Answer:
Step-by-step explanation:
A)
10 10 10 1 1
/ / \ --> / \ / \
12 12 1 12 10 12 10
/
14
1 1 1 1
/ \ / \ / \ / \
12 10 --> 6 10 6 10 --> 6 5
/ \ / \ / \ / / \ /
14 6 14 12 14 12 5 14 12 10
1 1 1 1
/ \ / \ / \ / \
6 5 6 5 6 5 --> 3 5
/ \ / \ / \ / \ / \ / \ / \ / \
14 12 10 8 14 12 10 8 14 12 10 8 6 12 10 8
/ / \ / \
15 15 3 15 14
After inserting all 1
/ \
3 2
/ \ / \
6 7 5 4
/ \ / \ / \ / \
15 14 12 9 10 11 13 8
b)
First level build : 10
/ \
12 1
/ \ / \
14 6 5 8
/ \ / \ / \ / \
15 3 9 7 4 11 13 2
Heap bottom level: 10
/ \
12 1
/ \ / \
3 6 4 2
/ \ / \ / \ / \
15 14 9 7 5 11 13 8
Heap next level up: 10
/ \
3 1
/ \ / \
12 6 4 2
/ \ / \ / \ / \
15 14 9 7 5 11 13 8
Final heap: 1
/ \
3 2
/ \ / \
12 6 4 8
/ \ / \ / \ / \
15 14 9 7 5 11 13 10
c)
Duing the first time,
First, assume the last element, the 8, is at the root and bubble down.
Then, assume the last element, the 13, is at the root and bubble down.
Then, assume the last element, the 11, is at the root and bubble down.
Final heap:
4
/ \
6 5
/ \ / \
13 7 10 8
/ \ / \ /
15 14 12 9 11
In the next iteration,
First, assume the last element, the 10, is at the root and bubble down.
Then, assume the last element, the 13, is at the root and bubble down.
Then, asssume the last element, the 11, is at the root and bubble down.
So, after performing all operations, the heap looks like below:
4
/ \
6 5
/ \ / \
12 7 10 8
/ \ / \ /
15 14 9 13 11