Post-order traversal

Programs that utilize tree structures need to process nodes in a tree (represented as circles in below diagram). Nodes contain information about an object. For now, let's assume each node contains a letter.

Post-order traversal is a type of tree traversal algorithm. Post-order occurs when the root is postponed until its two subtrees are processed.

Steps to post-order traversal

Given a non-empty tree,

1. Process the nodes in the left subtree with a recursive call
2. Process the nodes in the right subtree with a recursive call
3. Process the root

template 
int postorder_print(const binary_tree_nodes* ptr)
// ptr is a pointer to a node in a binary tree OR null
// meaning empty tree.
{
   if (ptr != NULL)
   {
       postorder_print( ptr->left() );
       postorder_print( ptr->right() );
       std::cout << ptr->data() << std::endl;
   }
   return 0;
}

data Tree a = ET | Node(a, Tree a, Tree a)

postorder :: Tree a -> [a]
postorder ET = []
postorder (Node (x, left,right)) = (postorder left) ++ (postorder right) ++ [x]