Max Heap and Min Heap

Which of the following best describes the property of a max heap?

In a min heap, the root node always contains the largest element.

In a complete binary tree structured as a max heap, where is the maximum element located?

A min heap is a complete binary tree where the value of the parent node is always ______ than or equal to the value of its children.

What is a common property of both max and min heaps?

In a max heap, a child node can have a higher value than its parent node.

What is the primary difference between a max heap and a min heap in terms of the parent-child relationship?

In a ______ heap, the minimum element is always located at the root of the tree.

Which statement accurately describes how elements are organized in a max heap?

A binary search tree has the same properties and structure as a min heap.

What characteristic defines a 'complete' binary tree, which is a requirement for both max and min heaps?

In terms of the value of their nodes, a parent node in a max heap is always ______ than or equal to its children.

What is the significance of the root node in a min heap?

A heap can only be either a max heap or a min heap, not both simultaneously.

Why is it important for a heap to be a 'complete' binary tree?

For any node in a max heap, its value must be ______ than the value of each of its children.

Which of the following is NOT a characteristic of a min heap?

In a max heap, the parent node can contain a value equal to one of its child nodes.

If you're implementing a priority queue where you need to quickly retrieve the element with the highest priority, would you use a max heap or a min heap? Explain.

In a min heap, to maintain the heap property after inserting a new element, you might need to perform a process called ______.

Match the heap type with its property:

Which data structure ensures efficient retrieval of both maximum and minimum elements in $O(1)$ time?

Removing an element other than root from a max heap involves heapifying to restore max-heap property.

What is the typical time complexity to find the minimum element in a min-heap?

The operation to restore heap properties (max or min) after an insertion or deletion is called ______.

When inserting a new element in a max heap, where is it typically placed initially?

Heapsort can be implemented with either a max heap or a min heap.

What fundamental property of Complete Binary Trees enables heaps to function efficiently?

If you intend to sort elements in ascending order, it is best to utilize a ______ heap with the Heapsort algorithm.

What is the primary advantage to heaps over linked lists for priority queue implementation?

Max and min heaps cannot be implemented without the use of Complete Binary Trees.

What is the average time complexity for removing the smallest element from a Min Heap?

Dijkstra's shortest path algorithm uses a ______ to efficiently determine the next node to explore.

If you were to visualize a max heap, which direction does the element value generally increase?

In a min heap, the leaf nodes always contain the largest values.

How does min and max heap influence retrieval and insertion rates?

In a complete Min Heap, inserting an element that is smaller than root elements leads to a ______ operation.

The time complexity of the heapify operation is typically dependent on what factor of the heap's shape?

When we implement a heap using arrays for efficiency, the index of a node's left child can be calculated using: $2 * index + 1$, assuming 0-based indexing.