The Floyd-Warshall Algorithm is a dynamic programming-based graph algorithm used to find the shortest paths between all pairs of vertices in a weighted graph. It can handle negative edge weights but not negative cycles. This algorithm is widely used in networking, route optimization, and transitive closure problems due to its simplicity and efficiency for dense […]

Graph traversal is a fundamental operation in computer science, used in networking, AI, and pathfinding. Breadth-First Search (BFS) explores neighbors level by level, making it ideal for finding the shortest path in unweighted graphs. Depth-First Search (DFS) explores as far as possible along each branch before backtracking, which is useful for connectivity, topological sorting, and

Dijkstra’s Algorithm is a graph-based algorithm used to find the shortest path from a source node to all other vertices in a weighted graph with non-negative edge weights. It is widely used in networking, route optimization, and mapping applications. Understanding Dijkstra’s Algorithm helps in solving real-world problems involving optimal paths efficiently. Think of a map

Deleting a node from a BST is one of the most important operations because it affects the tree’s structure and the ordering property. Proper handling ensures that the BST property — all left descendants are smaller and all right descendants are larger — is maintained. This operation requires careful management of pointers and consideration of

Reverse level order traversal is a variation of the traditional level order traversal. In this method, we visit nodes level by level, but instead of printing from top to bottom, we print from bottom to top. This makes the traversal useful for problems where deeper levels should be processed before higher ones, such as evaluating

Zigzag or spiral traversal is a variation of level order traversal where nodes are printed alternately from left to right and right to left at each level. This makes the traversal follow a zigzag pattern across the tree. It is particularly useful when you want to visualize hierarchical data in an alternating fashion. Understanding the

A Binary Search Tree (BST) is a special type of binary tree where each node follows a strict ordering property: the left child contains values less than the parent node, and the right child contains values greater than the parent node. BSTs allow efficient searching, insertion, and deletion operations, making them fundamental in algorithms requiring

Level order traversal is a method of visiting nodes in a binary tree level by level from top to bottom and from left to right. It uses a queue to keep track of nodes that need to be visited. This traversal is also called Breadth-First Traversal (BFS) because it explores each level fully before moving

Counting the total number of nodes in a binary tree is a fundamental operation in tree data structures. It helps in understanding the size of the tree, which is useful for performance analysis and in algorithms that require tree metrics. Both recursive and iterative methods can be used to count nodes efficiently. Understanding the Problem

Deleting a node from a binary tree involves removing a specified node while maintaining the structure of the tree. Unlike binary search trees, where specific rules help maintain ordering, general binary tree deletion may replace the node with the deepest rightmost node. Understanding deletion is essential for memory management and maintaining proper tree structure. Understanding