A d$-$ary heap is like a binary heap, but non$-$leaf nodes have d children instead of $2$ children. a$.$ How would you represent a d$-$ary heap in an array A$[0....($n$-1)]?$ 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$.$