In data structures, multilinked structures have nodes with more than one link field. Which of the following options lists typical applications where multilinked structures are especially useful?

Introduction / Context:
Multilinked data structures are those in which each node contains more than one link field, allowing navigation along multiple dimensions or relationships. Examples include nodes with pointers to next and previous elements, or nodes that participate in several linked lists at once. Such structures are valuable for representing data that has multiple logical connections. This question asks you to recognise typical application areas where multilinked structures provide clear advantages over simple single linked lists or arrays.

Given Data / Assumptions:

• A multilinked structure may have two or more pointers in each node, enabling traversal along rows and columns, or across different categories.
• Applications often involve complex relationships, sparse connectivity, or multiple views of the same underlying data.
• Simple linear containers do not fully exploit the power of multilinked nodes.
• The options distinguish between rich, relational application domains and trivial storage scenarios.

Concept / Approach:
Multilinked structures are well suited for representing sparse matrices, where non zero elements are scattered and it is inefficient to store entire dense arrays. Each node may link to the next non zero element in its row and the next non zero element in its column. They are also used in polynomial manipulation, where each term can be linked by exponent order or coefficient grouping. In database indexing and graph structures, nodes may need multiple links to represent relationships such as adjacency lists, parent child relationships, or multiple access paths. These applications benefit from the flexibility of multilinked nodes, which support efficient traversals along different logical dimensions without duplicating data.

Step-by-Step Solution:
Step 1: Recall examples from textbooks where multilinked structures are used for sparse matrices, with row and column pointers. Step 2: Remember that polynomial expressions with many terms also use linked representations, sometimes with multiple pointers for ordering and manipulation. Step 3: Consider how database indices and graph structures require nodes to have more than one link to represent complex relationships or access paths. Step 4: Examine option a, which explicitly lists sparse matrices, polynomial manipulation, and complex data models such as database indices or graph structures, matching common multilinked applications. Step 5: Reject the other options that describe simple scalar variables, basic arrays, or single pointer stacks, which do not require multilinked nodes.

Verification / Alternative check:
Data structure references often present examples of orthogonal lists for sparse matrices, where each non zero element is stored in a node with pointers to the next element in the same row and the next element in the same column. This is a classic multilinked structure. Similarly, graphs may be represented by adjacency lists where nodes have lists of outgoing edges and sometimes separate lists of incoming edges. Database internals also use multilinked structures in certain index implementations. These well known examples support the application set described in option a.

Why Other Options Are Wrong:
Option b refers to storing single scalar variables like temperature, which does not require any links or structural complexity. Option c mentions simple one dimensional arrays for fixed size computations; although arrays are fundamental structures, they do not involve multilinked nodes. Option d focuses on basic stacks with a single top pointer; stacks can be implemented using simple arrays or singly linked lists without multiple link fields per node.

Common Pitfalls:
A common pitfall is to assume that multilinked structures are overkill for most problems and to overlook their advantages in specific domains with multidimensional relationships. Another mistake is confusing multilinked structures with simple doubly linked lists; while doubly linked lists are a form of multilinked nodes, the term usually refers to more general cases where each node participates in multiple structures or dimensions. For exam questions, remember typical applications: sparse matrices, polynomial handling, and complex relational models such as graphs and indices.

Final Answer:
Multilinked structures are especially useful for representing sparse matrices, implementing polynomial manipulation, and building complex data models such as database indices or graph structures.