Question

\((\) Printing Trees) Write a recursive method outputTree to display a binary tree object on the screen. The method should output the tree row by row, with the top of the tree at the left of the screen and the bottom of the tree toward the right of the screen. Each row is output vertically. For example, the binary tree illustrated in Fig. 17.20 is output as shown in Fig. 17.21 The rightmost leaf node appears at the top of the output in the rightmost column and the root node appears at the left of the output. Each column starts five spaces to the right of the preceding column. Method outputTree should receive an argument total Spaces representing the number of spaces preceding the value to be output. (This variable should start at zero so that the root node is output at the left of the screen.) The method uses a modified inorder traversal to output the tree- it starts at the rightmost node in the tree and works back to the left. The algorithm is as follows: While the reference to the current node is not null, perform the following: Recursively call outputTree with the right subtree of the current node and totalSpaces +5 Use a for statement to count from 1 to totalSpaces and output spaces. Output the value in the current node. Set the reference to the current node to refer to the left subtree of the current node. Increment totalSpaces by 5

Short answer

Use a recursive inorder traversal starting from the rightmost node with increasing indentation for each level.

Step-by-step solution

Understanding the Function

The exercise requires us to write a recursive function `outputTree` to print a binary tree on the screen. The tree should be printed level by level, with the rightmost node at the top of the screen. The function uses an inorder traversal starting at the rightmost node and prints nodes with increasing indentation as it moves towards the left.

Defining the Base Case

In a recursive function, the base case is when the current node is `null`. If it is `null`, the function should not perform any operations and simply return. This avoids unnecessary processing and prevents infinite recursive calls.

Recursive Traversal of the Right Subtree

First, recursively call `outputTree` with the right subtree of the current node and `totalSpaces + 5`. This step ensures that we begin displaying the tree from the rightmost node.

Display Spacing

Use a for loop to print spaces based on `totalSpaces` before printing the value of the current node. This indentation ensures that each level of depth is visualized further to the right.

Print the Current Node Value

Once the spacing is done, output the value stored in the current node. This displays the node vertically aligned as per the indentation calculated.

Recursive Traversal of the Left Subtree

Finally, continue the recursive traversal by calling `outputTree` on the left subtree of the current node, passing `totalSpaces + 5`. This completes the inorder traversal from rightmost to leftmost nodes.

Key concepts

Recursive Method

A recursive method is a function that calls itself in order to solve a problem. This method plays a vital role in many computer science applications, including binary tree traversals. By breaking problems into smaller, more manageable sub-problems—each of which is a smaller instance of the original problem—a recursive method offers simplicity and elegance. When dealing with binary trees, recursion is often preferred due to its ability to naturally reflect the tree's hierarchical structure.
The recursive nature of functions requires defining a base case clearly. This is the condition under which the recursion stops, preventing infinite loops and ensuring function termination. For example, in a binary tree, when a node is `null`, the recursive call ceases. This forms the backbone of operations like tree traversal, sorting algorithms, and solving complex mathematical problems.
In practical implementations, recursive methods can be more intuitive, especially when dealing with recursive data structures like binary trees. They mirror how such data structures are logically organized. However, be mindful of stack overflow risks in environments with limited stack space or trees with deep nesting.

Inorder Traversal

Inorder traversal is a common method of visiting all the nodes in a binary tree, typically done in the following order:

• Visit the left subtree
• Visit the root node
• Visit the right subtree

However, in some specialized uses, such as the modified inorder traversal used in this exercise, the sequence may be altered. Here, we start from the rightmost node before moving towards the left, effectively reversing the usual inorder progression.
This traversal method can be particularly useful for operations that require nodes to be processed in a specific order. For example, inorder traversal of a binary search tree produces a sorted sequence of node values. This characteristic makes it vital in scenarios where the natural order is needed for further processing.
The effectively modified inorder method used in the exercise helps in visualizing the binary tree in a structured format on screen, showcasing the tree from top (rightmost node) to bottom (leftmost node) while maintaining vertical alignment through spacing.

Binary Tree Visualization

Visualizing a binary tree is a key task in understanding its structure and operation. Binary tree visualization involves displaying the tree such that each node's relationship with its parent and children is clear.
In programming, particularly when debugging or understanding complex algorithms, seeing how a tree is structured can greatly enhance comprehension. The exercise describes a method for visualizing a binary tree on-screen using text. This is performed by executing a modified inorder traversal that starts from the right and moves left, with indentation representing different levels of depth.
In such visualizations:

• The rightmost child is displayed at the top
• The spaces denote the tree’s depth level, increasing with each level
• This allows for an effective top-to-bottom visual perspective of the tree structure

Understanding these visual representations can be instrumental in both learning and applying tree operations in coding tasks, providing an intuitive grasp of complex tree algorithms.

Tree Data Structure

The tree data structure is a way of organizing information in a hierarchical manner. Unlike linear structures such as arrays and linked lists, trees allow for storing data in a parent-child relationship format, with a single "root" element that branches out into child nodes.
Binary trees specifically restrict each node to have at most two children, referred to as the left and right child. This structure is highly versatile and underlies many algorithms and data types, such as binary search trees (BST), heaps, and syntax trees.
Some key characteristics of binary trees include:

• The topmost node without a parent is the root
• Nodes with no children are called leaves
• A node's depth is the number of edges from the root to the node
• The height of a tree is the number of edges on the longest downward path

Binary trees efficiently implement search and sort operations, making them essential in computer science education. They strike a balance between flexibility and complexity, allowing easy data manipulation while maintaining considerable structural integrity.