Information is present in the screenshot and below. Based on that need help in solving the code for this problem in python. The time complexity has to be as less as possible (nlogn or n at best, no n^2). Apply greedy algorithm. Include and use necessary libraries and packages. Make sure ALL test cases return expected outputs by providing output screenshots. Output FormatThe output contains one line with a single integer: the minimum instability you can achieve modulo 10^9 + 7.Sample Input 02 1 12343Sample Output 030Sample Input 12 2 2142151Sample Output 140Sample Input 22 5 64670132061622Sample Output 2214The actual code"""This function solves a test case.Parameters:l : int - # of length cutting points of quatrum clusterw : int - # of width cutting points of quatrum clusterd : int - # of depth cutting points of quatrum clusterlength_costs : array-like - list of length cutting point instability factorswidth_costs : array-like - list of width cutting point instability factorsdepth_costs : array-like - list of depth cutting point instability factorsReturns:An integer indicating the smallest attainable instability after cutting the cluster down to 1 x 1 x 1 cubes"""def solve(l,w,d,length_costs,width_costs,depth_costs): MOD = int(1e9 + 7) # TODOl,w,d = list(map(int,input().split(" ")))length_costs = [int(input()) for i in range(l)]width_costs = [int(input()) for i in range(w)]depth_costs = [int(input()) for i in range(d)]print(solve(l,w,d,length_costs,width_costs,depth_costs)) If we make the first cut along the first length cutting point, the instability increases by 1 multiplied by thenumber of section being cut through. Since this is our first cut, the only section is the entire cluster itself. Afterthe cut, there are now two sections, lengthwise.If we make another cut along the length, this is still only cutting through one segment since this cut will beparallel to the previous cut, and thus will also only cut through one section of the cluster. However, consider ifwe cut through the first width cutting point. Since this cut is orthogonal to the initial cut, we are now cuttingthrough 2 sections of the cluster. Thus, our instability increases by 1 x 2, where 1 is the instability factor ofthe first width cutting point, and 2 is the number of sections we are cutting through.At this point, using one of the length cutting points will cut through 2 sections, since we already cut throughone of the width cutting points. Likewise, using a width cutting point will cut through 2 sections since wealready cut through one of the length cutting points. Consider, however, if we cut using the first depth cuttingpoint. This now passes through 4 sections, since the cross section was cut into two sections lengthwise, andtwo sections widthwise, yielding a total of 4 sections.You want to cut this entire cube into L W D cubes of size 1 x 1 x 1. Find the minimum instability indexattainable. Since this number can be very large, print it modulo 10⁹ + 7.Input FormatInput begins with a line containing three space-separated integers: L – 1, W – 1, and D – 1, indicating thenumber of length, width, and depth cutting points of the quatrum cluster respectively.L - 1 lines follow, the ith of which contains I1,, the instability factor of the ith length cutting point.W - 1 lines follow, the ith of which contains I2,;, the instability factor of the ith width cutting point.D - 1 lines follow, the ith of which contains I3,;, the instability factor of the ith depth cutting point.Constraints1 ≤ L, W, D≤ 1000010 ≤ I1,i, I2,i, I3,i ≤ 10⁹ Algo-Man and his students, belonging to the Class of '25, while studying algorithms and complexity,accidentally stumbled upon a polynomial time algorithm to one of the illustrious NP-Complete problems. Thiscaused a Quatro Tunnel to appear in their classroom and Algo-Man and his class were sucked into the QuatroRealm. This is a realm where only excellence exists, and if you are deemed inferior by the fabric of existence inthis realm, it wilt halt your ontological inertia and you will cease to exist.Seeking to escape this realm of excellence, Algo-Man and his students are now hatching up a plan to escapeback into their reality. They are able to find the remains of a time and space travelling machine known as theTARDIS (Time And Relative Dimension In Space) and are seeking to repair it to get back to their world.One of the components in need of repair is the energy core of the TARDIS. Algo-Man has determined that oneof the cracked quatrum clusters nearby can be broken down and fed to the TARDIS' energy core.A quatrum cluster is a rectangular prism in dimensions L x W x D. Additionally, due to their inherentperfection, quatrum clusters always have integral dimensions. The TARDIS only accepts 1 x 1 x 1 cubes.Algo-Man has determined that the optimal cutting points of the quatrum clusters is at the integer markers.Using the spare equipment in the TARDIS, Algo-Man has identified the instability factor of each of the cuttingpoints.When cutting across the length of the cluster, there are L 1 cutting points. The ith of these has aninstability factor of I1,i.When cutting across the width of the cluster, there are W- 1 cutting points. The ith of these has aninstability factor of I2,i.When cutting across the depth of the cluster, there are D - 1 cutting points. The ith of these has aninstability factor of I3,i.When cutting through one of the designated cutting points, this increases the instability of the cluster. Theinstability increases by the instability factor multiplied by the sections of the cluster being cut through.Take for example a 4 x 4 x 4 cluster. The instability factors of the length cutting points is 1, 2, 3. Theinstability factors of the width cutting points is 1, 3, 5. The instability factors of the depth cutting points is4, 1, 2.

Sort Instability Factors: Sort the instability factors of each dimension's cutting points in…

Answered: Information is present in the…

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

See similar textbooks

Related questions

Question

Information is present in the screenshot and below. Based on that need help in solving the code for this problem in python. The time complexity has to be as less as possible (nlogn or n at best, no n^2). Apply greedy algorithm. Include and use necessary libraries and packages. Make sure ALL test cases return expected outputs by providing output screenshots.

Output Format
The output contains one line with a single integer: the minimum instability you can achieve modulo 10^9 + 7.

Sample Input 0
2 1 1
2
3
4
3

Sample Output 0
30

Sample Input 1
2 2 2
1
4
2
1
5
1

Sample Output 1
40

Sample Input 2
2 5 6
4
6
7
0
1
3
2
0
6
1
6
2
2

Sample Output 2
214

The actual code

"""
This function solves a test case.

Parameters:
l : int - # of length cutting points of quatrum cluster
w : int - # of width cutting points of quatrum cluster
d : int - # of depth cutting points of quatrum cluster
length_costs : array-like - list of length cutting point instability factors
width_costs : array-like - list of width cutting point instability factors
depth_costs : array-like - list of depth cutting point instability factors

Returns:
An integer indicating the smallest attainable instability after cutting the
cluster down to 1 x 1 x 1 cubes
"""
def solve(l,w,d,length_costs,width_costs,depth_costs):
MOD = int(1e9 + 7)
# TODO

l,w,d = list(map(int,input().split(" ")))
length_costs = [int(input()) for i in range(l)]
width_costs = [int(input()) for i in range(w)]
depth_costs = [int(input()) for i in range(d)]

print(solve(l,w,d,length_costs,width_costs,depth_costs))

If we make the first cut along the first length cutting point, the instability increases by 1 multiplied by the
number of section being cut through. Since this is our first cut, the only section is the entire cluster itself. After
the cut, there are now two sections, lengthwise.
If we make another cut along the length, this is still only cutting through one segment since this cut will be
parallel to the previous cut, and thus will also only cut through one section of the cluster. However, consider if
we cut through the first width cutting point. Since this cut is orthogonal to the initial cut, we are now cutting
through 2 sections of the cluster. Thus, our instability increases by 1 x 2, where 1 is the instability factor of
the first width cutting point, and 2 is the number of sections we are cutting through.
At this point, using one of the length cutting points will cut through 2 sections, since we already cut through
one of the width cutting points. Likewise, using a width cutting point will cut through 2 sections since we
already cut through one of the length cutting points. Consider, however, if we cut using the first depth cutting
point. This now passes through 4 sections, since the cross section was cut into two sections lengthwise, and
two sections widthwise, yielding a total of 4 sections.
You want to cut this entire cube into L W D cubes of size 1 x 1 x 1. Find the minimum instability index
attainable. Since this number can be very large, print it modulo 10⁹ + 7.
Input Format
Input begins with a line containing three space-separated integers: L – 1, W – 1, and D – 1, indicating the
number of length, width, and depth cutting points of the quatrum cluster respectively.
L - 1 lines follow, the ith of which contains I1,, the instability factor of the ith length cutting point.
W - 1 lines follow, the ith of which contains I2,;, the instability factor of the ith width cutting point.
D - 1 lines follow, the ith of which contains I3,;, the instability factor of the ith depth cutting point.
Constraints
1 ≤ L, W, D≤ 100001
0 ≤ I1,i, I2,i, I3,i ≤ 10⁹

Algo-Man and his students, belonging to the Class of '25, while studying algorithms and complexity,
accidentally stumbled upon a polynomial time algorithm to one of the illustrious NP-Complete problems. This
caused a Quatro Tunnel to appear in their classroom and Algo-Man and his class were sucked into the Quatro
Realm. This is a realm where only excellence exists, and if you are deemed inferior by the fabric of existence in
this realm, it wilt halt your ontological inertia and you will cease to exist.
Seeking to escape this realm of excellence, Algo-Man and his students are now hatching up a plan to escape
back into their reality. They are able to find the remains of a time and space travelling machine known as the
TARDIS (Time And Relative Dimension In Space) and are seeking to repair it to get back to their world.
One of the components in need of repair is the energy core of the TARDIS. Algo-Man has determined that one
of the cracked quatrum clusters nearby can be broken down and fed to the TARDIS' energy core.
A quatrum cluster is a rectangular prism in dimensions L x W x D. Additionally, due to their inherent
perfection, quatrum clusters always have integral dimensions. The TARDIS only accepts 1 x 1 x 1 cubes.
Algo-Man has determined that the optimal cutting points of the quatrum clusters is at the integer markers.
Using the spare equipment in the TARDIS, Algo-Man has identified the instability factor of each of the cutting
points.
When cutting across the length of the cluster, there are L 1 cutting points. The ith of these has an
instability factor of I1,i.
When cutting across the width of the cluster, there are W- 1 cutting points. The ith of these has an
instability factor of I2,i.
When cutting across the depth of the cluster, there are D - 1 cutting points. The ith of these has an
instability factor of I3,i.
When cutting through one of the designated cutting points, this increases the instability of the cluster. The
instability increases by the instability factor multiplied by the sections of the cluster being cut through.
Take for example a 4 x 4 x 4 cluster. The instability factors of the length cutting points is 1, 2, 3. The
instability factors of the width cutting points is 1, 3, 5. The instability factors of the depth cutting points is
4, 1, 2.

Expert Solution

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

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.