When the load factor exceeds a certain threshold, the hash table is typically resized and all existing entries are rehashed to maintain efficient access times.

A poor hash function can lead to higher collision rates, which degrades the performance of the hash table.

The hash function converts keys into indices, allowing for efficient data retrieval in the hash table.

The hash function converts keys into hash codes, which are then used to determine the index in the hash table where the corresponding value is stored.

In a max-heap, the value of a parent node must be greater than or equal to its children, so the maximum value of the children can be 20.

The height of a max-heap is log(n) because it is a complete binary tree, where n is the number of elements.

In a max-heap, the parent node is always greater than or equal to its child nodes.

In a max-heap, the root node is always the largest element, as the heap property ensures that each parent node is greater than or equal to its children.

In a max-heap, the parent node is always greater than or equal to its children, maintaining the max-heap property.

In a max-heap, each parent node must be greater than or equal to its children to maintain the heap property.

In a min-heap, the parent node is always less than or equal to its children, ensuring the minimum element is at the root.

In a min-heap, the root is the smallest element, and all parent nodes are smaller than their children.

In a min-heap, the parent node is always less than or equal to its children, ensuring that the smallest element is at the root.

When the heap property is violated, the heap is restructured to restore the property, typically through a process called 'heapify'.

When the maximum element is removed, the last element is placed at the root, and then the heap is restructured to maintain the heap property.

The priority of elements in a priority queue can be determined by a custom comparator function that defines how priorities are assigned.

Dijkstra's algorithm uses a priority queue to efficiently select the next vertex with the smallest distance from the source.

A cycle in a graph is defined as a path that starts and ends at the same vertex without repeating any edges.

The 'Union by Rank' optimization keeps track of the height of trees to minimize depth, ensuring that the smaller tree is always added under the root of the larger tree.

The 'Union by Rank' technique merges two sets based on their depth, ensuring that the smaller tree is always added under the root of the larger tree to keep the overall tree shallow.

The 'Union' operation combines two sets into one in the Disjoint Set Union data structure.

Union by rank refers to the strategy of combining two sets by attaching the smaller tree under the root of the larger tree, thus keeping the overall tree shallow.

The Disjoint Set Union is commonly used for detecting cycles in a graph, particularly in algorithms like Kruskal's for finding the minimum spanning tree.

Hash tables provide average-case O(1) time complexity for lookups, making them preferable when quick access is needed.

When the load factor exceeds a certain threshold, the hash table is typically resized to maintain efficient access times.

Priority queues are often used in scheduling systems to manage tasks based on their priority.

Hash tables allow for average-case constant time complexity O(1) for data retrieval, making them ideal for database indexing.

A common strategy for resizing a hash table is to double its size when the load factor exceeds a certain threshold to maintain performance.

Hash tables can require more memory than arrays due to the need for additional space to handle collisions and maintain performance.

Hash tables can require more memory due to the need for additional space to handle collisions and maintain performance.