Exercise 5-7

Given the implementation of frame in S5.8.1/93, and the following code fragment

vector<string> v;
frame(v);

describe what happens in this call. In particular, trace through how both the width function and the frame function operate. Now, run this code. If the results differ from your expectations, first understand why your expectations and the program differ, and then change one to match the other.

Solution

The frame function has a return type of vector<string>. To “frame” the vector<string> v means to pad all the string elements within v to the full optimum width as defined by the width function. (i.e. the length of the longest string element in v).

My expectation of running this code fragment:

1. The first statement of the code fragment creates an empty vector<string> v.
2. The second statement of the code fragment attempts to frame this empty vector<string> v.
3. When we apply frame(v), the width function returns a maxlen of 0 (i.e. the initialised maxlen value) – i.e. implying no elements in v.
4. The frame function by default however, always return a top and bottom border of four asterisks (*). So even though the for loop within the frame function processes an empty vector<string> v, at a minimum, frame(v) should return the top and bottom borders. i.e. element 0 contains “****”, and element 1 contains “****”. This is it!

If we however populate the vector<string> v with some elements, the frame function should behave as demonstrated in the text book Chapter 5, or Solution to Exercise 5-0 (Part 3/3). i.e. equal length string elements with width of at least 5. e.g. if vector<string> v contains just one string element “a”, then,  frame(v) will return:

• element 0: “*****”
• element 1:”* a *”   (note there is a space around the string element)
• element 2: “*****

Test Program

Though we have used the frame function multiple times in the previous exercises already, for completeness sake I shall include my test program here and run a couple of tests, for prove of concept purposes – to confirm the test result agrees with my expectation.

main.cpp

#include <iostream>
#include <string>      // string
#include <vector>      // vector
#include <algorithm>   // max

using std::string;
using std::vector;
using std::max;
using std::cin;
using std::cout;
using std::endl;

string::size_type width(const vector<string>& v)
{
    string::size_type maxlen = 0;
    for(vector<string>::size_type i = 0; i != v.size(); ++i)
        maxlen = max(maxlen, v[i].size());
    return maxlen;
}

vector<string> frame(const vector<string>& v)
{
    vector<string> ret;
    string::size_type maxlen = width(v);
    string border(maxlen + 4, '*');

    // write the top border
    ret.push_back(border);

    // write each interior row, bordered by an asterisk and a space
    for (vector<string>::size_type i = 0; i != v.size(); ++i)
        ret.push_back("* " + v[i] + string(maxlen - v[i].size(), ' ') + " *");

    // write the bottom border
    ret.push_back(border);

    return ret;
}

int main()
{
    string s;            // line
    vector<string> v;    // paragraph
    while (getline(cin, s))
        v.push_back(s);

    vector<string> framedV = frame(v);

    for (vector<string>::const_iterator iter = framedV.begin();
         iter != framedV.end(); ++iter)
    {
        cout << (*iter) << endl;
    }

    return 0;
}

Test 1 – empty vector<string> v

As expected, if we frame an empty vector<string> v, by default the frame function should return the top and bottom border at the minimum default width of four asterisks (*).

^Z
****
****

Test 2 – non-empty vector<string> v

If we frame a non-empty vector<string> v, the output should be just as described in Chapter 5 – equal length string elements, with the width determined by the longest string (line) element.

This is
a test
over over
^Z
*************
* This is   *
* a test    *
* over over *
*************

Let’s do one more. Let’s verify our expectation if we only submit a string element “a”.

a
^Z
*****
* a *
*****

Bingo!

Reference

Koenig, Andrew & Moo, Barbara E., Accelerated C++, Addison-Wesley, 2000

Exercise 5-6

Rewrite the extract_fails function from S5.1.1/77 so that instead of erasing each failing student from the input vector students, it copies the records for the passing students to the beginning of students, and then uses the resize function to remove the extra elements from the end of students. How does the performance of this version compare with the one in S5.1.1/77?

Solution

The original (version 2) extract_fail function in the text book S5.1.1/77 looks like this – it uses the vector<XXX>::erase function.

{
    Student_group fail;
    Student_group::size_type i = 0;

    // invariant: elements [0,i) of students represent passing grades
    while (i != students.size())
    {
        if (fgrade(students[i]))
        {
            fail.push_back(students[i]);
            students.erase(students.begin() + i);
        }
        else
            ++ i;
    }
    return fail;
}

Note that I have used the technique developed from my Solution to Exercise 5-4, in which all the vector<Student_info> are replaced by Student_group, using the C++ typedef. (Just trust me for now there is a typdef somewhere else that defines Student_group) I believe it makes sense to build on what we have learnt!

The newly “re-written” function will look like this it uses a combination of vector<XXX>::insert and vector<XXX>::resize functions.

Student_group extract_fails_v2_5p6(Student_group& students)
{
    Student_group fail;
    typedef Student_group::size_type VecSize;
    VecSize countPass = 0;

    // invariant: elements [0,i) of students represent passing grades
    VecSize i = 0;
    while (i != students.size())
    {
        if (fgrade(students[i]))
            fail.push_back(students[i]);
        else
        {
            students.insert(students.begin(), students[i++]);
            ++countPass;
        }
        ++i;
    }
    students.resize(countPass);

    return fail;
}

If after skimping through this new code and you fully understand the concepts / what’s going on, then congratulation you are done!

From a series of tests the new version happens to take 50% more time than the original version (when reaching around 10,000 lines of input) – performance results can be found at the bottom of the page under the Test Result section.

If you however would like to know more in details, such as how I derive this new code logic, then read on!

Code Logic – The insert/resize Method

The way I derive the eventual code was simply doing some sketches on paper (In face this is how I usually solve problems – making sketches and pictures!). Below shows the diagrams that I drawn – essentially I started with a hypothetical example and just work my way through using logic. Some notes:

• The countPass is a counter to keep track of the number of passing students – this will be used later on to feed the vector<XXX>::resize function.
• The i, is just an incrementing variable (our good old friend), to facilitate a while loop.

Have we reached the end of the vector? (yes)

Use the resize function to keep only the passing students in vector<Student_info> students.

And these are the final output!

An Important Learning – iterator

This exercise has exposed an interesting fact: iterator does NOT work when the underlying vector changes size! i.e. the following code will not work (even though it looks correct). One must use vector indexing instead! (I spent an hour debugging this – a hard lesson learnt!). Must be a feature of vector iterator vs vector index.

Student_group extract_fails_v2_5p6(Student_group& students)
{
    Student_group fail;
    Student_group::iterator i = students.begin();
    Student_group::size_type countPass = 0;

    // invariant: elements [0,i) of students represent passing grades
    while (i != students.end())
    {
        if (fgrade(*i))
            fail.push_back(*i);
        else
        {
            students.insert(students.begin(), *i);
            ++countPass;
            ++i;
        }
        ++i;
    }
    students.resize(countPass);

    return fail;
}

The Project

Here are the complete set of header and source files that enable me to perform the test.

Source File List

• main.cpp
• extract_fails.cpp
• grade.cpp
• median.cpp
• Student_info.cpp

Header File List

• extract_fails.h
• grade.h
• median.h
• Student_group.h
• Student_info.h

Source Files

main.cpp

#include <iostream>
#include <iomanip>
#include <ios>
#include <ctime>
#include "Student_info.h"
#include "Student_group.h" // switch between vector and list based Student_group here
#include "grade.h"
#include "extract_fails.h"

using std::cin;
using std::cout;
using std::endl;
using std::setprecision;
using std::streamsize;

int main()
{

    Student_group students;
    Student_info record;

    // read and store all the student's data.
    while (read(cin, record))
        students.push_back(record);

    // Extract the failed students and time-stamp it!
    clock_t startTime = clock();
    Student_group students_failed = extract_fails_v2(students);
    /* Student_group students_failed = extract_fails_v2_5p6(students);   */
    clock_t endTime = clock();
    clock_t clockTicksTaken = endTime - startTime;
    double timeInSeconds = clockTicksTaken / (double) CLOCKS_PER_SEC;


    streamsize prec = cout.precision();
    cout << "Elapsed (in seconds): " << setprecision(30) << timeInSeconds
         << setprecision(prec) << endl;

    // Uncomment the following block to display passing and failing students
    /*
    cout << endl;

    // Report passing students
    cout << "These students have passed." << endl;
    for (Student_group::const_iterator iter = students.begin();
         iter != students.end(); ++iter)
        cout << iter->name << " (" << grade(*iter) << ")" << endl;

    cout << endl;

    // Report failing students
    cout << "These students have failed." << endl;
    for (Student_group::const_iterator iter = students_failed.begin();
         iter != students_failed.end(); ++iter)
        cout << iter->name << " (" << grade(*iter) << ")" << endl;
    */

    return 0;
}

extract_fails.cpp

#include "Student_info.h"
#include "Student_group.h"
#include "grade.h"

// separate passing and failing student records
// derived from S5.1.1/77
Student_group extract_fails_v2(Student_group& students)
{
    Student_group fail;
    Student_group::size_type i = 0;

    // invariant: elements [0,i) of students represent passing grades
    while (i != students.size())
    {
        if (fgrade(students[i]))
        {
            fail.push_back(students[i]);
            students.erase(students.begin() + i);
        }
        else
            ++ i;
    }
    return fail;
}

// Required by Exercise 5-6
Student_group extract_fails_v2_5p6(Student_group& students)
{
    Student_group fail;
    typedef Student_group::size_type VecSize;
    VecSize countPass = 0;

    // invariant: elements [0,i) of students represent passing grades
    VecSize i = 0;
    while (i != students.size())
    {
        if (fgrade(students[i]))
            fail.push_back(students[i]);
        else
        {
            students.insert(students.begin(), students[i++]);
            ++countPass;
        }
        ++i;
    }
    students.resize(countPass);

    return fail;
}

grade.cpp

#include <stdexcept>
#include <vector>
#include "grade.h"
#include "median.h"
#include "Student_info.h"

using std::domain_error;
using std::vector;

// definitions for the grade functions from S4.1/52, S4.1.2/54, S4.2.2/63

// compute a student's overall grade from midterm and final exam
// grades and homework grade (S4.1/52)
double grade(double midterm, double final, double homework)
{
    return 0.2 * midterm + 0.4 * final + 0.4 * homework;
}

// compute a student's overall grade from midterm and final exam grades
// and vector of homework grades.
// this function does not copy its argument, because median (function) does it for us.
// (S4.1.2/54)
double grade(double midterm, double final, const vector<double>& hw)
{
    if (hw.size() == 0)
        throw domain_error("student has done no homework");
    return grade(midterm, final, median(hw));
}

// this function computes the final grade for a Student_info object
// (S4.2.2/63)
double grade(const Student_info& s)
{
    return grade(s.midterm, s.final, s.homework);
}

// predicate to determine whether a student failed
// (S5.1/75)
bool fgrade(const Student_info& s)
{
    return grade(s) < 60;
}

median.cpp

// source file for the median function
#include <algorithm>
#include <stdexcept>
#include <vector>

using std::domain_error;
using std::sort;
using std::vector;

// compute the median of a vector<double>
double median(vector<double> vec)
{
    typedef vector<double>::size_type vec_sz;

    vec_sz size = vec.size();
    if (size == 0)
        throw domain_error("median of an empty vector");

    sort(vec.begin(),vec.end());

    vec_sz mid = size/2;

    return size % 2 == 0 ? (vec[mid] + vec[mid-1]) / 2 : vec[mid];
}

Student_info.cpp

#include "Student_info.h"

using std::istream;
using std::vector;

// we are interested in sorting the Student_info object by the student's name
bool compare(const Student_info& x, const Student_info& y)
{
    return x.name < y.name;
}

// read student's name, midterm exam grade, final exam grade, and homework grades
// and store into the Student_info object
// (as defined in S4.2.2/62)
istream& read(istream& is, Student_info& s)
{
    // read and store the student's name and midterm and final exam grades
    is >> s.name >> s.midterm >> s.final;

    // read and store all the student's homework grades
    read_hw(is, s.homework);
    return is;
}

// read homework grades from an input stream into a vector<double>
// (as defined in S4.1.3/57)
istream& read_hw(istream& in, vector<double>& hw)
{
    if (in)
    {
        // get rid of previous contents
        hw.clear();

        // read homework grades
        double x;
        while (in >> x)
            hw.push_back(x);

        // clear the stream so that input will work for the next student
        in.clear();
    }
    return in;
}

Header Files

extract_fails.h

#ifndef GUARD_EXTRACT_FAILS_H
#define GUARD_EXTRACT_FAILS_H

// extract_fails.h
#include "Student_group.h"

Student_group extract_fails_v2(Student_group&);
Student_group extract_fails_v2_5p6(Student_group&);

#endif // GUARD_EXTRACT_FAILS_H

grade.h

#ifndef GUARD_GRADE_H
#define GUARD_GRADE_H

// grade.h
#include <vector>
#include "Student_info.h"

double grade(double, double, double);
double grade(double, double, const std::vector<double>&);
double grade(const Student_info&);
bool fgrade(const Student_info&);

#endif // GUARD_GRADE_H

median.h

#ifndef GUARD_MEDIAN_H
#define GUARD_MEDIAN_H

// median.h
#include <vector>
double median(std::vector<double>);

#endif // GUARD_MEDIAN_H

Student_group.h

#ifndef GUARD_STUDENT_GROUP_H
#define GUARD_STUDENT_GROUP_H

// Student_group.h
#include <list>
#include <vector>
#include "Student_info.h"

// ********************* AMEND THIS ***************************
// Solution to Exercise 5-4: Pick one of the followings
typedef std::vector<Student_info> Student_group;
//typedef std::list<Student_info> Student_group;
// ************************************************************

#endif // GUARD_STUDENT_GROUP_H

Student_info.h

#ifndef GUARD_STUDENT_INFO_H
#define GUARD_STUDENT_INFO_H

// Student_info.h
#include <iostream>
#include <string>
#include <vector>

struct Student_info
{
    std::string name;
    double midterm, final;
    std::vector<double> homework;
};

bool compare(const Student_info&, const Student_info&);
std::istream& read(std::istream&, Student_info&);
std::istream& read_hw(std::istream&, std::vector<double>&);

#endif // GUARD_STUDENT_INFO_H

Test Program

Just simply amend the following line in the main() program accordingly for test purposes.

Student_group students_failed = extract_fails_v2(students);
/* Student_group students_failed = extract_fails_v2_5p6(students); */

Performance Comparison

I’ve run a few tests and recorded the job run time for the extract_fail step. from this it looks like the insert/resize method is actually slower than the erase method. But then, I guess it depends on the input file – i.e. depending on the ratio of passing students to failing students, the sequence of the passing and failing students, and potentially other factors.

	v2 (erase)	v2_5p6 (insert/resize)
10 lines	0.001 seconds	0.000 seconds
100 lines	0.003 seconds	0.004 seconds
1,000 lines	0.156 seconds	0.212 seconds
10,000 lines	9.79 seconds	16.6 seconds

Reference

Koenig, Andrew & Moo, Barbara E., Accelerated C++, Addison-Wesley, 2000