Description
Introduction
Welcome to your first Programming Assignment in the Data Structures course of the Data Structures and
Algorithms Specialization!
In this programming assignment, you will be practicing implementing basic data structures and using
them to solve algorithmic problems. In some of the problems, you just need to implement and use a data
structure from the lectures, while in the others you will also need to invent an algorithm to solve the problem
using some of the basic data structures.
In this programming assignment, the grader will show you the input and output data if your solution fails
on any of the tests. This is done to help you to get used to the algorithmic problems in general and get some
experience debugging your programs while knowing exactly on which tests they fail. However, note that for
very big inputs the grader cannot show them fully, so it will only show the beginning of the input for you to
make sense of its size, and then it will be clipped. You will need to generate big inputs for yourself. For all
the following programming assignments, the grader will show the input data only in case your solution fails
on one of the first few tests (please review the questions 5.4 and 5.5 in the FAQ section for a more detailed
explanation of this behavior of the grader).
Learning Outcomes
Upon completing this programming assignment you will be able to:
1. Apply the basic data structures you’ve just studied to solve the given algorithmic problems.
2. Given a piece of code in an unknown programming language, check whether the brackets are used
correctly in the code or not.
3. Implement a tree, read it from the input and compute its height.
4. Simulate processing of computer network packets.
Passing Criteria: 2 out of 3
Passing this programming assignment requires passing at least 2 out of 3 code problems from this assignment.
In turn, passing a code problem requires implementing a solution that passes all the tests for this problem
in the grader and does so under the time and memory limits specified in the problem statement.
Contents
1 Problem: Check brackets in the code 3
1
2 Problem: Compute tree height 6
3 Advanced Problem: Network packet processing simulation 9
4 General Instructions and Recommendations on Solving Algorithmic Problems 12
4.1 Reading the Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.2 Designing an Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.3 Implementing Your Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.4 Compiling Your Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.5 Testing Your Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.6 Submitting Your Program to the Grading System . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.7 Debugging and Stress Testing Your Program . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5 Frequently Asked Questions 15
5.1 I submit the program, but nothing happens. Why? . . . . . . . . . . . . . . . . . . . . . . . . 15
5.2 I submit the solution only for one problem, but all the problems in the assignment are graded.
Why? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
5.3 What are the possible grading outcomes, and how to read them? . . . . . . . . . . . . . . . . 15
5.4 How to understand why my program fails and to fix it? . . . . . . . . . . . . . . . . . . . . . 16
5.5 Why do you hide the test on which my program fails? . . . . . . . . . . . . . . . . . . . . . . 16
5.6 My solution does not pass the tests? May I post it in the forum and ask for a help? . . . . . . 17
5.7 My implementation always fails in the grader, though I already tested and stress tested it a
lot. Would not it be better if you give me a solution to this problem or at least the test cases
that you use? I will then be able to fix my code and will learn how to avoid making mistakes.
Otherwise, I do not feel that I learn anything from solving this problem. I am just stuck. . . . 17
2
1 Problem: Check brackets in the code
Problem Introduction
In this problem you will implement a feature for a text editor to find errors in the usage of brackets in the
code.
Problem Description
Task. Your friend is making a text editor for programmers. He is currently working on a feature that will
find errors in the usage of different types of brackets. Code can contain any brackets from the set
[]{}(), where the opening brackets are [,{, and ( and the closing brackets corresponding to them
are ],}, and ).
For convenience, the text editor should not only inform the user that there is an error in the usage
of brackets, but also point to the exact place in the code with the problematic bracket. First priority
is to find the first unmatched closing bracket which either doesn’t have an opening bracket before it,
like ] in ](), or closes the wrong opening bracket, like } in ()[}. If there are no such mistakes, then
it should find the first unmatched opening bracket without the corresponding closing bracket after it,
like ( in {}([]. If there are no mistakes, text editor should inform the user that the usage of brackets
is correct.
Apart from the brackets, code can contain big and small latin letters, digits and punctuation marks.
More formally, all brackets in the code should be divided into pairs of matching brackets, such that in
each pair the opening bracket goes before the closing bracket, and for any two pairs of brackets either
one of them is nested inside another one as in (foo[bar]) or they are separate as in f(a,b)-g[c].
The bracket [ corresponds to the bracket ], { corresponds to }, and ( corresponds to ).
Input Format. Input contains one string 𝑆 which consists of big and small latin letters, digits, punctuation
marks and brackets from the set []{}().
Constraints. The length of 𝑆 is at least 1 and at most 105
.
Output Format. If the code in 𝑆 uses brackets correctly, output “Success” (without the quotes). Otherwise,
output the 1-based index of the first unmatched closing bracket, and if there are no unmatched closing
brackets, output the 1-based index of the first unmatched opening bracket.
Time Limits. C: 1 sec, C++: 1 sec, Java: 1 sec, Python: 1 sec. C#: 1.5 sec, Haskell: 2 sec, JavaScript: 3
sec, Ruby: 3 sec, Scala: 3 sec.
Memory Limit. 512MB.
Sample 1.
Input:
[]
Output:
Success
Explanation:
The brackets are used correctly: there is just one pair of brackets [ and ], they correspond to each
other, the left bracket [ goes before the right bracket ], and no two pairs of brackets intersect, because
there is just one pair of brackets.
3
Sample 2.
Input:
{}[]
Output:
Success
Explanation:
The brackets are used correctly: there are two pairs of brackets — first pair of { and }, and second
pair of [ and ] — and these pairs do not intersect.
Sample 3.
Input:
[()]
Output:
Success
Explanation:
The brackets are used correctly: there are two pairs of brackets — first pair of [ and ], and second
pair of ( and ) — and the second pair is nested inside the first pair.
Sample 4.
Input:
(())
Output:
Success
Explanation:
Pairs with the same types of brackets can also be nested.
Sample 5.
Input:
{[]}()
Output:
Success
Explanation:
Here there are 3 pairs of brackets, one of them is nested into another one, and the third one is separate
from the first two.
Sample 6.
Input:
{
Output:
1
Explanation:
The code { doesn’t use brackets correctly, because brackets cannot be divided into pairs (there is just
one bracket). There are no closing brackets, and the first unmatched opening bracket is {, and its
position is 1, so we output 1.
4
Sample 7.
Input:
{[}
Output:
3
Explanation:
The bracket } is unmatched, because the last unmatched opening bracket before it is [ and not {. It
is the first unmatched closing bracket, and our first priority is to output the first unmatched closing
bracket, and its position is 3, so we output 3.
Sample 8.
Input:
foo(bar);
Output:
Success
Explanation:
All the brackets are matching, and all the other symbols can be ignored.
Sample 9.
Input:
foo(bar[i);
Output:
10
Explanation:
) doesn’t match [, so ) is the first unmatched closing bracket, so we output its position, which is 10.
Starter Files
There are starter solutions only for C++, Java and Python3, and if you use other languages, you need
to implement solution from scratch. Starter solutions read the code from the input and go through the
code character-by-character and provide convenience methods. You need to implement the processing of the
brackets to find the answer to the problem and to output the answer.
What to Do
To solve this problem, you can slightly modify the IsBalanced algorithm from the lectures to account not
only for the brackets, but also for other characters in the code, and return not just whether the code uses
brackets correctly, but also what is the first position where the code becomes broken.
Need Help?
Ask a question or see the questions asked by other learners at this forum thread.
5
2 Problem: Compute tree height
Problem Introduction
Trees are used to manipulate hierarchical data such as hierarchy of categories of a retailer or the directory
structure on your computer. They are also used in data analysis and machine learning both for hierarchical clustering and building complex predictive models, including some of the best-performing in practice
algorithms like Gradient Boosting over Decision Trees and Random Forests. In the later modules of this
course, we will introduce balanced binary search trees (BST) — a special kind of trees that allows to very
efficiently store, manipulate and retrieve data. Balanced BSTs are thus used in databases for efficient storage
and actually in virtually any non-trivial programs, typically via built-in data structures of the programming
language at hand.
In this problem, your goal is to get used to trees. You will need to read a description of a tree from the
input, implement the tree data structure, store the tree and compute its height.
Problem Description
Task. You are given a description of a rooted tree. Your task is to compute and output its height. Recall
that the height of a (rooted) tree is the maximum depth of a node, or the maximum distance from a
leaf to the root. You are given an arbitrary tree, not necessarily a binary tree.
Input Format. The first line contains the number of nodes 𝑛. The second line contains 𝑛 integer numbers
from −1 to 𝑛 − 1 — parents of nodes. If the 𝑖-th one of them (0 ≤ 𝑖 ≤ 𝑛 − 1) is −1, node 𝑖 is the root,
otherwise it’s 0-based index of the parent of 𝑖-th node. It is guaranteed that there is exactly one root.
It is guaranteed that the input represents a tree.
Constraints. 1 ≤ 𝑛 ≤ 105
.
Output Format. Output the height of the tree.
Time Limits. C: 1 sec, C++: 1 sec, Java: 6 sec, Python: 3 sec. C#: 1.5 sec, Haskell: 2 sec, JavaScript: 3
sec, Ruby: 3 sec, Scala: 3 sec.
Memory Limit. 512MB.
Sample 1.
Input:
5
4 -1 4 1 1
Output:
3
Explanation:
The input means that there are 5 nodes with numbers from 0 to 4, node 0 is a child of node 4, node 1
is the root, node 2 is a child of node 4, node 3 is a child of node 1 and node 4 is a child of node 1. To
see this, let us write numbers of nodes from 0 to 4 in one line and the numbers given in the input in
the second line underneath:
0 1 2 3 4
4 -1 4 1 1
Now we can see that the node number 1 is the root, because −1 corresponds to it in the second line.
Also, we know that the nodes number 3 and number 4 are children of the root node 1. Also, we know
that the nodes number 0 and number 2 are children of the node 4.
6
root 1
3 4
0 2
The height of this tree is 3, because the number of vertices on the path from root 1 to leaf 2 is 3.
Sample 2.
Input:
5
-1 0 4 0 3
Output:
4
Explanation:
The input means that there are 5 nodes with numbers from 0 to 4, node 0 is the root, node 1 is a child
of node 0, node 2 is a child of node 4, node 3 is a child of node 0 and node 4 is a child of node 3. The
height of this tree is 4, because the number of nodes on the path from root 0 to leaf 2 is 4.
root 0
1 3
4
2
Starter Files
The starter solutions in this problem read the description of a tree, store it in memory, compute the height
in a naive way and write the output. You need to implement faster height computation. Starter solutions
are available for C++, Java and Python3, and if you use other languages, you need to implement a solution
from scratch.
What to Do
To solve this problem, change the height function described in the lectures with an implementation which
will work for an arbitrary tree. Note that the tree can be very deep in this problem, so you should be careful
to avoid stack overflow problems if you’re using recursion, and definitely test your solution on a tree with
the maximum possible height.
Suggestion: Take advantage of the fact that the labels for each tree node are integers in the range 0..𝑛−1:
you can store each node in an array whose index is the label of the node. By storing the nodes in an array,
you have 𝑂(1) access to any node given its label.
Create an array of 𝑛 nodes:
7
allocate 𝑛𝑜𝑑𝑒𝑠[𝑛]
for 𝑖 ← 0 to 𝑛 − 1:
𝑛𝑜𝑑𝑒𝑠[𝑖] =new 𝑁𝑜𝑑𝑒
Then, read each parent index:
for 𝑐ℎ𝑖𝑙𝑑_𝑖𝑛𝑑𝑒𝑥 ← 0 to 𝑛 − 1:
read 𝑝𝑎𝑟𝑒𝑛𝑡_𝑖𝑛𝑑𝑒𝑥
if 𝑝𝑎𝑟𝑒𝑛𝑡_𝑖𝑛𝑑𝑒𝑥 == −1:
𝑟𝑜𝑜𝑡 ← 𝑐ℎ𝑖𝑙𝑑_𝑖𝑛𝑑𝑒𝑥
else:
𝑛𝑜𝑑𝑒𝑠[𝑝𝑎𝑟𝑒𝑛𝑡_𝑖𝑛𝑑𝑒𝑥].𝑎𝑑𝑑𝐶ℎ𝑖𝑙𝑑(𝑛𝑜𝑑𝑒𝑠[𝑐ℎ𝑖𝑙𝑑_𝑖𝑛𝑑𝑒𝑥])
Once you’ve built the tree, you’ll then need to compute its height. If you don’t use recursion, you needn’t
worry about stack overflow problems. Without recursion, you’ll need some auxiliary data structure to keep
track of the current state (in the breadth-first seach code in lecture, for example, we used a queue).
Need Help?
Ask a question or see the questions asked by other learners at this forum thread.
8
3 Advanced Problem: Network packet processing simulation
We strongly recommend you start solving advanced problems only when you are done with the basic problems
(for some advanced problems, algorithms are not covered in the video lectures and require additional ideas
to be solved; for some other advanced problems, algorithms are covered in the lectures, but implementing
them is a more challenging task than for other problems).
Problem Introduction
In this problem you will implement a program to simulate the processing of network packets.
Problem Description
Task. You are given a series of incoming network packets, and your task is to simulate their processing.
Packets arrive in some order. For each packet number 𝑖, you know the time when it arrived 𝐴𝑖 and the
time it takes the processor to process it 𝑃𝑖 (both in milliseconds). There is only one processor, and it
processes the incoming packets in the order of their arrival. If the processor started to process some
packet, it doesn’t interrupt or stop until it finishes the processing of this packet, and the processing of
packet 𝑖 takes exactly 𝑃𝑖 milliseconds.
The computer processing the packets has a network buffer of fixed size 𝑆. When packets arrive, they are stored in the buffer before being processed. However, if the buffer is full when a packet
arrives (there are 𝑆 packets which have arrived before this packet, and the computer hasn’t finished
processing any of them), it is dropped and won’t be processed at all. If several packets arrive at the
same time, they are first all stored in the buffer (some of them may be dropped because of that —
those which are described later in the input). The computer processes the packets in the order of
their arrival, and it starts processing the next available packet from the buffer as soon as it finishes
processing the previous one. If at some point the computer is not busy, and there are no packets in
the buffer, the computer just waits for the next packet to arrive. Note that a packet leaves the buffer
and frees the space in the buffer as soon as the computer finishes processing it.
Input Format. The first line of the input contains the size 𝑆 of the buffer and the number 𝑛 of incoming
network packets. Each of the next 𝑛 lines contains two numbers. 𝑖-th line contains the time of arrival
𝐴𝑖 and the processing time 𝑃𝑖 (both in milliseconds) of the 𝑖-th packet. It is guaranteed that the
sequence of arrival times is non-decreasing (however, it can contain the exact same times of arrival in
milliseconds — in this case the packet which is earlier in the input is considered to have arrived earlier).
Constraints. All the numbers in the input are integers. 1 ≤ 𝑆 ≤ 105
; 1 ≤ 𝑛 ≤ 105
; 0 ≤ 𝐴𝑖 ≤ 106
;
0 ≤ 𝑃𝑖 ≤ 103
; 𝐴𝑖 ≤ 𝐴𝑖+1 for 1 ≤ 𝑖 ≤ 𝑛 − 1.
Output Format. For each packet output either the moment of time (in milliseconds) when the processor
began processing it or −1 if the packet was dropped (output the answers for the packets in the same
order as the packets are given in the input).
Time Limits. C: 2 sec, C++: 2 sec, Java: 6 sec, Python: 8 sec. C#: 3 sec, Haskell: 4 sec, JavaScript: 6 sec,
Ruby: 6 sec, Scala: 6 sec.
Memory Limit. 512MB.
Sample 1.
Input:
1 0
Output:
9
Explanation:
If there are no packets, you shouldn’t output anything.
Sample 2.
Input:
1 1
0 0
Output:
0
Explanation:
The only packet arrived at time 0, and computer started processing it immediately.
Sample 3.
Input:
1 2
0 1
0 1
Output:
0
-1
Explanation:
The first packet arrived at time 0, the second packet also arrived at time 0, but was dropped, because
the network buffer has size 1 and it was full with the first packet already. The first packet started
processing at time 0, and the second packet was not processed at all.
Sample 4.
Input:
1 2
0 1
1 1
Output:
0
1
Explanation:
The first packet arrived at time 0, the computer started processing it immediately and finished at
time 1. The second packet arrived at time 1, and the computer started processing it immediately.
Starter Files
The starter solutions for C++, Java and Python3 in this problem read the input, pass the requests for
processing of packets one-by-one and output the results. They declare a class that implements network
buffer simulator. The class is partially implemented, and your task is to implement the rest of it. If you use
other languages, you need to implement the solution from scratch.
What to Do
To solve this problem, you can use a list or a queue (in this case the queue should allow accessing its last
element, and such queue is usually called a deque). You can use the corresponding built-in data structure in
your language of choice.
10
One possible solution is to store in the list or queue finish_time the times when the computer will
finish processing the packets which are currently stored in the network buffer, in increasing order. When
a new packet arrives, you will first need to pop from the front of finish_time all the packets which are
already processed by the time new packet arrives. Then you try to add the finish time for the new packet in
finish_time. If the buffer is full (there are already 𝑆 finish times in finish_time), the packet is dropped.
Otherwise, its processing finish time is added to finish_time.
If finish_time is empty when a new packet arrives, computer will start processing the new packet
immediately as soon as it arrives. Otherwise, computer will start processing the new packet as soon as it
finishes to process the last of the packets currently in finish_time (here is when you need to access the
last element of finish_time to determine when the computer will start to process the new packet). You will
also need to compute the processing finish time by adding 𝑃𝑖 to the processing start time and push it to the
back of finish_time.
You need to remember to output the processing start time for each packet instead of the processing finish
time which you store in finish_time.
Need Help?
Ask a question or see the questions asked by other learners at this forum thread.
11
4 General Instructions and Recommendations on Solving Algorithmic Problems
Your main goal in an algorithmic problem is to implement a program that solves a given computational
problem in just few seconds even on massive datasets. Your program should read a dataset from the standard
input and write an answer to the standard output.
Below we provide general instructions and recommendations on solving such problems. Before reading
them, go through readings and screencasts in the first module that show a step by step process of solving
two algorithmic problems: link.
4.1 Reading the Problem Statement
You start by reading the problem statement that contains the description of a particular computational task
as well as time and memory limits your solution should fit in, and one or two sample tests. In some problems
your goal is just to implement carefully an algorithm covered in the lectures, while in some other problems
you first need to come up with an algorithm yourself.
4.2 Designing an Algorithm
If your goal is to design an algorithm yourself, one of the things it is important to realize is the expected
running time of your algorithm. Usually, you can guess it from the problem statement (specifically, from the
subsection called constraints) as follows. Modern computers perform roughly 108–109 operations per second.
So, if the maximum size of a dataset in the problem description is 𝑛 = 105
, then most probably an algorithm
with quadratic running time is not going to fit into time limit (since for 𝑛 = 105
, 𝑛
2 = 1010) while a solution
with running time 𝑂(𝑛 log 𝑛) will fit. However, an 𝑂(𝑛
2
) solution will fit if 𝑛 is up to 103 = 1000, and if
𝑛 is at most 100, even 𝑂(𝑛
3
) solutions will fit. In some cases, the problem is so hard that we do not know
a polynomial solution. But for 𝑛 up to 18, a solution with 𝑂(2𝑛𝑛
2
) running time will probably fit into the
time limit.
To design an algorithm with the expected running time, you will of course need to use the ideas covered
in the lectures. Also, make sure to carefully go through sample tests in the problem description.
4.3 Implementing Your Algorithm
When you have an algorithm in mind, you start implementing it. Currently, you can use the following
programming languages to implement a solution to a problem: C, C++, C#, Haskell, Java, JavaScript,
Python2, Python3, Ruby, Scala. For all problems, we will be providing starter solutions for C++, Java, and
Python3. If you are going to use one of these programming languages, use these starter files. For other
programming languages, you need to implement a solution from scratch.
4.4 Compiling Your Program
For solving programming assignments, you can use any of the following programming languages: C, C++,
C#, Haskell, Java, JavaScript, Python2, Python3, Ruby, and Scala. However, we will only be providing
starter solution files for C++, Java, and Python3. The programming language of your submission is detected
automatically, based on the extension of your submission.
We have reference solutions in C++, Java and Python3 which solve the problem correctly under the given
restrictions, and in most cases spend at most 1/3 of the time limit and at most 1/2 of the memory limit.
You can also use other languages, and we’ve estimated the time limit multipliers for them, however, we have
no guarantee that a correct solution for a particular problem running under the given time and memory
constraints exists in any of those other languages.
Your solution will be compiled as follows. We recommend that when testing your solution locally, you
use the same compiler flags for compiling. This will increase the chances that your program behaves in the
12
same way on your machine and on the testing machine (note that a buggy program may behave differently
when compiled by different compilers, or even by the same compiler with different flags).
∙ C (gcc 5.2.1). File extensions: .c. Flags:
gcc – pipe – O2 – std = c11 < filename > – lm
∙ C++ (g++ 5.2.1). File extensions: .cc, .cpp. Flags:
g ++ – pipe – O2 – std = c ++14 < filename > – lm
If your C/C++ compiler does not recognize -std=c++14 flag, try replacing it with -std=c++0x flag
or compiling without this flag at all (all starter solutions can be compiled without it). On Linux
and MacOS, you most probably have the required compiler. On Windows, you may use your favorite
compiler or install, e.g., cygwin.
∙ C# (mono 3.2.8). File extensions: .cs. Flags:
mcs
∙ Haskell (ghc 7.8.4). File extensions: .hs. Flags:
ghc – O2
∙ Java (Open JDK 8). File extensions: .java. Flags:
javac – encoding UTF -8
java – Xmx1024m
∙ JavaScript (Node v6.3.0). File extensions: .js. Flags:
nodejs
∙ Python 2 (CPython 2.7). File extensions: .py2 or .py (a file ending in .py needs to have a first line
which is a comment containing “python2”). No flags:
python2
∙ Python 3 (CPython 3.4). File extensions: .py3 or .py (a file ending in .py needs to have a first line
which is a comment containing “python3”). No flags:
python3
∙ Ruby (Ruby 2.1.5). File extensions: .rb.
ruby
∙ Scala (Scala 2.11.6). File extensions: .scala.
scalac
13
4.5 Testing Your Program
When your program is ready, you start testing it. It makes sense to start with small datasets (for example,
sample tests provided in the problem description). Ensure that your program produces a correct result.
You then proceed to checking how long does it take your program to process a massive dataset. For
this, it makes sense to implement your algorithm as a function like solve(dataset) and then implement an
additional procedure generate() that produces a large dataset. For example, if an input to a problem is a
sequence of integers of length 1 ≤ 𝑛 ≤ 105
, then generate a sequence of length exactly 105
, pass it to your
solve() function, and ensure that the program outputs the result quickly.
Also, check the boundary values. Ensure that your program processes correctly sequences of size 𝑛 =
1, 2, 105
. If a sequence of integers from 0 to, say, 106
is given as an input, check how your program behaves
when it is given a sequence 0, 0, . . . , 0 or a sequence 106
, 106
, . . . , 106
. Check also on randomly generated
data. For each such test check that you program produces a correct result (or at least a reasonably looking
result).
In the end, we encourage you to stress test your program to make sure it passes in the system at the first
attempt. See the readings and screencasts from the first week to learn about testing and stress testing: link.
4.6 Submitting Your Program to the Grading System
When you are done with testing, you submit your program to the grading system. For this, you go the
submission page, create a new submission, and upload a file with your program. The grading system then
compiles your program (detecting the programming language based on your file extension, see Subsection 4.4)
and runs it on a set of carefully constructed tests to check that your program always outputs a correct result
and that it always fits into the given time and memory limits. The grading usually takes no more than a
minute, but in rare cases when the servers are overloaded it might take longer. Please be patient. You can
safely leave the page when your solution is uploaded.
As a result, you get a feedback message from the grading system. The feedback message that you will love
to see is: Good job! This means that your program has passed all the tests. On the other hand, the three
messages Wrong answer, Time limit exceeded, Memory limit exceeded notify you that your program
failed due to one these three reasons. Note that the grader will not show you the actual test you program
have failed on (though it does show you the test if your program have failed on one of the first few tests;
this is done to help you to get the input/output format right).
4.7 Debugging and Stress Testing Your Program
If your program failed, you will need to debug it. Most probably, you didn’t follow some of our suggestions
from the section 4.5. See the readings and screencasts from the first week to learn about debugging your
program: link.
You are almost guaranteed to find a bug in your program using stress testing, because the way these
programming assignments and tests for them are prepared follows the same process: small manual tests,
tests for edge cases, tests for large numbers and integer overflow, big tests for time limit and memory limit
checking, random test generation. Also, implementation of wrong solutions which we expect to see and stress
testing against them to add tests specifically against those wrong solutions.
Go ahead, and we hope you pass the assignment soon!
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5 Frequently Asked Questions
5.1 I submit the program, but nothing happens. Why?
You need to create submission and upload the file with your solution in one of the programming languages C,
C++, Java, or Python (see Subsections 4.3 and 4.4). Make sure that after uploading the file with your solution
you press on the blue “Submit” button in the bottom. After that, the grading starts, and the submission
being graded is enclosed in an orange rectangle. After the testing is finished, the rectangle disappears, and
the results of the testing of all problems is shown to you.
5.2 I submit the solution only for one problem, but all the problems in the
assignment are graded. Why?
Each time you submit any solution, the last uploaded solution for each problem is tested. Don’t worry: this
doesn’t affect your score even if the submissions for the other problems are wrong. As soon as you pass the
sufficient number of problems in the assignment (see in the pdf with instructions), you pass the assignment.
After that, you can improve your result if you successfully pass more problems from the assignment. We
recommend working on one problem at a time, checking whether your solution for any given problem passes
in the system as soon as you are confident in it. However, it is better to test it first, please refer to the
reading about stress testing: link.
5.3 What are the possible grading outcomes, and how to read them?
Your solution may either pass or not. To pass, it must work without crashing and return the correct answers
on all the test cases we prepared for you, and do so under the time limit and memory limit constraints
specified in the problem statement. If your solution passes, you get the corresponding feedback “Good job!”
and get a point for the problem. If your solution fails, it can be because it crashes, returns wrong answer,
works for too long or uses too much memory for some test case. The feedback will contain the number of
the test case on which your solution fails and the total number of test cases in the system. The tests for the
problem are numbered from 1 to the total number of test cases for the problem, and the program is always
tested on all the tests in the order from the test number 1 to the test with the biggest number.
Here are the possible outcomes:
Good job! Hurrah! Your solution passed, and you get a point!
Wrong answer. Your solution has output incorrect answer for some test case. If it is a sample test case from
the problem statement, or if you are solving Programming Assignment 1, you will also see the input
data, the output of your program and the correct answer. Otherwise, you won’t know the input, the
output, and the correct answer. Check that you consider all the cases correctly, avoid integer overflow,
output the required white space, output the floating point numbers with the required precision, don’t
output anything in addition to what you are asked to output in the output specification of the problem
statement. See this reading on testing: link.
Time limit exceeded. Your solution worked longer than the allowed time limit for some test case. If it
is a sample test case from the problem statement, or if you are solving Programming Assignment 1,
you will also see the input data and the correct answer. Otherwise, you won’t know the input and the
correct answer. Check again that your algorithm has good enough running time estimate. Test your
program locally on the test of maximum size allowed by the problem statement and see how long it
works. Check that your program doesn’t wait for some input from the user which makes it to wait
forever. See this reading on testing: link.
Memory limit exceeded. Your solution used more than the allowed memory limit for some test case. If it
is a sample test case from the problem statement, or if you are solving Programming Assignment 1,
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you will also see the input data and the correct answer. Otherwise, you won’t know the input and the
correct answer. Estimate the amount of memory that your program is going to use in the worst case
and check that it is less than the memory limit. Check that you don’t create too large arrays or data
structures. Check that you don’t create large arrays or lists or vectors consisting of empty arrays or
empty strings, since those in some cases still eat up memory. Test your program locally on the test of
maximum size allowed by the problem statement and look at its memory consumption in the system.
Cannot check answer. Perhaps output format is wrong. This happens when you output something
completely different than expected. For example, you are required to output word “Yes” or “No”, but
you output number 1 or 0, or vice versa. Or your program has empty output. Or your program outputs
not only the correct answer, but also some additional information (this is not allowed, so please follow
exactly the output format specified in the problem statement). Maybe your program doesn’t output
anything, because it crashes.
Unknown signal 6 (or 7, or 8, or 11, or some other). This happens when your program crashes. It
can be because of division by zero, accessing memory outside of the array bounds, using uninitialized
variables, too deep recursion that triggers stack overflow, sorting with contradictory comparator, removing elements from an empty data structure, trying to allocate too much memory, and many other
reasons. Look at your code and think about all those possibilities. Make sure that you use the same
compilers and the same compiler options as we do. Try different testing techniques from this reading:
link.
Internal error: exception… Most probably, you submitted a compiled program instead of a source
code.
Grading failed. Something very wrong happened with the system. Contact Coursera for help or write in
the forums to let us know.
5.4 How to understand why my program fails and to fix it?
If your program works incorrectly, it gets a feedback from the grader. For the Programming Assignment 1,
when your solution fails, you will see the input data, the correct answer and the output of your program
in case it didn’t crash, finished under the time limit and memory limit constraints. If the program crashed,
worked too long or used too much memory, the system stops it, so you won’t see the output of your program
or will see just part of the whole output. We show you all this information so that you get used to the
algorithmic problems in general and get some experience debugging your programs while knowing exactly
on which tests they fail.
However, in the following Programming Assignments throughout the Specialization you will only get so
much information for the test cases from the problem statement. For the next tests you will only get the
result: passed, time limit exceeded, memory limit exceeded, wrong answer, wrong output format or some
form of crash. We hide the test cases, because it is crucial for you to learn to test and fix your program
even without knowing exactly the test on which it fails. In the real life, often there will be no or only partial
information about the failure of your program or service. You will need to find the failing test case yourself.
Stress testing is one powerful technique that allows you to do that. You should apply it after using the other
testing techniques covered in this reading.
5.5 Why do you hide the test on which my program fails?
Often beginner programmers think by default that their programs work. Experienced programmers know,
however, that their programs almost never work initially. Everyone who wants to become a better programmer
needs to go through this realization.
When you are sure that your program works by default, you just throw a few random test cases against
it, and if the answers look reasonable, you consider your work done. However, mostly this is not enough. To
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make one’s programs work, one must test them really well. Sometimes, the programs still don’t work although
you tried really hard to test them, and you need to be both skilled and creative to fix your bugs. Solutions
to algorithmic problems are one of the hardest to implement correctly. That’s why in this Specialization you
will gain this important experience which will be invaluable in the future when you write programs which
you really need to get right.
It is crucial for you to learn to test and fix your programs yourself. In the real life, often there will be no
or only partial information about the failure of your program or service. Still, you will have to reproduce the
failure to fix it (or just guess what it is, but that’s rare, and you will still need to reproduce the failure to
make sure you have really fixed it). When you solve algorithmic problems, it is very frequent to make subtle
mistakes. That’s why you should apply the testing techniques described in this reading to find the failing
test case and fix your program.
5.6 My solution does not pass the tests? May I post it in the forum and ask
for a help?
No, please do not post any solutions in the forum or anywhere on the web, even if a solution does not
pass the tests (as in this case you are still revealing parts of a correct solution). Recall the third item
of the Coursera Honor Code: “I will not make solutions to homework, quizzes, exams, projects, and other
assignments available to anyone else (except to the extent an assignment explicitly permits sharing solutions).
This includes both solutions written by me, as well as any solutions provided by the course staff or others”
(link).
5.7 My implementation always fails in the grader, though I already tested and
stress tested it a lot. Would not it be better if you give me a solution to
this problem or at least the test cases that you use? I will then be able to
fix my code and will learn how to avoid making mistakes. Otherwise, I do
not feel that I learn anything from solving this problem. I am just stuck.
First of all, you always learn from your mistakes.
The process of trying to invent new test cases that might fail your program and proving them wrong
is often enlightening. This thinking about the invariants which you expect your loops, ifs, etc. to keep and
proving them wrong (or right) makes you understand what happens inside your program and in the general
algorithm you’re studying much more.
Also, it is important to be able to find a bug in your implementation without knowing a test case and
without having a reference solution. Assume that you designed an application and an annoyed user reports
that it crashed. Most probably, the user will not tell you the exact sequence of operations that led to a crash.
Moreover, there will be no reference application. Hence, once again, it is important to be able to locate a
bug in your implementation yourself, without a magic oracle giving you either a test case that your program
fails or a reference solution. We encourage you to use programming assignments in this class as a way of
practicing this important skill.
If you have already tested a lot (considered all corner cases that you can imagine, constructed a set of
manual test cases, applied stress testing), but your program still fails and you are stuck, try to ask for help
on the forum. We encourage you to do this by first explaining what kind of corner cases you have already
considered (it may happen that when writing such a post you will realize that you missed some corner cases!)
and only then asking other learners to give you more ideas for tests cases.
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