Could someone please help me with these questions about d-ary heaps? I'm a bit confused on how to solve them. If you could explain with steps, I would be very thankful! Heaps in which non-leaf nodes (except possibly the right-most one) have d children.

a.How would you represent a d-ary heap in an array? Answer this question by:

• Giving an expression for J-th-Child(i,j):the index of the j-th child as a function of the index i of the given node, and the child index j within the given node.
• Giving an expression for D-Ary-Parent(i):the index of the parent of a node as a function of its index i within the array.

Checking that your solution works by showing that D-Ary-Parent(J-th-Child(i,j)) = i (when you start at node i, and apply your formula to go to a child, and then your other formula to go back to the parent, you must end up back at i).

b.What is the height of a d-ary heap of n elements as a function of n andd? By what factor does this height differ from that of a binary heap of n elements?

c. Give an efficient implementation of Extract-Max in a d-ary max-heap. (Hint: How would you modify the existing code?) Analyze the running time of your implementation in terms of n and d. (Note that d must be part of your expression even if it occurs in a constant term.)

d. Give an efficient implementation of Insert in a d-ary max-heap. Analyze its running time in terms of n and d.