Chapter 20: Problem 12

Write a pseudocode algorithm for inserting a node in a tree.

Short Answer

Expert verified

Question: Write an algorithm for inserting a node into a binary tree while maintaining its structure and order.

Step by step solution

1. Define the Node structure

Create a Node class or structure with two attributes - a value for storing integer data, and left and right pointers for storing references to left and right children in the tree.

2. Define the insertion function

Create an insertion function that takes the following parameters: the root of the tree and the value to be inserted. The function should have the following signature: `InsertNode(root, key)`.

3. Check if the tree is empty

In the insertion function, check if the root of the tree is `null`. If the tree is empty, create a new node with the given value and assign it as the root of the tree. Then, return the root.

4. Traverse the tree

Traverse the tree to find the correct position for the new node. Compare the value to be inserted with the value of the current node. If the value is smaller than or equal to the current node's value, traverse to its left subtree. If the value is greater than the current node's value, traverse to its right subtree.

5. Recursion

Repeat step 4 using a recursive call to the insertion function. Pass the left or right child (depending on the comparison in step 4) of the current node as the new root, along with the value to be inserted

6. Insert the new node

Once a null position is reached during the traversal, create a new node with the given value and link it as the left or right child of its parent, depending on the comparison in step 4. Then, return the root. Here is the pseudocode for the algorithm: ``` class Node value left right function InsertNode(root, key) if (root is null) newNode = new Node(key) root = newNode return root endif if (key <= root.value) root.left = InsertNode(root.left, key) else root.right = InsertNode(root.right, key) endif return root ``` This algorithm will correctly insert the given value into the binary tree, maintaining its structure and order.

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Write a pseudocode algorithm for inserting a node in a tree.

Short Answer

Step by step solution

1. Define the Node structure

2. Define the insertion function

3. Check if the tree is empty

4. Traverse the tree

5. Recursion

6. Insert the new node

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