Rotation is a common balancing technique used in binary search trees. It involves reorganizing the nodes in the tree to maintain balance, ensuring that the height of the tree is minimized, and search operations remain efficient.

The Fibonacci sequence appears in the arrangement of planetary orbits, where the ratio of the orbital periods of planets often corresponds to Fibonacci numbers. This phenomenon is known as Bode's law, highlighting the connection between mathematics and celestial patterns.

The brute-force approach to finding the Longest Palindromic Substring works by systematically checking all possible substrings of the given string and identifying the longest palindrome among them. This method has a quadratic time complexity.

Topological sorting is applied to schedule courses in a curriculum with prerequisites. It guarantees that prerequisite courses are scheduled before any course that depends on them, ensuring students take foundational courses before advanced ones.

Binary search can lead to unpredictable behavior when applied to non-sorted arrays. Without the assurance of sorted elements, the algorithm may yield incorrect results or even result in infinite loops.

When attempting to remove an element from an empty queue, the operation is usually silently ignored. This is because there are no elements in the queue, and there is nothing to remove.

The Last In, First Out (LIFO) principle in stacks means that the last element added is the first one to be removed. This principle is essential for operations like push (adding an element to the stack) and pop (removing the last added element).

Linear search can be applied to non-numeric data types by comparing elements using equality. Whether the data is numeric or non-numeric, the key is to determine equality between the search element and the elements in the array. Linear search doesn't rely on the numeric nature of the data; it only requires a condition for equality comparison, making it applicable to a wide range of data types.

In a priority queue, elements are arranged for retrieval based on a specific priority assigned to each element. The element with the highest priority is retrieved first. This ensures that higher-priority elements take precedence over lower-priority ones.

Bellman-Ford algorithm can handle graphs with variable edge weights and detect negative weight cycles. It is capable of handling graphs with both positive and negative edge weights, making it suitable for a wider range of scenarios compared to some other algorithms.