A d-ary heap is like a binary heap, but (with one possible exception) non-leafnodes have d children instead of 2 children. a. How would you represent a d-ary heap in an array?b. What is the height of a d-ary heap of n elements in terms of n and d?c. Give an efficient implementation of EXTRACT-MAX in a d-ary max-heap. Analyzeits running time in terms of d and n. d. Give an efficient implementation of INSERT in a d-ary max-heap. Analyze itsrunning time in terms of d and n. e. Give an efficient implementation of INCREASE-KEY. A; i; k/, which flags anerror if k < AOEi , but otherwise sets AOEi D k and then updates the d-ary maxheapstructure appropriately. Analyze its running time in terms of d and n.