The worst-case time complexity of the bubble sort algorithm is O(n^2), where n represents the number of elements in the array. This means that the time taken to sort the array increases quadratically with the number of elements. Bubble sort repeatedly iterates through the array, comparing adjacent elements and swapping them if they are in the wrong order. Due to its nested loops, bubble sort has poor performance, especially for large datasets, making it inefficient for real-world applications.

The time complexity of the dynamic programming approach for finding the Longest Common Subsequence (LCS) is O(n^2), where 'n' and 'm' are the lengths of the input strings. This is achieved by filling up a 2D table in a bottom-up manner.

Quick Sort's behavior in an array with identical elements is problematic as it often results in uneven partitions, leading to poor performance. To improve performance, a modification could involve implementing a pivot selection strategy that chooses a pivot intelligently, such as median-of-three or random pivot selection, to mitigate the issue of uneven partitions.

Quick Sort divides the array by selecting a pivot, placing smaller elements to its left and larger elements to its right. This process is repeated recursively for the sub-arrays, leading to a sorted result.

The first two numbers of the Fibonacci sequence are 0 and 1. These are the initial values used to generate subsequent numbers in the sequence.

A linked list consists of nodes. Each node contains data and a reference (or link) to the next node in the sequence. Unlike arrays, linked lists do not have a fixed size, allowing for dynamic memory allocation.

Priority Queue is commonly used in implementing Dijkstra's algorithm. It allows efficient retrieval of the node with the smallest tentative distance, optimizing the algorithm's overall time complexity.

To optimize the vending machine's algorithm for giving change efficiently, you would apply the concepts of the coin change problem by implementing dynamic programming. This involves precalculating the optimal number of coins for various amounts and using this information to quickly determine the most efficient way to provide change for each transaction. The dynamic programming approach ensures that the vending machine consistently dispenses the minimum number of coins required for change.

In Kruskal's algorithm, a Disjoint Set, also known as Union-Find, is commonly used to efficiently determine if adding an edge will create a cycle in the graph. This data structure helps in maintaining disjoint sets and quickly checking whether two vertices belong to the same set, enabling the algorithm to avoid adding edges that would create cycles.

Edit Distance is crucial in spell checking, where it helps identify and correct misspelled words by calculating the minimum number of operations (insertions, deletions, substitutions) required to transform one word into another.