Step 1: Explanation of algorithms and data structures.
- **BFS (Breadth-First Search)**: BFS uses a **Queue** data structure to explore the graph level by level (A - IV).
- **DFS (Depth-First Search)**: DFS uses a **Stack** to explore the graph deeply by visiting nodes along a path before backtracking (B - I).
- **Heap Sort**: Heap Sort uses a **Priority Queue** to efficiently retrieve the maximum or minimum element (C - III).
- **Storage on Secondary Storage Devices**: Secondary storage devices like hard disks or SSDs often use **B Trees** for efficient searching and indexing (D - II).
Step 2: Conclusion.
The correct matching is **(A) - (IV), (B) - (II), (C) - (III), (D) - (I)**.
The maximum value of \(x\) such that the edge between the nodes B and C is included in every minimum spanning tree of the given graph is __________ (answer in integer).
The value printed by the given C program is __________ (Answer in integer).