Graph Connectedness Explained: Connected Strongly Connected and Weakly Connected
Posted inComputer Science Data Structures Graphs

Graph Connectedness Explained: Connected Strongly Connected and Weakly Connected

This video explains graph connectedness for both undirected and directed graphs. For undirected graphs a connected graph means every node can reach every other node through a path. Disconnected graphs have nodes that cannot reach others and may contain separate subgraphs. For directed graphs the terms change to strongly connected where every node reaches every other node following edge directions and weakly connected where the graph is connected if directions are ignored. Step by step examples show how adding edges turns a graph from not connected to weakly connected and finally to strongly connected.
AVL Tree Rotations Tutorial: Fixing Imbalance After Adding a Node
Posted inAVL Trees Binary Search Trees Computer Science

AVL Tree Rotations Tutorial: Fixing Imbalance After Adding a Node

Learn how to maintain balance in AVL trees through rotations. This tutorial shows inserting a new node into an AVL tree, recalculating balance factors up the path to the root, identifying the first imbalanced node, selecting X Y Z nodes based on subtree heights, and executing a double right rotation to restore the AVL property while preserving binary search tree ordering.
AVL Tree Rotation Types Explained for Self-Balancing Binary Search Trees
Posted inAVL Trees Binary Search Trees Computer Science

AVL Tree Rotation Types Explained for Self-Balancing Binary Search Trees

In AVL trees, when we find a node with a balance factor of 2 or worse, we perform rotations on the trinode subtree. There are four input patterns that all resolve to the same balanced output pattern through single or double rotations. Single rotations handle straight line imbalances while double rotations address the zigzag cases. Each rotation rearranges parent-child pointers to reduce the height from 3 to 2, helping keep the overall tree balanced for log time operations.
AVL Tree Tutorial: Balance Factors and Why They Fix Slow BSTs
Posted inAVL Trees Binary Search Trees Computer Science

AVL Tree Tutorial: Balance Factors and Why They Fix Slow BSTs

AVL trees are self-balancing binary search trees that prevent the tree from becoming unbalanced. We compute balance factors as the absolute value of left subtree height minus right subtree height. If any node has a balance factor of 2 or worse, we rebalance using rotations on trinode subtrees. This keeps search, insert, and other operations efficient at logarithmic time.