Levelorder

Levelorder, or level-order traversal, is a method of visiting nodes in a tree or graph in order of increasing depth, beginning at a designated root node and proceeding level by level from top to bottom and left to right within each level. In trees, level-order is a form of breadth-first traversal.

Implementation typically relies on a queue. The root is enqueued; while the queue is not empty, a node is dequeued and processed, and its children are enqueued in a defined order. In binary trees, the left child is enqueued before the right child.

For graphs, the traversal is known as breadth-first search (BFS). To avoid visiting the same node multiple times, a set of visited nodes is maintained.

Complexity: Visiting n nodes requires O(n) time in a tree or graph. The space usage is O(w), where w is the maximum width of the structure; in the worst case, O(n).

Common uses include serializing and deserializing trees in level-order form, printing trees level by level, and computing shortest paths in unweighted graphs via BFS. Levelorder representations are also used in various programming tasks and interview problems that require processing nodes by level rather than by a depth-first pattern.

See also: breadth-first search, BFS, and other tree traversal orders such as pre-order, in-order, and post-order. Levelorder is a practical approach for problems where level-by-level information is important or where a shallow, wide exploration is desired.