27 Jan - DS - Tree Traversal + BST
Duration: 1 hr 10 min
This video lesson is available to enrolled students.
AI Summary
An AI-generated summary of this video lecture.
This video is a comprehensive lecture on tree data structures, focusing on binary trees and their traversal methods. The session begins with an introduction to the general concept of a tree, defining key terms like root, node, edge, and subtree. It then transitions to the specific case of a binary tree, explaining its properties, such as each node having at most two children, and its representation in memory using a linked structure with a 'struct node' containing data and pointers to left and right children. The core of the lecture is dedicated to tree traversals, where the instructor explains and demonstrates pre-order (Root, Left, Right), in-order (Left, Root, Right), and post-order (Left, Right, Root) traversals using a sample tree. The video concludes with a series of GATE exam questions that test the application of these concepts, including problems on finding the number of nodes with two children, calculating the height of a tree from its traversals, and identifying the correct traversal sequence for a given tree.
Chapters
0:00 – 2:00 00:00-02:00
The video starts with a title slide for 'Session-8' by 'Ekagra Sir'. The instructor, Sanchit Jain, appears in a small window in the top right corner. The session is about tree data structures, as indicated by the title slide.
2:00 – 5:00 02:00-05:00
The lecture begins with a definition of a tree as a non-linear data structure representing hierarchical relationships. Key terms are defined: Root Node (topmost node), Edge (connection between nodes), Child Node (descendant of a parent), Internal Node (has at least one child), Leaf Node (has no children), Degree of a Node (number of children), Level/Depth (steps from root), and Path (sequence of connected nodes). A diagram of a tree with nodes A through K is shown.
5:00 – 10:00 05:00-10:00
The focus shifts to Binary Trees. The instructor defines a binary tree as a tree where each node has at most two children, referred to as left and right. The properties of a binary tree are listed: it can be empty, has a unique root, and its remaining nodes are partitioned into two disjoint subtrees (left and right). The two main representations are discussed: Sequential (using an array) and Linked (using a self-referential structure). A C++ struct definition for a node is shown on the board.
10:00 – 15:00 10:00-15:00
The instructor continues to explain the linked representation of a binary tree. He draws a diagram of a node with data and pointers to left and right children. He then discusses the properties of a binary search tree, noting that it is ordered and has no duplicate values. He begins to solve a GATE 2025 question about the number of nodes with exactly two children in a binary tree with 'n' nodes.
15:00 – 20:00 15:00-20:00
The instructor solves a GATE 2025 question. The question asks for the number of nodes with exactly two children in a binary tree with 'n' nodes. He explains that the formula is (n-1)/2, which is derived from the relationship between the number of nodes and the number of edges in a tree. He then moves to a GATE 2017 question about the minimum and maximum possible heights of a binary search tree with 15 nodes.
20:00 – 25:00 20:00-25:00
The instructor solves a GATE 2017 question. He calculates the minimum height of a binary search tree with 15 nodes by finding the smallest integer 'h' such that 2^(h+1) - 1 >= 15, which gives h=3. The maximum height is the worst case, a skewed tree, which is 14. He then moves to a GATE 2015 question about the maximum and minimum number of nodes in a binary tree of height 5.
25:00 – 30:00 25:00-30:00
The instructor solves a GATE 2015 question. He calculates the maximum number of nodes in a binary tree of height 5 as 2^6 - 1 = 63. The minimum number of nodes is 6, which occurs in a skewed tree. He then presents a GATE 1987 question about whether a tree with a number of leaves not a power of 2 can be a binary tree.
30:00 – 35:00 30:00-35:00
The instructor discusses a GATE 1987 question: 'If the number of leaves in a tree is not a power of 2, then it is not a binary tree?'. He explains that this is false, as a binary tree can have any number of leaves. He then transitions to a new topic: 'Tree Traversal & Construction'.
35:00 – 40:00 35:00-40:00
The instructor introduces the concept of tree traversal. He draws a sample binary tree with nodes A, B, C, D, E, F, G, H, I, J, K. He begins to explain pre-order traversal, writing the formula 'Pre: Root, Left, Right' and then starts to list the sequence for the given tree.
40:00 – 45:00 40:00-45:00
The instructor continues to demonstrate tree traversals. He completes the pre-order traversal for the sample tree: A, B, D, H, I, E, J, C, F, G, K. He then explains in-order traversal (Left, Root, Right) and post-order traversal (Left, Right, Root), writing the formulas and beginning to list the sequences.
45:00 – 50:00 45:00-50:00
The instructor completes the traversal sequences for the sample tree. He writes the in-order traversal as B, D, H, I, E, J, A, C, F, G, K. He then writes the post-order traversal as H, I, D, J, E, B, K, G, F, C, A. He then moves to a GATE 19 question about identifying the post-order traversal of a given tree.
50:00 – 55:00 50:00-55:00
The instructor solves a GATE 19 question. The question asks for the post-order traversal of a binary tree with root 'a' and subtrees 'b' and 'e'. He identifies the correct answer as 'c' (gcdbfea) by applying the post-order rule: traverse the left subtree, then the right subtree, then visit the root.
55:00 – 60:00 55:00-60:00
The instructor solves a GATE 2018 question. Given the post-order (8, 9, 7, 4, 5, 2, 3, 1) and in-order (8, 6, 9, 4, 7, 5, 3, 1) traversals, he reconstructs the tree. The root is 1 (last in post-order). The left subtree has nodes 8, 6, 9, 4, 7, 5, 3. The right subtree is empty. He then calculates the height of the tree as 4.
60:00 – 65:00 60:00-65:00
The instructor solves a GATE 2008 question. The question presents three sequences and asks to identify which are pre-order and in-order. He analyzes the sequences and concludes that sequence II (KAMCBYPFH) is the in-order traversal, and the other two are pre-order and post-order, but cannot be distinguished without more information.
65:00 – 70:00 65:00-70:00
The instructor solves a GATE 2007 question. Given the in-order (a b d e c f g) and pre-order (b a e f c g) traversals, he reconstructs the tree. The root is 'b' (first in pre-order). The left subtree has 'a', and the right subtree has 'a e f c g'. He then determines the post-order traversal is 'e d b f g c a'.
70:00 – 70:26 70:00-70:26
The instructor presents a GATE 2004 question asking which of four binary tree diagrams has an in-order traversal of 'BC' and a pre-order traversal of 'AC'. He analyzes the options and identifies that diagram (a) matches the given traversals.
This video provides a structured and comprehensive lecture on tree data structures, progressing from fundamental definitions to complex problem-solving. It begins by establishing the core concepts of trees and binary trees, including their properties and memory representations. The central focus is on tree traversals, with clear explanations and visual demonstrations of pre-order, in-order, and post-order methods. The lecture is heavily application-oriented, using a series of GATE exam questions to test and reinforce the concepts. The instructor methodically works through each problem, demonstrating how to apply the theoretical knowledge to find solutions, such as calculating tree height from traversals or reconstructing a tree from its traversals. The progression from basic definitions to advanced problem-solving makes it a valuable resource for students preparing for competitive exams in computer science.