Prove the following statements regarding the maximum item in

Prove the following statements regarding the maximum item in a binary heap (don’t have to show a formal proof but, at least, you need to clearly justify your answers):

a)Every leaf must be examined to find it.

Solution

A binary heap is a complete binary tree which satisfies the heap ordering property the ordering can be one of the two types the min-heap property:the value of each node is greater than or equal to its value of the parent with the minimum value at the root

In a heap the highest (or lowest) priority element is always stored at the root, hence the name \"heap\". A heap is not a sorted structure and can be regarded as partially ordered. As you see from the picture, there is no particular relationship among nodes on any given level, even among the siblings.

Since a heap is a complete binary tree, it has a smallest possible height - a heap with N nodes always has O(log N) height.

A heap is useful data structure when you need to remove the object with the highest (or lowest) priority. A common use of a heap is to implement a priority queue.