Advanced Data Structures-Part I-TREE ADT

Explore the tree as a nonlinear, acyclic abstract data type of linked nodes arranged hierarchically with a root and children, enabling traversal and diverse applications.

Explore core tree terminology, including nodes, edges, and paths; identify roots, leaves, internal nodes, and relationships like parent, ancestor, sibling, subtree, and forest, plus height, level, and degree definitions.

Understand binary trees as a simplified general tree with at most two children, featuring recursive definitions and the full, complete, and perfect types, plus height and node relationships.

Implement binary trees using array-based and linked list representations, with root at index one and left/right children at 2k and 2k+1, and compare memory efficiency and insertion and deletion trade-offs.

Explore how binary trees support search, insertion, deletion, and the three traversals—preorder, inorder, and postorder—along with level-order insertion and traversal-based reconstruction.

Explore binary tree applications, including expression trees for compilers, decision trees, and data compression via halfman coding; learn to construct and evaluate expression trees using postfix notation and stacks.

Explore binary search trees, where left subtree values are less than or equal to the node and right subtree values are greater, and how insertion builds BSTs for efficient search.

Explore binary search tree operations: insertion, deletion, searching, minimum, maximum, successor, predecessor, and dynamic set operations; in-order traversal yields sorted data, with performance depending on tree height.

Delete a node in a binary search tree across three cases—no child, one child, two children—using successor or predecessor replacements while preserving BST properties and maintaining height for logarithmic operations.

Explore the applications of binary search trees, including dictionary ADT and priority queue implementations, using range searches on ordered keys to retrieve records efficiently.

This lecture shows constructing a binary max heap from an array using max-heapify, explains heap properties for max and min heaps, and discusses array representation and heap size.

Learn in-place heap sort by building a max heap, swapping the root with the last unsorted element, shrinking the heap, yielding O(n log n) time and not stable order.

Explain how AVL trees maintain height balance in binary search trees through rotations, using balance factors to keep left and right subtree heights within one.

learn how insertions affect AVL tree height and trigger rebalancing through rotations; cover single and double rotations (left-left, right-right, left-right, right-left) to preserve balance.

Delete in AVL trees removes a node with zero, one, or two children and rebalances through single or double rotations to maintain balance factors along the ancestors.

Introduce red-black trees, a self-balancing BST with red and black nodes, root and leaves black, no consecutive red, and height bound. Insertions and deletions trigger rotations and recoloring.

Explore red-black tree insertion, locating leaf, inserting key, coloring the new node red, and resolving violations through three cases and their mirror images with rotations to restore red-black properties.

Learn deletion in red-black trees, including red and black node cases, double black handling, predecessor or successor use, rotations, and color changes to preserve properties.

Explore the construction and maintenance of red-black trees through a detailed insertion and deletion example, illustrating rebalancing rotations and color changes to preserve tree properties.

Contrast AVL and red-black trees, emphasizing height bounds, rotations, and log-time insertions and deletions. Highlight applications in information retrieval, parallel dictionaries, spell check, image retrieval, and Linux process scheduling.

Introduce B-tree fundamentals: multiway structure, balance properties, and node roles; compare with B+ trees and explain use in database indexing for fast disk access.

Explore how B-tree searching generalizes binary search with multi-way branching and multiple pointers, and how insertion uses splitting, median up, and rebalancing through the tree.

Learn how to delete in a B-tree, handling leaf and internal deletions by preserving minimum keys, borrowing from siblings, or merging nodes, with parent and root adjustments.

Explore how B-trees minimize disk access with a high branching factor, lowering height and data access in database and file system indexing, and compare with B plus three trees.