Trees are a fundamental data structure in computer science, and their traversal is a common operation in many algorithms. There are several ways to traverse a tree, each with its own advantages and disadvantages. One of the most straightforward and widely used tree traversals is the level-order traversal. In this article, we will take a closer look at what level-order traversal is, how it works, and when it can be useful.

What is Level-Order Traversal?

Level-order traversal is a type of tree traversal algorithm that visits the nodes of a tree by level. This means that all the nodes at the same depth are visited before moving on to the next level.

In other words, the tree is traversed level-by-level from top to bottom, and the nodes are processed in a breadth-first manner. This is in contrast to other tree traversals, such as in-order and post-order traversals, which process nodes in a depth-first manner.

How Does it Work?

Level-order traversal is implemented using a queue. The process starts by adding the root node to the queue.

Then, for each node in the queue, its children (if any) are added to the queue. This process is repeated until the queue is empty, at which point the level-order traversal is complete.

The key idea behind level-order traversal is that it visits all the nodes at a given level before moving on to the next level. This is achieved by using a queue to store the nodes that need to be processed.

As the algorithm processes each node, its children are added to the end of the queue. This ensures that all the nodes at a given level are processed before any nodes at the next level are processed.

lets implement the level-order traversal

abstract class Tree<T> {
  int _height(Node<T> node);
  void _levelOrderTraversal(Node<T>? node);
} 

  void levelOrderTraversal() {
    _levelOrderTraversal(root);
  }

@override
  void _levelOrderTraversal(Node<T>? node) {
    if (root == null) {
      return;
    }
    var queue = Queue<Node<T>>();
    while (queue.isNotEmpty) {
      var node = queue.removeFirst();
      print(node.data);
      if (node.left != null) {
        queue.add(node.left!);
      } else if (node.right != null) {
        queue.add(node.right!);
      }
    }
  }

int height() {
    return _height(root);
  }

// if we want calculate the height
@override
  int _height(Node<T>? node) {
    if (node == null) {
      return 0;
    } else {
      int lheight = _height(node.left);
      int rheight = _height(node.right);
      if (lheight > rheight) {
        return lheight + 1;
      } else {
        return rheight + 1;
      }
    }
  }

For full code: the https://sumanmanna.hashnode.dev/binary-treet-implementation-using-dart

This is a function that performs a level-order traversal of a binary tree represented by a generic type Node<T> object. The function uses a queue to store the nodes as they are visited. The function starts by checking if the root node is null, in which case it returns immediately.

If the root node is not null, the function initializes an empty queue and enters a while loop that continues as long as the queue is not empty. In each iteration of the loop, the first node in the queue is removed and its data is printed.

The left and right children of the current node are then added to the queue if they are not null.

When is Level-Order Traversal Useful?

Level-order traversal is useful in a variety of situations. Some of the most common use cases include:

• Printing the nodes of a tree in level-order: This is a simple and straightforward way to print all the nodes in a tree.

• Computing the height of a tree: The height of a tree can be computed by counting the number of levels in the tree.

• Finding the shortest path in a tree: Level-order traversal can be used to find the shortest path in a tree, for example, in a binary search tree.

• Breadth-first search (BFS) algorithms: BFS algorithms can be implemented using level-order traversal. For example, BFS can be used to find the shortest path in a graph.

Conclusion

In conclusion, level-order traversal is a simple and effective way to traverse a tree. Whether you are printing the nodes of a tree, computing its height, finding the shortest path, or implementing a BFS algorithm, level-order traversal is a useful tool to have in your toolkit.