Consider the following array.
0 1 2 3 4 5 6 7 8 9 10 +----+----+----+----+----+----+----+----+----+----+----+ | 7 | 12 | 5 | 27 | 2 | -8 | 17 | 15 | 4 | 9 | 13 | +----+----+----+----+----+----+----+----+----+----+----+ |
Viewed as a complete binary tree, the array looks like this:
7
/ \
/ \
/ \
/ \
/ \
/ \
12 5
/ \ / \
/ \ / \
/ \ / \
/ \ / \
27 2 -8 17
/ \ / \
/ \ / \
15 4 9 13
|
Apply the HeapSort algorithm to the array and show what the array/tree looks like at particular points in time. Specifically:
1. Phase 1 of HeapSort applies siftDown to each non-leaf node in the tree. Show what the array/tree looks like after each such application. (Your answer should include five trees.)
2. Each iteration of Phase 2 of HeapSort swaps the values in the root node and the last node that is still part of the max-heap built during Phase 1. (That last node is then no longer part of the max-heap.) Then it applies siftDown to the root. Show what the array/tree looks like after each of the ten iterations that are carried out during Phase 2.