Consider the array t = [1, 2, 3, 4, 5, 8, 0 , 7, 6] of size n = 9, . a) Draw the complete tree representation for t. b) What is the index of the first leaf of the tree in Part a (in level order)? In general, give a formula for the index of the first leaf in the corresponding complete binary tree for an arbitrary array of size n. c) Redraw the tree from Part a after each call to fixheap, in Phase 1 of heapsort. Remember, the final tree obtained will be a maxheap. d) Now, starting with the final tree obtained in Part c, redraw the tree after each call to fixheap in Phase 2 of heap sort. For each tree, only include the elements from index 0 to index right (since the other elements are no longer considered part of the tree). e) For the given array t, how many calls to fixheap were made in Phase 1? How many calls to fixheap were made in Phase 2? f) In general , give a formula for the total number of calls to fixheap in Phase 1, when heapsort is given an arbitrary array of size n. Justify your answer. g) In general, give a formula for the total number of calls to fixheap in Phase 2,when heapsort is given an arbitrary array of size n. Justify your answer.
Consider the array t = [1, 2, 3, 4, 5, 8, 0 , 7, 6] of size n = 9, .
a) Draw the complete tree representation for t.
b) What is the index of the first leaf of the tree in Part a (in level order)? In general, give a formula for the index of the first leaf in the corresponding complete binary tree for an arbitrary array of size n.
c) Redraw the tree from Part a after each call to fixheap, in Phase 1 of heapsort. Remember, the final tree obtained will be a maxheap.
d) Now, starting with the final tree obtained in Part c, redraw the tree after each call to fixheap in Phase 2 of heap sort. For each tree, only include the elements from index 0 to index right (since the other elements are no longer considered part of the tree).
e) For the given array t, how many calls to fixheap were made in Phase 1? How many calls to fixheap were made in Phase 2?
f) In general , give a formula for the total number of calls to fixheap in Phase 1, when heapsort is given an arbitrary array of size n. Justify your answer.
g) In general, give a formula for the total number of calls to fixheap in Phase 2,when heapsort is given an arbitrary array of size n. Justify your answer.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 3 images
