CS301 Final Term Latest Past Papers 2025 

Expression Trees

welcome to vuexpertsolutions.pk In our previous lecture, we explored expression trees in detail. Trees, in general, find extensive use across various domains of computer science. Two notable examples are compilers and databases. In the context of compilers, tree-like structures play a crucial role in transforming programming languages into their equivalent machine-level code. We have also seen a mathematical expression represented as an expression tree. Let’s delve deeper into the advantages of expression trees and how to build them effectively.

The following diagram illustrates a basic expression tree. Let’s consider the process of constructing such a tree. We often start with mathematical expressions that involve binary operators. To build an expression tree, we first need to convert an infix expression into postfix notation. Earlier in this course, we discussed how to convert infix expressions (which are typical in spreadsheets and calculators) to postfix expressions. Once the infix expression is converted to postfix, we can then create an expression tree based on this new format. For instance, if a user types an infix expression into a spreadsheet, it must first be transformed into postfix notation before it can be used to construct an expression tree.

Huffman Encoding

Another interesting use of binary trees lies in data compression, specifically through Huffman Encoding. Data compression has become increasingly significant in computer networking, where the aim is to send data faster and more efficiently. To achieve this, there are generally two approaches: either increase the data transfer rate of the transmission media or reduce the amount of data to be sent. However, it’s essential to ensure that despite compression, the actual information remains intact and complete.

For example, when you need to send data to another computer, you might compress the file using tools like WinZip. The receiver subsequently extracts or decompresses the file to obtain the complete original data. Another approach to faster data transfer is to increase bandwidth by upgrading the transmission medium for instance, by using fiber optic cables or faster modems. These improvements fall within the domain of communication and electrical engineering. Today, fiber optic technology is widely used to boost transmission speeds and efficiency in computer networks.

Properties of Binary Trees

Previously, we discussed some properties of binary trees, especially the relationship between internal and external nodes. Specifically, if a binary tree has NNN internal nodes, it will have N+1N+1N+1 external nodes. Building on this, today’s discussion focuses on another essential property, particularly concerning the relationship between the links and internal nodes of a binary tree.

To illustrate, consider a binary tree diagram that highlights not just the links connecting internal nodes but also includes external nodes depicted as square shapes. These external nodes and their respective links to the internal nodes are represented by lines extending from the internal structure. This visual representation helps us better understand how these links contribute to the overall structure of the binary tree.

Inorder Traversal in Threaded Trees

Let’s move on to the topic of inorder traversal in threaded binary trees. In a threaded tree, special links (called threads) are used to point to a node’s inorder successor or predecessor. We have already introduced the concept of threads and developed the nextInorder function, which relies on the availability of the root node to properly execute the inorder traversal. Essentially, this traversal begins at the leftmost node and uses the threads to navigate efficiently through the rest of the tree.

Complete Binary Tree

Previously, we discussed some key properties of binary trees, including internal and external nodes. Now, let's focus on another important property related to how binary trees are stored, especially complete binary trees and the heap data structure.

Different books may describe a complete binary tree in slightly varied ways. Ideally, a fully complete binary tree has all its leaf nodes on the same level. But in a complete binary tree, every node has both left and right children except for those at the very last level, where some nodes might be missing. At this bottom level, nodes appear consecutively from left to right, although this level may not be fully filled.

When building binary trees or similar data structures, we usually decide whether to use arrays or pointers for storing the data. Arrays are helpful because they allow quick access to any element by simply using an index. This makes adding or removing elements fast and straightforward, as you can jump directly to the position you need.

Because of this, arrays are preferred whenever they meet the requirements of the problem, thanks to their speed and direct support from compilers. However, there are cases where pointers are more useful. For example, balancing an AVL tree is easier and more efficient with pointers because arrays would require moving many elements around to maintain balance.

Pointers help manage memory dynamically, meaning the program only uses as much memory as needed at any time, rather than reserving a fixed large amount. This efficient use of memory and time is crucial when designing data structures. The goal is to build structures that allow programs to run quickly without wasting memory.

To sum up, a complete binary tree is a type of binary tree where nodes are filled sequentially, level by level, from left to right. The choice between using arrays or pointers depends on the needs of the implementation.

Conclusion

In summary, expression trees play a pivotal role in areas such as compilers, where they help convert and evaluate expressions. Huffman Encoding further demonstrates how binary trees can be applied to data compression for faster data transmission in networks. Meanwhile, understanding binary tree properties allows us to grasp the underlying structure of these trees, including the critical relationship between internal and external nodes and their connecting links. Finally, the inorder traversal of threaded trees highlights the power of using threads to traverse trees efficiently, especially when direct links are not sufficient.

By understanding these topics thoroughly, we gain a comprehensive insight into how data structures like binary trees enhance computing systems, enabling faster processing, efficient data compression, and better organization of data. These concepts not only strengthen our understanding of computer science fundamentals but also prepare us for more advanced applications in real-world scenarios.