CScD-320, Algorithms, Spring 2009
Assignment 8: Binary Heap — Key
Sahni, DSAAJ, Problem 13.9 (p. 515), initial data altered and expanded.
Consider the array theHeap = [-, 12, 8, 1, 4, 2, 13, 10, 16, 15, 5, 7, 6]. Note that Sahni has the
heap rooted at subscript [1].
a. Draw the corresponding complete binary tree.
Initial state:
12
8 1
4 2 13 10
16 15 5 7 6
b. Heapify the tree as a min heap by making appropriate use of the method of Program 13.4
[equivalent with the method covered in lecture]. [In other words, if using Program 13.4,
adjust for min heap versus max heap.] Show each step in tree format and show the final
result in both tree and array format.
Adjusting from 6 down:
12
8 1
4 2 6 10
16 15 5 7 13
Adjusting from 5 down:
12
8 1
4 2 6 10
16 15 5 7 13
Adjusting from 4 down:
12
8 1
4 2 6 10
16 15 5 7 13
Adjusting from 3 down:
12
8 1
4 2 6 10
16 15 5 7 13
Adjusting from 2 down:
12
2 1
4 5 6 10
16 15 8 7 13
Adjusting from 1 down:
1
2 6
4 5 12 10
16 15 8 7 13
[-, 1, 2, 6, 4, 5, 12, 10, 16, 15, 8, 7, 13]
Printed 2020/ 11 月/30 at 02:27 Page 1
