderSubtree(Position<E> p, List<Position<E>> snapshot) { 
		// 1. Recurse through children
		for(Position<E> c : children(p)) {
			postorderSubtree(c,snapshot);
		}

		// 2. Perform visit action for Position p
		snapshot.add(p);
	}

Related Pages

Graphs:

• Graphs#Graph Traversals
• Graphs/Depth First Traversal
• Graphs/Breadth First Traversal
• Graphs/Euler Tour
• Graphs/Euler Circuit

Traversals on trees:

• Trees/Preorder
• Trees/Postorder
• Trees/Inorder

Breadth-first search and traversal on trees:

• BFS - breadth first search
• BFT - breadth first traversal

Depth-first search and traversal on trees:

• DFS - depth first search
• DFT - depth first traversal

OOP design patterns:

• Tree Traversal/Traversal Method Template

Category:Traversal