A poor hash function can lead to higher collision rates, which degrades the performance of the hash table and increases the time complexity for operations.

'Union by rank' optimization involves always attaching the smaller tree under the larger tree to keep the overall tree height minimized.

The average time complexity for searching an element in a hash table is O(1) due to the direct access provided by the hash function.

A poor hash function can lead to more collisions, which decreases the performance of the hash table due to longer search times.

An ideal load factor is typically around 0.5, balancing space and time efficiency while minimizing collisions.

When n elements are added to a Disjoint Set Union, the initial state is that all elements are in separate sets.

When first created, each element in a Disjoint Set Union is its own set, meaning they are all disjoint.

The main advantage of using path compression is that it flattens the structure of the tree, leading to faster future queries by reducing the depth of the trees.

The main advantage of using path compression in the 'Find' operation is that it reduces the time complexity of future operations by flattening the structure of the tree.

The main advantage of using union by rank is that it minimizes the height of the trees, leading to more efficient 'Find' operations.

Open addressing can lead to clustering, where a group of consecutive slots are filled, which can degrade performance during searches and insertions.

The maximum height of a binary heap is log n, as it is a complete binary tree.

The maximum number of elements in a binary heap of height h is 2^(h+1) - 1, as it is a complete binary tree.

A binary heap allows for faster deletion of the maximum (or minimum) element compared to an unsorted array, where deletion would take O(n) time.

Fibonacci heaps provide a faster decrease-key operation, which is beneficial in algorithms like Dijkstra's.

The primary advantage of a priority queue is that elements are processed based on their priority rather than their order of arrival.

The primary differences include that binary heaps are complete binary trees used for priority queues, while binary search trees are not necessarily complete and are used for searching.

A hash function maps data to a fixed size, allowing for efficient indexing in a hash table.

The primary purpose of the Disjoint Set Union (Union Find) data structure is to manage a collection of disjoint sets, allowing for efficient union and find operations.

A priority queue is used to manage tasks based on their priority, allowing for efficient retrieval of the highest (or lowest) priority task.

The hash function's purpose is to map keys to indices in the hash table, allowing for efficient data retrieval.

A poor hash function can lead to more collisions, which degrades the performance of the hash table and increases the time complexity for operations.

The 'decrease key' operation reduces the value of a key and may require re-heapifying to maintain the heap property.

Performing a 'Union' operation on two sets A and B merges them into one set, effectively combining their elements.

The 'Union' operation creates a new set containing elements from both sets, effectively merging them into a single set.

Performing a 'Union' operation on two sets that are already connected leaves the sets unchanged.

If two sets are already connected, performing a 'Union' operation on them will leave the sets unchanged, as they are already part of the same set.

Heap sort transforms the array into a max-heap and then repeatedly extracts the maximum element, resulting in a sorted array.

Performing a union operation on two sets A and B merges them into one set, effectively combining their elements.

The space complexity of a binary heap storing n elements is O(n) because it needs to store all n elements.