When it comes to traversing a tree in a level order, one data structure that is commonly used is the queue. Level order traversal, also known as breadth-first traversal, visits all the nodes of a tree or graph level by level. It starts from the root node and explores all the nodes at the current level before moving on to the next level.
The concept of Level Order Traversal
In level order traversal, we visit the root node first and then visit all the children of the root node. After visiting all the children of the root node, we move on to visit their children and so on. This process continues until we have visited all the nodes in the tree.
This type of traversal is called “level order” because it visits nodes at each level before moving on to nodes at deeper levels.
Using a Queue for Level Order Traversal
The main reason why a queue is used for level order traversal is because it follows a FIFO (First-In-First-Out) approach. This means that elements are processed in the same order as they were inserted into the queue.
To perform a level order traversal using a queue, we start by inserting the root node into an empty queue. Then, while there are still elements in the queue, we:
- Dequeue an element from the front of the queue.
- Process (print or manipulate) this element.
- If there are any children for this element,
- Enqueue each child into the back of the queue.
This process continues until the queue becomes empty, which means we have visited all the nodes in the tree.
Let’s consider the following binary tree:
1 / \ 2 3 / \ / \ 4 5 6 7
The level order traversal of this tree would be: 1, 2, 3, 4, 5, 6, 7.
If we use a queue to perform level order traversal of this tree, the sequence of operations would be as follows:
- Enqueue(1) – Insert the root node into the queue.
- Dequeue(1) – Remove and process the front element (1).
- Enqueue(2) – Insert the left child (2) into the queue.
- Enqueue(3) – Insert the right child (3) into the queue.
- Enqueue(4) – Insert the left child (4) into the queue.
- Enqueue(5) – Insert the right child (5) into the queue.
..and so on until all elements are dequeued and processed.
The queue data structure is well-suited for level order traversal due to its FIFO nature. By using a queue to process nodes at each level before moving on to deeper levels, we can ensure that all nodes in a tree are visited in a level-wise manner.
Remember to keep the concept of level order traversal and the usage of a queue in mind when working with trees or graphs. It is a fundamental technique that can be extremely useful in various algorithms and applications.