Binary Tree Traversals: Preorder, Inorder, Postorder

This exercise builds on Binary Tree Basics and adds the three classic ways to visit every node in a binary tree: preorder, inorder, and postorder traversal. All three reuse the same Node<T> / BinTree<T> classes and the same 12-node sample tree from that exercise.

Traversal orders

• Preorder -- visit the node itself, then its left subtree, then its right subtree (root, left, right).
• Inorder -- visit the left subtree, then the node itself, then the right subtree (left, root, right). For a binary search tree, this visits values in sorted order.
• Postorder -- visit the left subtree, then the right subtree, then the node itself (left, right, root).

Each is naturally recursive: at every node, recurse into the children in the right order and visit ("print") the node itself at the right point relative to those two recursive calls.

private void preOrder(Node<T> node) {
    if (node != null) {
        System.out.printf(node.data + ", ");
        preOrder(node.left);
        preOrder(node.right);
    }
}

private void inOrder(Node<T> node) {
    if (node != null) {
        inOrder(node.left);
        System.out.printf(node.data + ", ");
        inOrder(node.right);
    }
}

private void postOrder(Node<T> node) {
    if (node != null) {
        postOrder(node.left);
        postOrder(node.right);
        System.out.printf(node.data + ", ");
    }
}

The sample tree

1
|- left: 2
|    |- left: 4
|    |    `- left: 8
|    `- right: 5
|         `- left: 9
`- right: 3
     |- left: 6
     `- right: 7
          |- left: 10
          `- right: 11
               `- right: 12

See the Solutions tab for the full Java implementation, including the sample tree's getTree() helper.

This is a foundational exercise -- there are no graded test cases for it, since the traversals print rather than return a value. The three outputs below (verified by hand against the tree above) serve as worked examples instead.