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Chapter 19: Problem 15

Give an algorithm for a function vold Increment (TreeNode "tree) that increments the value in every node of a binary tree by one.

Short Answer

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Question: Write a short answer explaining the key steps to increment all the values of a binary tree by one. Answer: The key steps to increment all values of a binary tree by one are: understanding the input (a binary tree represented by a TreeNode), determining the traversal method (pre-order, in-order, or post-order), creating a recursive function called `Increment`, writing a pseudocode for the `Increment` function, and implementing the algorithm using the chosen traversal method in a programming language.

Step by step solution

01

Understand the Input

The input to the function is a TreeNode "tree" representing the binary tree's root node. The binary tree is a data structure that consists of nodes, with each node having at most two child nodes.
02

Determine the Type of Traversal

Since we need to visit all nodes in the binary tree and update their values, we can use any traversal method (pre-order, in-order, or post-order) to accomplish the task, as long as we visit all nodes exactly once.
03

Create a Recursive Function

We will create a recursive function called `Increment` that takes a node as input, updates its value, and recursively calls the function on its child nodes.
04

Write the Pseudocode for Increment Function

The pseudocode for the whole process looks like the following: ``` Function Increment (tree) If tree is not NULL Increment treeNode value by 1 Increment(tree.left) Increment(tree.right) ```
05

Implement the Algorithm

The implementation of the Increment function in a programming language depends on the language's syntax and data structure used for the binary tree. Please note that this would vary based on the programming language you're using, so make sure to use a language-specific implementation.

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Most popular questions from this chapter

A binary tree node's left and right pointers point to the node's __________.

A ternary tree is like a binary tree, except each node in a ternary tree may have three children: a left child, a middle child, and a right child. Write an analogue of the TreeNode declaration that can be used to represent the nodes of a ternary tree.

A node with no children is called a(n) __________.

In what ways is a binary tree similar to a linked list?

Suppose the following values are inserted into a binary search tree, in the order given: \\[12,7,9,10,22,24,30,18,3,14,20\\] Draw a diagram of the resulting binary tree.
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