Data Structures and Algorithms

Yes, all of the above are the applications of the stack data structure.

Yes, all of the above are the true statements.

A stack is a last in first out type of data structure. Here, the insertion and deletion of elements can be done only from one end.

Arranging the records in some logical order is referred to as sorting.

It gives the address of the first element of the array.

Vector consists of contiguous memory location and is the appropriate choice.

It is a linear data structure. A linear data structures elements are arranged in a list.

Kruskal's algorithm uses edge sorting and union-find. Sorting |E| edges takes O(|E| log |E|) ≈ O(|E| log |V|) since |E| ≤ |V|². Union-find operations are nearly O(1) with path compression and union by rank. The dominant cost is sorting, giving O(|E| log |V|). Adjacency list representation is standard.

Prim's algorithm on an adjacency matrix requires scanning all vertices to find the minimum weight edge, taking O(|V|) per vertex. With |V| iterations, total is O(|V|²). With Fibonacci heap + adjacency list, it becomes O(|E| + |V| log |V|), but O(|V|²) is the standard answer for basic implementation.

Prim's algorithm using a binary heap performs O(|E|) extract-min and O(|V|) decrease-key operations, each costing O(log|V|). The dominant term is |E|log|V| because the number of edges is typically greater than vertices. Option B incorrectly writes V as base and E as exponent, while C and D are not the correct complexity for heap-based Prim's.

It inserts data into the list, so that the length increases.

Structures in C++ can contain members of different data types (int, float, char, etc.) unlike arrays which require similar types. This makes structs versatile for grouping related data.

Traversal is the process of systematically visiting each element in a data structure exactly once. This fundamental operation is essential for accessing, processing, or analyzing every element in an array, linked list, tree, or other data structure. It forms the basis for many algorithms including searching, sorting, and counting operations.

Both linear search and binary search are fundamental approaches to search operations. Linear search works on unsorted data by checking each element sequentially, while binary search requires sorted data and repeatedly divides the search interval in half, making it much faster for large datasets.

Linear search traverses sequentially through a list to locate a specific item. It examines each element one by one from the beginning until the target is found or the list ends. This simple approach works on any list but is less efficient than binary search for large, sorted datasets.