Using Figure 6.4 as a model, illustrate the operation of HEAPSORT on the array A = ¬5, 13, 2, 25, 7, 17, 20, 8, 4¬.
Answer to relevant QuestionsIllustrate the operation of MAX-HEAP-INSERT (A, 10) on the heap A = 15, 13, 9, 5, 12, 8, 7, 4, 0, 6, 2, 1. Use the heap of Figure 6.5 as a model for the HEAP-INCREASE-KEY call.Show that there is no comparison sort whose running time is linear for at least half of the n! input of length n. What about a fraction of 1/n of the inputs of length n? What about a fraction 1/2n?Show that the second smallest of n elements can be found with n + ⌈lg n⌉ - 2 comparisons in the worst case.Suggest how storage for elements can be allocated and deal located within the hash table itself by linking all unused slots into a free list. Assume that one slot can store a flag and either one element plus a pointer or two ...Show that the longest simple path from a node x in a red-black tree to a descendant leaf has length at most twice that of the shortest simple path from node x to a descendant leaf.
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