Consider a billboard that consists of n vertical panels of width 1 and varying integer heights, hanged down and held by a horizontal roller from the top. The panel i has a height hi. For the objective of placing two banners, it is allowed to move each panel up by any integer length using the roller. Once the necessary moves are completed, you may place two banners completely inside of the panels. Based on the above description, what is the maximum total area that you can provide for the two posters? Input The first line of input contains one integer n (1

Computer Networking: A Top-Down Approach (7th Edition)
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Consider a billboard that consists of n vertical
panels of width 1 and varying integer heights,
hanged down and held by a horizontal roller
from the top. The panel i has a height hi.
hi
For the objective of placing two banners, it is
allowed to move each panel up by any integer
length using the roller. Once the necessary
moves are completed, you may place two
banners completely inside of the panels.
Based on the above description, what is the
maximum total area that you can provide for the
two posters?
Input
The first line of input contains one integer n (1<n<1000) – the number of vertical panels.
The second line of input contains n integers h,h.,.,h. (1<h<1000) – the heights of the n vertical
panels.
Output
Print a single integer – the maximum total area the two posters can cover together.
Example 1:
Input:
2 2 3 5 4 5
Output: 18
6
Note
In this sample test, we can choose two
areas:12 and 6 as illustrated in the image.
12
Example 2:
Input:
4 5 3 4 3
Output: 17
a) Design a brute-force algorithm to solve this problem using a (Pseudocode) and find its
complexity.
b) Implement your brute-force algorithm using Python
of 7 vertical panels with different heights to demonstrate your solution.
c) Can a more efficient solution be designed? If yes, demonstrate it using Pseudocode
and analyze its complexity. .
d) Provide a brief report (250 words) that explains the difference between the two
solution.
and invent an example
Transcribed Image Text:Consider a billboard that consists of n vertical panels of width 1 and varying integer heights, hanged down and held by a horizontal roller from the top. The panel i has a height hi. hi For the objective of placing two banners, it is allowed to move each panel up by any integer length using the roller. Once the necessary moves are completed, you may place two banners completely inside of the panels. Based on the above description, what is the maximum total area that you can provide for the two posters? Input The first line of input contains one integer n (1<n<1000) – the number of vertical panels. The second line of input contains n integers h,h.,.,h. (1<h<1000) – the heights of the n vertical panels. Output Print a single integer – the maximum total area the two posters can cover together. Example 1: Input: 2 2 3 5 4 5 Output: 18 6 Note In this sample test, we can choose two areas:12 and 6 as illustrated in the image. 12 Example 2: Input: 4 5 3 4 3 Output: 17 a) Design a brute-force algorithm to solve this problem using a (Pseudocode) and find its complexity. b) Implement your brute-force algorithm using Python of 7 vertical panels with different heights to demonstrate your solution. c) Can a more efficient solution be designed? If yes, demonstrate it using Pseudocode and analyze its complexity. . d) Provide a brief report (250 words) that explains the difference between the two solution. and invent an example
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