Problem Statement: We can store k stacks in a single array if we use the data structure suggested in Figure 1 shown below, for the case k = 3. We push and pop from each stack as suggested in connection with Figure 2 below. However, if pushing onto stack i causes TOP(i) to equal BOTTOM(i – 1), we first move all the stacks so that there is an appropriate size gap between each adjacent pair of stacks. For example, we might make the gaps above all stacks equal, or we might make the gap above stack i proportional to the current size of stack i (on the theory that larger stacks are likely to grow sooner, and we want to postpone as long as possible the next reorganization). 1 stack 1 3 stack 2 bottom

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
icon
Related questions
Question

Please solve the problem and show the execution step by step with output result.

Problem Statement: We can store k stacks in a single array if we use the data structure suggested
in Figure 1 shown below, for the case k = 3. We push and pop from each stack as suggested in
connection with Figure 2 below. However, if pushing onto stack i causes TOP(i) to equal
BOTTOM(i – 1), we first move all the stacks so that there is an appropriate size gap between each
adjacent pair of stacks. For example, we might make the gaps above all stacks equal, or we might
make the gap above stack i proportional to the current size of stack i (on the theory that larger
stacks are likely to grow sooner, and we want to postpone as long as possible the next
reorganization).
1
stack 1
3
stack 2
bottom
1
2
stack 3
3
top
stackspace
Figure 1
top
first element
second element
maxlength
last element
elements
Figure 2
1. On the assumption that there is a procedure reorganize to call when stacks collide, write
code for the five stack operations.
2. On the assumption that there is a procedure MakeNewTops that computes newtop[i], the
"appropriate" position for the top of stack i, for 1 <i<k, write the procedure reorganize.
Hint. Note that stack i could move up or down, and it is necessary to move stack i before
stack j if the new position of stack j overlaps the old position of stack i. Consider stacks 1,
2,..., k in order, but keep a stack of "goals," each goal being to move a particular stack.
If on considering stack i, we can move it safely, do so, and then reconsider the stack whose
number is on top of the goal stack. If we cannot safely move stack i, push i onto the goal
stack.
3. What is an appropriate implementation for the goal stack in (2)? Do we really need to keep
it as a list of integers, or will a more succinct representation do?
4. Implement MakeNewTops in such a way that space above each stack is proportional to the
current size of that stack.
The implementation of this stack management software should be as structured as possible.
Transcribed Image Text:Problem Statement: We can store k stacks in a single array if we use the data structure suggested in Figure 1 shown below, for the case k = 3. We push and pop from each stack as suggested in connection with Figure 2 below. However, if pushing onto stack i causes TOP(i) to equal BOTTOM(i – 1), we first move all the stacks so that there is an appropriate size gap between each adjacent pair of stacks. For example, we might make the gaps above all stacks equal, or we might make the gap above stack i proportional to the current size of stack i (on the theory that larger stacks are likely to grow sooner, and we want to postpone as long as possible the next reorganization). 1 stack 1 3 stack 2 bottom 1 2 stack 3 3 top stackspace Figure 1 top first element second element maxlength last element elements Figure 2 1. On the assumption that there is a procedure reorganize to call when stacks collide, write code for the five stack operations. 2. On the assumption that there is a procedure MakeNewTops that computes newtop[i], the "appropriate" position for the top of stack i, for 1 <i<k, write the procedure reorganize. Hint. Note that stack i could move up or down, and it is necessary to move stack i before stack j if the new position of stack j overlaps the old position of stack i. Consider stacks 1, 2,..., k in order, but keep a stack of "goals," each goal being to move a particular stack. If on considering stack i, we can move it safely, do so, and then reconsider the stack whose number is on top of the goal stack. If we cannot safely move stack i, push i onto the goal stack. 3. What is an appropriate implementation for the goal stack in (2)? Do we really need to keep it as a list of integers, or will a more succinct representation do? 4. Implement MakeNewTops in such a way that space above each stack is proportional to the current size of that stack. The implementation of this stack management software should be as structured as possible.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 1 images

Blurred answer
Knowledge Booster
Stack
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Database System Concepts
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education