Advanced Structures: Heaps and Graphs

Implement a priority queue using a binary heap.

Apply a priority queue to solve a selection or scheduling problem (e.g., k-th largest element).

Represent graphs using adjacency matrices and adjacency lists, analyzing their trade-offs.

Implement Depth-First Search (DFS) and its applications (e.g., pathfinding, connectivity).

Implement Breadth-First Search (BFS) and its applications (e.g., shortest path in unweighted graphs).

Detect cycles in both directed and undirected graphs using DFS.

Implement topological sorting for a Directed Acyclic Graph (DAG).