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.

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.

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.

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.

The best-case time complexity of Insertion Sort is O(1). This occurs when the input array is already sorted, and the algorithm needs only to check each element once.

Radix sort is often used to sort data represented in the hexadecimal numeric base. It operates by processing digits from the least significant digit to the most significant digit.

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.

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.

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.

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.