Introduction to Depth$-$First Search $($DFS$)$

Depth$-$First Search is an algorithm used to traverse or explore graph data structures. It starts at a selected node and explores as deep as possible along each branch. This algorithm follows a path to the deepest node before backtracking. DFS is particularly useful in scenarios that require exploring all possible solutions. It is commonly implemented in programming tasks involving puzzles or network analyses.

Explanation:

In this step, we introduce the Depth$-$First Search $($DFS$)$ algorithm, explaining its purpose and method of operation. This sets the context by describing how DFS explores a graph or tree by going as deep as possible into its branches before backtracking.

Step $2$ of $2$

Step $2$

Evaluation of Options

Option A: Queue

A queue implements a First In First Out $($FIFO$)$ approach, which aligns well with Breadth$-$First Search $($BFS$)$ but not with DFS$.$ In BFS$,$ all adjacent nodes are visited before moving to the next depth level, which requires keeping track of nodes in the order they were added. For DFS$,$ a queue would complicate the process of diving deep and backtracking efficiently, as it would force the exploration of all nearby nodes before moving deeper, contrary to DFS$\text{'}$s goals.

Option B: Stack

A stack operates on a Last In First Out $($LIFO$)$ principle, making it highly suitable for the Depth$-$First Search algorithm. When using a stack, nodes are pushed onto the stack as they are visited, storing them for later backtracking. This enables DFS to dive deep into one path of the graph until it reaches a dead end or has visited all possible nodes along that route. The stack then allows for easy backtracking by popping the last visited node, ensuring a systematic exploration of the graph's depths.

This option is looking correct for the given question

Option C: Array

An array is a collection of elements identified by index. While arrays can be used to store graph representations $($like adjacency matrices or lists$),$ they are not inherently suitable for managing the traversal process in DFS$.$

Option D: Linked List

A linked list is a linear data structure where each element points to the next. Like arrays, linked lists can be used to represent graphs but are not typically used to manage the traversal process in DFS$.$

Explanation:

Understanding the operational principles of each data structure helps in discerning which one aligns with the needs of the DFS algorithm. DFS requires a mechanism to revisit nodes in a specific sequence $($LIFO$),$ making the stack the most appropriate choice.

Final solution

Final Solution:

The most appropriate data structure for implementing a depth$-$first search algorithm is the stack, as it efficiently manages the node visitation order required for deep traversal and backtracking in DFS$.$

b$)$ Stack

DFS uses a stack to keep track of the nodes that need to be explored.