In a depth-first search (DFS) traversal of a graph, which data structure is used to store visited vertices?StackQueueHeapHash table

Breakdown of the Problem

1. Identify the context: The question pertains to depth-first search (DFS) in graph traversal.
2. Understand DFS: In DFS, we explore as far down a branch as possible before backtracking.
3. Identify the data structure used to track visited vertices during this process.

Relevant Concepts

1. Depth-First Search (DFS): This traversal method uses a data structure that allows backtracking once a vertex's neighbors have been explored.
2. Data Structures: The relevant data structures to consider are:
   • Stack: Last In First Out (LIFO) structure, suitable for backtracking.
   • Queue: First In First Out (FIFO) structure, not ideal for DFS.
   • Heap: Used for priority-based storage, not typically used in DFS.
   • Hash Table: Good for storing visited vertices but does not support backtracking like a stack.

Analysis and Detail

1. Stack: In DFS, we push a vertex onto the stack when we visit it and pop it when we backtrack, which maintains the proper order of traversal.
2. Queue, Heap, and Hash Table:
   • Queue would lead to a breadth-first traversal, which is not what we need for DFS.
   • Heap is not suitable for maintaining traversal order in DFS.
   • Hash table could store visited vertices but does not facilitate the backtracking mechanism essential for DFS.

Verify and Summarize

1. The stack effectively manages the order of node visitation in DFS, allowing for proper backtracking and exploration of other paths.
2. Other structures (queue, heap, hash table) do not fulfill the requirement for backtracking in this context.

Final Answer

The data structure used to store visited vertices in a depth-first search (DFS) traversal of a graph is a Stack.