A common way to implement a queue using an array is to use two pointers, one for enqueue at the end and one for dequeue at the beginning. Elements are shifted as needed to accommodate new elements and maintain the order of the queue.

Bubble sort's time complexity can be improved to O(n) by implementing certain optimizations. With optimized versions such as the flag-based check and other enhancements, the algorithm can achieve linear time complexity in scenarios where the array is already sorted or nearly sorted, making it more efficient in specific use cases.

In each iteration of the inner loop in selection sort, where 'i' is the current iteration, n - i comparisons are performed. This is because the inner loop looks for the minimum element in the unsorted portion and places it at the beginning, reducing the number of comparisons in subsequent iterations.

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.