Finding the Longest Common Subsequence (LCS) has significant applications in tasks such as genome sequencing, where identifying common elements in sequences is vital, and version control systems, where it helps track changes in code or documents.

BFS guarantees finding the shortest path in an unweighted graph due to its Breadth-First approach. This means it explores all nodes at the current depth before moving on to nodes at the next depth level, ensuring that the shortest path is found first.

The time complexity of merge sort in the worst-case scenario is O(n log n), making it an efficient algorithm for sorting large datasets. This complexity arises from its divide-and-conquer approach.

Merge sort can efficiently handle the sorting of linked lists. Unlike array-based sorting algorithms, merge sort's divide-and-conquer approach is well-suited for linked lists as it involves splitting and merging without the need for random access to elements. This makes it a preferred choice for sorting linked structures.

The Knapsack Problem is distinct as it specifically aims to maximize the total value of selected items within certain constraints, making it a constrained optimization problem. Other optimization problems may have different objectives or constraints.

Radix sort is generally faster than comparison-based sorting algorithms for sorting small integers because it takes advantage of the fixed-size nature of integers and avoids comparisons.

In a static array, the size is fixed at compile time, while in a dynamic array, the size can be changed at runtime to accommodate varying data requirements.

A doubly linked list contains nodes that have two pointers: one pointing to the next node in the sequence and another pointing to the previous node. This allows for easy traversal in both directions.

Bubble sort performs well when the list is presorted or nearly sorted because it requires fewer comparisons to complete. In a nearly sorted list, many elements are already in their correct positions, reducing the number of swaps needed, making the algorithm more efficient in such scenarios.

The resulting linear ordering of vertices in topological sorting maintains the property of preserving edge direction. It ensures that for every directed edge (u, v), vertex 'u' comes before 'v' in the ordering, representing a valid sequence of dependencies.

The main idea behind Insertion Sort is to build the sorted array one element at a time. It starts with the first element and iteratively compares and inserts the current element into its correct position in the already sorted subarray. This process continues until the entire array is sorted.

Regular expression matching involves searching for patterns in text. Regular expressions are powerful tools for pattern matching and manipulation in strings.