How to determine the level of each node in the given tree?

Determining the Level of Each Node in a Tree

To determine the level of each node in a given tree, you can use a breadth-first search (BFS) algorithm. Here are the steps to accomplish this:

  1. Create a queue to store the nodes of the tree.
  2. Enqueue the root node of the tree into the queue.
  3. Initialize a variable level to 0, which represents the current level of the nodes.
  4. While the queue is not empty, do the following:
  5. Dequeue a node from the front of the queue.
  6. Assign the current level to the dequeued node.
  7. Enqueue all the children (if any) of the dequeued node into the queue.
  8. Repeat step 4 until the queue becomes empty.

At the end of this process, each node in the tree will have its corresponding level assigned to it.

Let's go through each step in detail:

  1. Create a queue to store the nodes of the tree.

  2. This queue will be used to perform the BFS traversal of the tree.

  3. Enqueue the root node of the tree into the queue.

  4. The root node is the starting point of the traversal.

  5. Initialize a variable level to 0, which represents the current level of the nodes.

  6. This variable will keep track of the level of each node as we traverse the tree.

  7. While the queue is not empty, do the following:

  8. Dequeue a node from the front of the queue.
    • This node will be the next node to be processed.
  9. Assign the current level to the dequeued node.
    • This assigns the level of the current node.

  10. Enqueue all the children (if any) of the dequeued node into the queue.

    • This ensures that the children nodes will be processed in the next iterations.

  11. Repeat step 4 until the queue becomes empty.

  12. This ensures that all nodes in the tree are processed.

At the end of this process, each node in the tree will have its corresponding level assigned to it.

Example:

Consider the following tree:

      A
    /   \
   B     C
  / \   / \
 D   E F   G

After applying the BFS algorithm to determine the level of each node, the levels will be as follows:

      A (level 0)
    /   \
   B     C (level 1)
  / \   / \
 D   E F   G (level 2)

In this example, node A is at level 0, nodes B and C are at level 1, and nodes D, E, F, and G are at level 2.

I hope this explanation helps! Let me know if you have any further questions.