In this assignment we examine and manipulate a doubly-linked list structure of different types of train cars:
engines, freight cars, passenger cars, dining cars, and sleeping cars.
Each engine weighs 150 tons and has
power = 3,000 horsepower, freight cars hold different weights (depending on the contents of the car), and
all other cars weigh 50 tons.
Note that a train can have multiple engines that work together to drive the
train, and these engines can be positioned at the front, the back, or even in the middle of the train! Your
task for this assignment is to perform a variety of basic train yard operations to connect, disconnect, and
reconnect cars into trains in preparation for service. Please read through the entire handout before beginning
Train Statistics: Speed and Passenger Comfort
Your first task is to calculate the maximum speed of a specific train (a doubly-linked list of TrainCars) on
a 2% incline. A very clearly-written tutorial for this real-world problem is available here:
Overly simplified, the formula for the theoretical maximum relates the overall train weight, the combined
engine horsepower, and the slope incline:
total horsepower ∗ 550lb-feet
sec ∗ 3600sec
20lb tractive effort
1% grade ∗ 2% grade ∗ 5280 feet
mile ∗ total weight in tons
Let’s look at an example, using the provided ASCII art printout of a TrainCar linked list:
—100 ——101 ——102 ——103 ——104 ——105
/ ENGINE | | | | | dine | | | | sleep |
-oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo-
#cars = 6; total weight = 400; speed on 2% incline = 70.3; avg distance to dining = 1.3; closest engine to sleeper = 5
Each TrainCar object has a unique ID number displayed in the upper right corner.
This number will help
us keep track of specific cars when we edit links between train objects. The unmarked cars are simple
passenger cars. The statistics printed below the ASCII output detail the total number of cars in the train
(including engines), the total weight of the train (in tons), and the calculated maximum speed (in mph)
on a 2% incline.
You will also need to calculate the final two numbers measuring the comfort level of the
passengers riding in the train. First, we would like to know how far the occupants of the passenger cars are
from the nearest dining car.
Passengers can walk from car to car (forward or backward) in the linked list
structure. However, passengers cannot walk through engine or freight cars. The number calculated is the
average across all passenger cars.
In this example, two passenger cars are 1 car length away from a dining
car, and one passenger car is 2 car lengths away. Thus, the average distance to the closest dining car for the
above example is (2 ∗ 1 + 1 ∗ 2)/3 = 1.3. Shorter average distance to dining values are more comfortable for
Finally, we measure the quiet comfort of the passengers in the sleeping cars. Since the engines
are the noisiest part of the train, we would like to know what is the worst case closest distance to an engine
car from any sleeping car in the train. Larger closest engine to sleeper values are more comfortable for the
passengers. In the event of an “infinte” statistic, you should represent it using a negative value.
Preparing Multiple Freight Trains
The first interesting algorithm we tackle is shipping a large quantity of freight in multiple trains. You will
write the function ShipFreight that takes in four arguments. The first two arguments are TrainCar pointers:
a collection of engines, and a collection of freight cars.
The third argument is the required minimum speed
to ship this freight and the fourth argument is the maximum number of cars allowed per train. The function
returns an STL vector of trains — actually TrainCar pointers to the first car / head node in a linked list
representing each complete train. Your goal is to ship all of the freight in the fewest number of trains, using
the fewest total number of engines.
This is a tricky optimization problem with more than one correct answer.
For the core assignment you must ensure that your trains achieve the minimum speed and maximum car per
For extra credit you can improve the algorithm and argue that your solution is indeed
optimal (fastest train speed and fewest number of engines and trains) for any provided input.
Here is one possible answer for ShipFreight called with 10 engines, 25 freight cars of varying weight, a train
length limit of 12 or fewer cars, and a minimum speed of 60 mph. Only 5 engines were necessary and the
freight is split into 3 trains. The weight (in tons) of each freight car is displayed in the center of the car.
—106 ——116 ——117 ——118 ——119 ——120 ——121 ——122
/ ENGINE | 40 | | 45 | | 30 | | 65 | | 35 | | 35 | | 35 |
-oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo-
#cars = 8, total weight = 435, speed on 2% incline = 64.7
—107 —108 ——123 ——124 ——125 ——126 ——127 ——128 ——129 ——130 ——131 ——132
/ ENGINE / ENGINE | 50 | | 85 | | 50 | | 45 | | 40 | | 85 | | 85 | | 45 | | 45 | | 65 |
-oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo-
#cars = 12, total weight = 895, speed on 2% incline = 62.8
—109 —110 ——133 ——134 ——135 ——136 ——137 ——138 ——139 ——140
/ ENGINE / ENGINE | 75 | | 40 | | 65 | | 65 | | 75 | | 45 | | 95 | | 90 |
-oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo-
#cars = 10, total weight = 850, speed on 2% incline = 66.2
Managing Train Car Rearrangement
The second significant algorithm you will implement is separating one big passenger train (with two or more
engines) into two smaller but similarly fast (and for extra credit, optimally comfortable) trains.
speed of the two smaller trains should be approximately the same as the original large train. First, we’ll
assume the input train has exactly two engines.
Here’s a sample input train:
—141 ——142 ——143 ——144 ——145 ——146 ——147 —148 ——149 ——150 ——151
/ ENGINE | | | | | dine | | sleep | | sleep | | | / ENGINE | | | dine | | |
-oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo-
#cars = 11; total weight = 750; speed on 2% incline = 75.0; avg distance to dining = 1.6; closest engine to sleeper = 2
After calling the Separate function, the original train nodes are split/re-organized into two trains:
—141 ——142 ——143 ——144 ——145
/ ENGINE | | | | | dine | | sleep |
-oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo-
#cars = 5; total weight = 350; speed on 2% incline = 80.4; avg distance to dining = 1.5; closest engine to sleeper = 4
——146 ——147 —148 ——149 ——150 ——151
| sleep | | | / ENGINE | | | dine | | |
-oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo- + -oo—oo-
#cars = 6; total weight = 400; speed on 2% incline = 70.3; avg distance to dining = inf; closest engine to sleeper = 2
Because the original train in this example had an odd number of non-engine cars, we cannot make the two
trains exactly match the speed of the original. Note that not all equal-speed train separations are as simple
as cutting one link.
Sometimes multiple links must be cut and cars must be pushed around the yard and
re-attached in a different configuration. Can you visualize those operations? Draw pictures!
With physical train cars there are real costs associated with each link or unlink of a pair of neighboring cars
and with pushing cars around the train yard.
The yard needs extra length of track, switches between the
tracks, and helper engines and extra staff to complete the operations. We will assume it costs 1 money unit
each to: unlink, link, or drag/shift a car one train length of track. We would like to minimize the total
cost of the reconfiguration, but still achieve the best speed-balanced separation of the original train.
There may be multiple different equal-cost solutions for a specific problem! Your code may return any of these
Draw at least three different test cases of challenging input to the Separate function. Also draw a corresponding
valid output configuration for each test case that minimizes the real physical costs associated with the
IMPORTANT: Bring these drawings to Lab 7 – you will need to show these drawings
as part of the lab checkpoints.
First, focus on the implementation of the Separate function to handle all input trains with exactly 2 engines.
Your code should not create any new nodes. Your code should not edit the type of any TrainCar object.
We provide a helper function that counts the number of unlink/link operations and the length of track that
cars must be dragged or shifted to produce a specific separation result.
Your first priority is to separate the
original train into two equal (or nearly equal) speed trains. Your second priority is to minimize the cost of
unlink, link, and shift operations necessary to complete the separation task.
Once the code is working for
trains with two engines, you can extend it to work for input trains with more than two engines.
In the above example, note that after separation the passenger comfort values improved in one train but
worsened in the other train. In fact, the average distance to dining is now “infinite” because the passengers in
car 147 cannot reach the dining car.
For extra credit, implement a SeparateComfort function that prioritizes
creating two equal speed but more comfortable trains (targeting smaller values for average distance to dining
and/or larger values for closest engine to sleeper).
The unlink/link/shift cost will likely be greater than the
original Separate function. Add plenty of test cases to main.cpp to demonstrate the success of your extra
Provided Framework, Implementation Requirements, Hints, & Suggestions
We provide the “traincar.h” file with the implementation of the TrainCar class. You are not allowed to
modify the traincar.h file. You will edit the “traincar_prototypes.h” file to complete several missing
function prototypes that operate on a train, a doubly linked list of TrainCar node objects. These are all nonmember functions. (Part of your task for this homework is to deduce the exact function prototypes.)
implement those functions in the “traincar.cpp” file. We also provide the “main.cpp” file with the ASCII
art PrintTrain function and a variety of sample tests of the different functions. We use the MersenneTwister
pseudo-random number generator (mtrand.h and mtrand.cpp) — you do not need to understand the details
of the MTRand class.
You should work on the assignment step-by-step, uncommenting each test case in main.cpp as you work.
You are encouraged to use simple recursion to implement some of the functions for this homework. Compile,
test, and fully debug each step before moving on to the next piece of implementation work. You should not
modify the provided code except where indicated, as we will be compiling and testing your submitted files
with different portions of the instructor solution file.
To earn full credit on this homework, your code must
also pass the memory error and memory leak checks by Dr. Memory.
Other than the return value of the ShipFreight function and test cases in main.cpp (TAs will be grading your
StudentTests cases), you will not use arrays, STL vectors, STL lists, iterators, or other STL containers in
Instead, you will be manipulating the low-level custom TrainCar objects, and the pointers
that link TrainCars to each other.
Use good coding style and detailed comments when you design and implement your program. You must do
this assignment on your own, as described in the “Collaboration Policy & Academic Integrity” handout.
you did discuss this assignment, problem solving techniques, or error messages, etc. with anyone, please list
their names in your README.txt file.
FINAL NOTE: If you earn 4 points on Test Cases 3, 7, 8, 9 on Submitty by 11:59pm on Wednesday, you
may submit your assignment on Friday without being charged a late day.
Q: What should I do about ____?
A: Before asking on the forum, review the handout and the provided output, many questions can be
answered by studying the provided output.
Q: Is the provided output the optimal (best) solution for ShipFreight and Separate? Do I have to match
A: The provided output shows reasonable solutions, but they aren’t guaranteed to be the best solution,
especially for the more complicated inputs. We do not grade based on if you matched the exact output or
not, instead the autograder will grade based on whether your solution meets the test case’s requirements.
Q: My speed calculation is wrong! I’m confused about the speed formula.
A: A common mistake is using 2 for “2% grade”, this should be 0.02. Another common mistake is using
ints which may not be big enough to hold the calculation. We recommend you use a float or double. For
integer constants you can alternately use an L, i.e. 5000LL to denote that 5000 is a “long long int”. (Just
doing L for ‘long int’ may still give you a 32-bit number if you’re on a 32-bit processor!)
Q: How should I start? What’s important to complete first?
A: You will need to finish everything up through ShipFreight, making sure to add the appropriate prototypes
to traincar prototypes.h and implementation in traincar.cpp . As a reminder, these are NOT member
functions of the Traincar class, they just happen to operate on trains. Once that’s done you will need at
least a basic Separate implementation – my first version just cuts the train in half, which will get enough
credit for the late day, but not pass any hidden Separate tests.
Q: How do I go about writing a better ShipFreight or Separate?
A: These are open-ended problems (there are many ways to try solving them). Start with something basic,
and then look at the requirements. There are several that are suggested in the handout, things we might
want to try to minimize or maximize. Start thinking about one (or more) of those and try implementing
them. Look at how that changes your results. Repeat this process over and over.
Q: Is there an exact target for things like the “similar in speed” requirement for the Separate tests?
A: No. Each test case will have different requirements, based on what is reasonable for the particular train(s)
you’re given as input.
Q: Will there be freight trains in a train passed to Separate?
Q: How is the cost calculated in Separate?
A: Every time a pair of cars has moved, let’s say car A and car B switch from AB to BA. That means B
moved forward one car, and A moved backward by one car. So this is actually a total of 2 movements. So
first, you can count how many positions each car has shifted by. But then you have to factor in the number of
links and unlinks. Add them up and you get your answer. So for example, in the provided output, Seperate
I see, 3 unlinks, 2 new links, and then looking at how much each car has shifted: 0,0,0,0,2 on the left train
(313 moves two cars backwards to connect with 310) and 1,1,0,0,0 on the right train (311 and 312 have to
move forward one each so that 312 is connected to 314 and 311 is still connected to 312) compared to their
(pdspDPEpse vs pdspEDPpse, capitalized the trains of interest)
So that’s 3+2+(2+1+1) = 5+4 = 9 units of money
Q: I can’t tell what’s going on with my trains because the printing is all messed up, like two lines got smushed
A: Some trains are very long so the output lines are long. Zoom out if you’re viewing on a web browser, or
redirect output to a file/copy the text into a text editor and make the font smaller.