Pre-order, In-order and Post-order Traversal

For a binary tree, pre-order processes the node, then the left subtree, then the right subtree. In-order processes left subtree, node, right subtree. Post-order processes left subtree, right subtree, node. An absent subtree contributes no visit.

These are recursive rules: “left subtree” means apply the whole same traversal there, not just visit its immediate root. A small tree with one node gives the same result for all three orders, so it is insufficient to distinguish whether a rule has been applied correctly.

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In-order traversal outputs keys in ascending order when the tree is a binary search tree under the stated ordering policy. An arbitrary binary tree does not become sorted simply because in-order traversal is used. The result follows from the combination of structure and algorithm.

Pre-order can record a parent before the structure below it, useful for some copying or serialisation tasks with sufficient structural information. Post-order handles children before their parent, useful for evaluating an expression tree or releasing child structures before a containing node.

Mark each recursive return point or write a small expansion for each subtree. This reduces the common error of switching from a depth-based rule to a breadth-based reading halfway through. For a proper tree, each node is processed once, giving O(V) total visits.

The call-stack depth follows the tree height, which can be logarithmic for a balanced tree or linear for a chain. A recursive implementation is concise but does not remove the need to consider an empty tree and resource limits. Distinguish the number of visits from the maximum simultaneous calls.

Attempt the task before opening its worked response. Record each change of state, explain the rule used, and check the result against the original requirements. Code examples labelled Python 3 use that language’s conventions; pseudocode states its own assumptions.