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Homework 10 — Performance and Big ’O’ Notation

In this final assignment for Data Structures, you will carry out a series of tests on the fundamental data

structures in the Standard Template Library to first hypothesize and then measure the relative performance

(running time & memory usage) of these data structures and solidify your understanding of algorithm

complexity analysis using Big ’O’ Notation. The five fundamental data structures we will study are: vector,

list, binary search tree (set / map), priority queue, and hash table (unordered set / unordered map).

Be sure to read the entire handout before beginning your implementation.

Overview of Operations

We will consider the following six simple, but moderately compute-intensive, operations that are common

subtasks of many interesting real-world algorithms and applications. We will test these operations using

integers and/or STL strings as noted below.

• Sort - we’ll use the default operator< for the specific data type.

• Remove duplicates from a sequence - without otherwise changing the overall order (keeping the first

occurrence of the element).

• Determine the mode – most frequently occurring element. If there is a tie, you may return any of the

most frequently occurring elements.

• Identify the closest pair of items within the dataset - integer data only. We’ll use operator- to

measure distance. If there is a tie in distance, you may return any of the pairs of closest distance.

• Output the first/smallest f items - a portion of the complete sorted output.

• Determine the longest matching substring between any two elements - STL string data only. For

example, if the input contains the words ‘antelope’, ‘buffalo’ and ‘elephant’, the longest substring

match is ‘ant’ (found within both ‘antelope’ and ‘elephant’). If there is a tie, you may return any of

the longest matching substrings.

See also the provided sample output for each of these operations.

“Rules” for comparison: For each operation, we will analyze the cost of a program/function that reads

the input from an STL input stream object (e.g., std::cin or std::ifstream) and writes the answer to an

STL output stream (e.g., std::cout or std::ofstream). The function should read through the input only

once and construct and use a single instance of the specified STL data structure to compute the output. The

function may not use any other data structure to help with the computation (e.g., storing data in a C-style

array).

Your Initial Predictions of Complexity Analysis

Before doing any implementation or testing, think about which data structures are better, similarly good, or

useless for tackling each operation.

Fill in the table on the next page with the big ’O’ notation for both the runtime and memory usage to

complete each operation using that data structure. If it is not feasible/sensible to use a particular data

structure to complete the specified operation put an X in the box. Hint: In the first 3 columns there should

only be 2 X’s! If two or more data structures have the same big ‘O’ notation for one operation, predict and

rank the data structures by faster running time for large data. We combine set & map (and unordered set

& unordered map) in this analysis, but be sure to specify which datatype of the two makes the most sense

for each operation.

For your answers, n is the number of elements in the input, f is the requested number of values in the output

(only relevant for the ‘first sorted’ operation), and l is the maximum length of each string (only use this

variable for the ‘longest substring match’ operation). Type your answers into your README.txt file.

You’ll also paste these answers into Submitty for autograding.

sort

remove

duplicates mode

closest

pair

first f

sorted

longest

substring

match

vector

list

BST (set/map)

priority queue/

binary heap

hash table

(unordered_set/

unordered_map)

Provided Framework

We provide a framework to implement and test these operations with each data structure and measure the

runtime and overall memory usage. The input will come from a file, redirected to std::cin on the command

line. Similarly, the program will write to std::cout and we can redirect that to write to a file. Some basic

statistics will be printed to std::cerr to help with complexity analysis. Here’s examples of how to compile

and run the provided code:

clang++ -g -Wall -Wextra performance*.cpp -o perf.out

./perf.out vector mode string < small_string_input.txt

./perf.out vector remove_duplicates string < small_string_input.txt > my_out.txt

diff my_out.txt small_string_output_remove_duplicates.txt

./perf.out vector closest_pair integer < small_integer_output_remove_duplicates.txt

./perf.out vector first_sorted string 3 < small_string_input.txt

./perf.out vector longest_substring string < small_string_output_remove_duplicates.txt

./perf.out vector sort string < medium_string_input.txt > vec_out.txt 2> vec_stats.txt

./perf.out list sort string < medium_string_input.txt > list_out.txt 2> list_stats.txt

diff vec_out.txt list_out.txt

2

The first example reads string input from small string input.txt, uses an STL vector to find the most

frequently occurring value (implemented by first sorting the data), and then outputs that string (the mode)

to std::cout.

The second example uses an STL vector to remove the duplicate values (without otherwise changing the

order) from small string input.txt storing the answer in my out.txt, and then uses diff to compare

that file to the provided answer.

The next 3 command lines show examples of how to run the closest pair, first sorted and

longest substring operations. Note that the first sorted operation takes an additional argument, the

number of elements to output from the sorted order. Also note that the closest pair and longest substring

operations are more interesting when the input does not contain duplicate values.

The final example sorts a larger input of random strings first using an STL vector, and then using an STL

list and confirms that the answers match.

Generating Random Input

We provide a small standalone program to generate input data files with random strings. Here’s how you

compile and use this program to generate a file named medium string input.txt with 10,000 strings, each

with 5 random letters (‘a’-‘z’). And also a file named medium integer input.txt with 10,000 integers, each

with 3-5 digits (ranging in value from 100-99999).

clang++ -g -Wall -Wextra generate_input.cpp -o generate_input.out

./generate.out string 10000 5 5 > medium_string_input.txt

./generate.out integer 10000 3 5 > medium_integer_input.txt

Measuring Performance

First, create and save several large randomly generated input files with different numbers of elements. Test the

vector code for each operation with each of your input files. The provided code uses the clock() function

to measure the processing time of the computation. The resolution accuracy of the timing mechanism is

system and hardware dependent and may be in seconds, milliseconds, or something else. Make sure you use

large enough inputs so that your running time for the largest test is about a second or more (to ensure the

measurement isn’t just noise). Record the results in a table like this:

Sorting random 5 letter strings using STL vector

# of strings vector sort operation time (sec)

10000 0.031

20000 0.067

50000 0.180

100000 0.402

As the dataset grows, does your predicted big ‘O’ notation match the raw performance numbers? We know

that the running time for sorting with the STL vector sorting algorithm is O(n log2 n) and we can estimate

the coefficient k in front of the dominant term from the collected numbers.

vector sort operation time(n) = kvector sort ∗ n log2 n

Thus, on the machine which produced these numbers, coefficient kvector sort ≈ 2.3 x 10−7

sec. Of course

these constants will be different on different operating systems, different compilers, and different hardware!

3

These constants will allow us to compare data structures / algorithms with the same big ‘O’ notation. The

STL list sorting algorithm is also O(n log2 n), but what is the estimate for klist sort?

Be sure to try different random string lengths because this number will impact the number of repeated/

duplicate values in the input. The ratio of the number of input strings to number of output strings is

reported to std::cerr with the operation running time. Which operations are impacted by the number of

repeated/duplicate values? What is the relative impact?

Operation Implementation using Different Data Structures

The provided code includes the implementation of each operation (except longest substring) for the vector

datatype. Your implementation task for this assignment is to extend the program to the other data structures

in the table. You should carefully consider the most efficient way (minimize the running time) to use each

data structure to complete the operation.

Focus on the first three operations from the table first (sort, remove duplicates, and mode). Once those

are debugged and tested, and you’ve analyzed the relative performance, you can proceed to implement the

other operations.

Estimate of Total Memory Usage

When you upload your code to Submitty, the autograder will measure not only the running time, but also

the total memory usage. Compare the memory used by the different data structures to perform the same

operation on the same input dataset. Does the total memory usage match your understanding of the relative

memory requirements for the internal representation of each data structure?

You can also run this tool on your local GNU/Linux machine (it may not work on other systems):

clang runstats.c -o runstats.out

./runstats.out ./perf.out vector sort string < medium_string_input.txt > my_out.txt

Results and Discussion

For each data type and each operation, run several sufficiently large tests and collect the operation time output

by the program. Organize these timing measurements in your README.txt file and estimate the coefficients

for the dominant term of your Big ‘O’ Notation. Do these measurements and the overall performance match

your predicted Big ‘O‘ Notation for the data type and operation? Did you update your initial answers for

the Big ‘O‘ Notation of any cell in the table?

Compare the relative coefficients for different data types that have the same Big ‘O’ Notation for a specific

operation. Do these match your intuition? Are you surprised by any of the results? Will these results impact

your data structure choices for future programming projects?

Submission

You must do this assignment on your own, as described in the “Collaboration Policy &

Academic Integrity”. If you did discuss the problem or error messages, etc. with anyone,

please list their names in your README.txt file. Important Note: Do not include any large test datasets

with your submission, because this may easily exceed the submission size. Instead describe any datasets you

created, citing the original source of the data as appropriate.

4

Homework 10 — Performance and Big ’O’ Notation

In this final assignment for Data Structures, you will carry out a series of tests on the fundamental data

structures in the Standard Template Library to first hypothesize and then measure the relative performance

(running time & memory usage) of these data structures and solidify your understanding of algorithm

complexity analysis using Big ’O’ Notation. The five fundamental data structures we will study are: vector,

list, binary search tree (set / map), priority queue, and hash table (unordered set / unordered map).

Be sure to read the entire handout before beginning your implementation.

Overview of Operations

We will consider the following six simple, but moderately compute-intensive, operations that are common

subtasks of many interesting real-world algorithms and applications. We will test these operations using

integers and/or STL strings as noted below.

• Sort - we’ll use the default operator< for the specific data type.

• Remove duplicates from a sequence - without otherwise changing the overall order (keeping the first

occurrence of the element).

• Determine the mode – most frequently occurring element. If there is a tie, you may return any of the

most frequently occurring elements.

• Identify the closest pair of items within the dataset - integer data only. We’ll use operator- to

measure distance. If there is a tie in distance, you may return any of the pairs of closest distance.

• Output the first/smallest f items - a portion of the complete sorted output.

• Determine the longest matching substring between any two elements - STL string data only. For

example, if the input contains the words ‘antelope’, ‘buffalo’ and ‘elephant’, the longest substring

match is ‘ant’ (found within both ‘antelope’ and ‘elephant’). If there is a tie, you may return any of

the longest matching substrings.

See also the provided sample output for each of these operations.

“Rules” for comparison: For each operation, we will analyze the cost of a program/function that reads

the input from an STL input stream object (e.g., std::cin or std::ifstream) and writes the answer to an

STL output stream (e.g., std::cout or std::ofstream). The function should read through the input only

once and construct and use a single instance of the specified STL data structure to compute the output. The

function may not use any other data structure to help with the computation (e.g., storing data in a C-style

array).

Your Initial Predictions of Complexity Analysis

Before doing any implementation or testing, think about which data structures are better, similarly good, or

useless for tackling each operation.

Fill in the table on the next page with the big ’O’ notation for both the runtime and memory usage to

complete each operation using that data structure. If it is not feasible/sensible to use a particular data

structure to complete the specified operation put an X in the box. Hint: In the first 3 columns there should

only be 2 X’s! If two or more data structures have the same big ‘O’ notation for one operation, predict and

rank the data structures by faster running time for large data. We combine set & map (and unordered set

& unordered map) in this analysis, but be sure to specify which datatype of the two makes the most sense

for each operation.

For your answers, n is the number of elements in the input, f is the requested number of values in the output

(only relevant for the ‘first sorted’ operation), and l is the maximum length of each string (only use this

variable for the ‘longest substring match’ operation). Type your answers into your README.txt file.

You’ll also paste these answers into Submitty for autograding.

sort

remove

duplicates mode

closest

pair

first f

sorted

longest

substring

match

vector

list

BST (set/map)

priority queue/

binary heap

hash table

(unordered_set/

unordered_map)

Provided Framework

We provide a framework to implement and test these operations with each data structure and measure the

runtime and overall memory usage. The input will come from a file, redirected to std::cin on the command

line. Similarly, the program will write to std::cout and we can redirect that to write to a file. Some basic

statistics will be printed to std::cerr to help with complexity analysis. Here’s examples of how to compile

and run the provided code:

clang++ -g -Wall -Wextra performance*.cpp -o perf.out

./perf.out vector mode string < small_string_input.txt

./perf.out vector remove_duplicates string < small_string_input.txt > my_out.txt

diff my_out.txt small_string_output_remove_duplicates.txt

./perf.out vector closest_pair integer < small_integer_output_remove_duplicates.txt

./perf.out vector first_sorted string 3 < small_string_input.txt

./perf.out vector longest_substring string < small_string_output_remove_duplicates.txt

./perf.out vector sort string < medium_string_input.txt > vec_out.txt 2> vec_stats.txt

./perf.out list sort string < medium_string_input.txt > list_out.txt 2> list_stats.txt

diff vec_out.txt list_out.txt

2

The first example reads string input from small string input.txt, uses an STL vector to find the most

frequently occurring value (implemented by first sorting the data), and then outputs that string (the mode)

to std::cout.

The second example uses an STL vector to remove the duplicate values (without otherwise changing the

order) from small string input.txt storing the answer in my out.txt, and then uses diff to compare

that file to the provided answer.

The next 3 command lines show examples of how to run the closest pair, first sorted and

longest substring operations. Note that the first sorted operation takes an additional argument, the

number of elements to output from the sorted order. Also note that the closest pair and longest substring

operations are more interesting when the input does not contain duplicate values.

The final example sorts a larger input of random strings first using an STL vector, and then using an STL

list and confirms that the answers match.

Generating Random Input

We provide a small standalone program to generate input data files with random strings. Here’s how you

compile and use this program to generate a file named medium string input.txt with 10,000 strings, each

with 5 random letters (‘a’-‘z’). And also a file named medium integer input.txt with 10,000 integers, each

with 3-5 digits (ranging in value from 100-99999).

clang++ -g -Wall -Wextra generate_input.cpp -o generate_input.out

./generate.out string 10000 5 5 > medium_string_input.txt

./generate.out integer 10000 3 5 > medium_integer_input.txt

Measuring Performance

First, create and save several large randomly generated input files with different numbers of elements. Test the

vector code for each operation with each of your input files. The provided code uses the clock() function

to measure the processing time of the computation. The resolution accuracy of the timing mechanism is

system and hardware dependent and may be in seconds, milliseconds, or something else. Make sure you use

large enough inputs so that your running time for the largest test is about a second or more (to ensure the

measurement isn’t just noise). Record the results in a table like this:

Sorting random 5 letter strings using STL vector

# of strings vector sort operation time (sec)

10000 0.031

20000 0.067

50000 0.180

100000 0.402

As the dataset grows, does your predicted big ‘O’ notation match the raw performance numbers? We know

that the running time for sorting with the STL vector sorting algorithm is O(n log2 n) and we can estimate

the coefficient k in front of the dominant term from the collected numbers.

vector sort operation time(n) = kvector sort ∗ n log2 n

Thus, on the machine which produced these numbers, coefficient kvector sort ≈ 2.3 x 10−7

sec. Of course

these constants will be different on different operating systems, different compilers, and different hardware!

3

These constants will allow us to compare data structures / algorithms with the same big ‘O’ notation. The

STL list sorting algorithm is also O(n log2 n), but what is the estimate for klist sort?

Be sure to try different random string lengths because this number will impact the number of repeated/

duplicate values in the input. The ratio of the number of input strings to number of output strings is

reported to std::cerr with the operation running time. Which operations are impacted by the number of

repeated/duplicate values? What is the relative impact?

Operation Implementation using Different Data Structures

The provided code includes the implementation of each operation (except longest substring) for the vector

datatype. Your implementation task for this assignment is to extend the program to the other data structures

in the table. You should carefully consider the most efficient way (minimize the running time) to use each

data structure to complete the operation.

Focus on the first three operations from the table first (sort, remove duplicates, and mode). Once those

are debugged and tested, and you’ve analyzed the relative performance, you can proceed to implement the

other operations.

Estimate of Total Memory Usage

When you upload your code to Submitty, the autograder will measure not only the running time, but also

the total memory usage. Compare the memory used by the different data structures to perform the same

operation on the same input dataset. Does the total memory usage match your understanding of the relative

memory requirements for the internal representation of each data structure?

You can also run this tool on your local GNU/Linux machine (it may not work on other systems):

clang runstats.c -o runstats.out

./runstats.out ./perf.out vector sort string < medium_string_input.txt > my_out.txt

Results and Discussion

For each data type and each operation, run several sufficiently large tests and collect the operation time output

by the program. Organize these timing measurements in your README.txt file and estimate the coefficients

for the dominant term of your Big ‘O’ Notation. Do these measurements and the overall performance match

your predicted Big ‘O‘ Notation for the data type and operation? Did you update your initial answers for

the Big ‘O‘ Notation of any cell in the table?

Compare the relative coefficients for different data types that have the same Big ‘O’ Notation for a specific

operation. Do these match your intuition? Are you surprised by any of the results? Will these results impact

your data structure choices for future programming projects?

Submission

You must do this assignment on your own, as described in the “Collaboration Policy &

Academic Integrity”. If you did discuss the problem or error messages, etc. with anyone,

please list their names in your README.txt file. Important Note: Do not include any large test datasets

with your submission, because this may easily exceed the submission size. Instead describe any datasets you

created, citing the original source of the data as appropriate.

4