Show the result of inserting 10, 12, 1, 14, 6, 5, 8, 15, 3, 9, 7, 4, 11, 13, and 2, one at a time, into an initially empty binary heap. b. Show the result of using the linear-time algorithm to build a binary heap using the same input. Show the result of performing three deleteMin operations in the heap of the previous exercise.

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

we can all learn from our past mistakes because we all have different ways of learning different types of techniques. my way may or may not another classmate remember and have the repetition to acknowledge such standard. such as remembering acronyms. using abbreviations to us remember keep things in order in our memory. this us figure out what comes next in the sequence. if so, what we have is a sentence of just letters all in caps. we either know the meaning or have no idea what it stands for. most of the time we know the meaning and context. but most of us who don't know, should learn by having a quick glance at what needs to be remembered. such as repetition in the memory for acronyms. one way that me, is the fact that i'm always doing math and english assignments. so we have to remember specific meanings such as soapstone for documents, such as citing correctly. or pemdas for doing the equations correctly, even if it's the super long way. this works for everyone. you just have to find what works for you by practicing and repetition daily.