1. Analysis of d-ary heaps (problem 6-2 in the text). A d-ary heap is like a binary heap, but (with one possible exception) non-leaf nodes 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. Analyze its running time in terms of d and n. (d) Give an efficient implementation of Insert in a d-ary max-heap. Analyze its running time in terms of d and n. (e) Give an efficient implementation of Increase-Key(A; i; k), which flags an error if k < A[i], but otherwise sets A[i] = k and then updates the d-ary max-heap structure appropriately. Analyze its running time in terms of d and n. 1
