The patience sorting algorithm is inspired by the card game Solitaire. In this algorithm, the process of sorting is similar to organizing a deck of cards in the game of Solitaire.

The time complexity of the binary search algorithm on a sorted array is O(log n), where 'n' is the number of elements in the array. This logarithmic time complexity makes binary search highly efficient for large datasets.

The effectiveness of the A* search algorithm heavily depends on the heuristic function, which should be admissible (never overestimates) and consistent. The heuristic guides the search towards the goal efficiently, influencing the algorithm's ability to find the optimal path in various applications.

Neither Prim's nor Kruskal's algorithms are designed to find the shortest path between two specific vertices. They are specifically used for finding minimum spanning trees, which may not necessarily correspond to the shortest path between two vertices. Additional algorithms like Dijkstra's or Bellman-Ford are more suitable for shortest path problems.

Consistently selecting the smallest or largest element as the pivot in Quick Sort can lead to uneven partitions, causing the algorithm's performance to degrade to worst-case time complexity. To address this issue, adjustments such as choosing a pivot using a median-of-three strategy or random pivot selection can help improve partition balance and overall performance.

The worst-case time complexity of the naive pattern matching algorithm is O(m * n), where 'm' is the length of the pattern and 'n' is the length of the text. This is because, in the worst case, the algorithm may need to compare each character of the pattern with each character of the text.

Dijkstra's algorithm relies on the use of a priority queue to keep track of the shortest distances to each node efficiently. The priority queue ensures that nodes are processed in order of increasing distance, optimizing the exploration of the graph and helping in finding the shortest paths.

The time complexity of the dynamic programming approach for the longest common substring problem is O(nm), where 'n' and 'm' are the lengths of the input strings. The algorithm uses a table of size n x m to store intermediate results, leading to a quadratic time complexity.

The Knuth-Morris-Pratt Algorithm uses a prefix table or failure function to optimize the search process. This allows the algorithm to skip unnecessary comparisons by taking advantage of the information about the pattern's own structure.

The optimal substructure property in dynamic programming for the Knapsack Problem ensures that the solution to the overall problem can be constructed from optimal solutions to its overlapping subproblems, making it suitable for dynamic programming approaches.