A k-ary heap is similar to a binary heap, but non-leaf nodes have k children instead of 2 children.

1. Write the formula to get the children of a node i and the parent of a node i.

2. What is the height of a k-ary heap, write it in terms of k and n.

3. Modify the binary heap functions Heapify, Extract, Increase Key and Insert to work on a k-ary heap.(Provide the pseudo code).

4. Provide the runtime of your algorithms.

5. What are the cases when it is better to use a k-ary heap than a binary heap.