Chapter 19: Problem 15

Give an algorithm for a function void increment (TreeNode *tree) that increments the value in every node of a binary tree by one.

Short Answer

Expert verified

Question: Write a function that increments the value of every node in a binary tree by one. Explain the approach used in the function. Answer: The function named `increment` takes a TreeNode pointer (representing the root of the binary tree) as its parameter. The approach used is the preorder traversal of the binary tree (Root, Left, Right). Firstly, it checks if the tree is empty; if it is, no operation is performed. Otherwise, the function increments the current node's value by 1 and recursively calls itself on the left and right children of the current node. This way, it ensures every node in the binary tree has their value incremented by 1.

Step by step solution

Function Declaration

Declare a function called `increment`. This function should receive a TreeNode pointer as its parameter, this TreeNode will represent the root of the binary tree. ``` void increment(TreeNode *tree) { // Code implementation here } ```

Check if the Tree is Empty

If the tree is empty, there is no need to perform any operation. We can check this by verifying if the TreeNode pointer is `null`. ```cpp if (tree == nullptr) { return; } ```

Preorder Traversal and Incrementing

The next step is to traverse the binary tree using preorder traversal (i.e., Root, Left, Right) and increment the value of each node by 1 during the traversal. For this, we can use a recursive function that first increments the current node value, then calls itself recursively on the left and right children of the current node. This way, it guarantees that every node value is incremented. ```cpp tree->value += 1; increment(tree->left); increment(tree->right); ```

Complete solution

Here is the complete solution for the 'increment' function: ```cpp void increment(TreeNode *tree) { // Check if the tree is empty if (tree == nullptr) { return; } // Increment the value of the current node tree->value += 1; // Recursively increment the left and right children of the current node increment(tree->left); increment(tree->right); } ``` This algorithm will increment the value of every node in the binary tree by one, ensuring that all nodes are visited during the preorder traversal.

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Give an algorithm for a function void increment (TreeNode *tree) that increments the value in every node of a binary tree by one.

Short Answer

Step by step solution

Function Declaration

Check if the Tree is Empty

Preorder Traversal and Incrementing

Complete solution

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