True False f(n)=O(h(n)) and g(n)=O(h(n))(f(n)+g(n))=O(h(n)) f(n)=O(h(n)) and g(n)=O(h(n))(f(n)g(n))=O(h(n)) log2(n)=(log10(n)) Quicksort, whose average case runtime is O(nlogn) and worst case runtime is O(n2), is an optimal comparison sorting algorithm. Mergesort, whosse average case runtime and worst case runtime are both O(nlogn) is asymptically better than Quicksort. Mergesort will always run faster than Quicksort on the same input. A heap, when implemented using a linked data structure rather than an array, still has O(logn) runtime for inserting a new element. The following process for building a heap takes (nlogn) time: given an array of n arbitrarily-ordered elements, start with the element at position n/2 and call HEAPIFY-DOWN. Continue with the element at position n/21 and repeat until you reach the first element. Given k and n, both non-constant, klogn=O(kn). Given k and n, both non-constant, klogn=O(nlogk)