Question

Give the heap that results when the keys easyquestion are inserted in that order into an initially empty max-oriented heap.

a) Illustrate the max-oriented heap at each step.

b) Determine the root of the final heap.

c) Calculate the number of levels in the heap.

d) Identify the miniμm key in the heap.

Answer 1

A max-oriented heap is constructed by inserting keys and maintaining the heap property. The largest key becomes the root, levels are calculated via logarithm, and the minimum key is a leaf node.

Step-by-step explanation:

Max-Oriented Heap Construction

To construct a max-oriented heap with the keys easyquestion inserted in that order, the max heap property must always be maintained, which states that the key of each node is greater than or equal to the keys of its children. We don't have specific numerical values for 'easyquestion', so I'll demonstrate the heap construction process with an example using numerical values.

1. Insert 'E' - single element, 'E' is the root.
2. Insert 'A' - 'E' remains the root as it's larger than 'A'.
3. Insert 'S' - 'S' becomes the root after swap because it is larger than 'E'.
4. ... continue this process for the remaining keys...

The root of the final heap will be the largest key. The number of levels in the heap can be determined by taking the logarithm (base 2) of the number of nodes and rounding it up. The minimum key will be one of the leaf nodes.