Part 1: Mapping Functions

In many situations you would like to apply the same function to lots of different pieces of data. For example, lets create two arrays of numbers, and use our add function to add pairs of numbers together. Create a C++ file called map.cpp and copy in the following;

#include <iostream>
#include <vector>

int sum(int x, int y)
{
    return x + y;
}

template<class T>
void print_vector(const std::vector<T> &values)
{
    std::cout << "[";

    for (const T &value : values)
    {
        std::cout << " " << value;
    }

    std::cout << " ]" << std::endl;
}

int main(int argc, char **argv)
{
    auto a = std::vector<int>( { 1, 2, 3, 4, 5 } );
    auto b = std::vector<int>( { 6, 7, 8, 9, 10 } );

    auto result = std::vector<int>( a.size() );

    for (int i=0; i<a.size(); ++i)
    {
        result[i] = sum( a[i], b[i] );
    }

    print_vector(result);

    return 0;
}

Compile and run using the commands

g++ --std=c++14 map.cpp -o map
./map

This should print

[7 9 11 13 15]

The above code has looped over every pair of numbers in the vectors a and b, and has called the function sum for each pair. Each result is placed into the vector result, which is printed at the end of the loop using the print_vector function.

Applying the same function to every item in a vector (or pair of vectors) of data is really common. For example, in a molecular simulation, you may want to loop over a vector of every molecule and call a calculate_energy function for each one. In a fluid dynamics simulation, you may want to loop over a vector of grid points and call a solve_gridpoint function for each one. This pattern, of calling the same function for each element of a vector (or set of vectors) of data, is called mapping. In the above example, we have mapped the function sum onto the vectors a and b, returning result.

The above code mapped the function sum. How about if we wanted to map our diff or multiply functions? One option would be to copy out this code again. A better solution would be to use functional programming to write our own mapping function.

Edit your map.cpp file and copy into it the following code;

#include <iostream>
#include <vector>

template<class FUNC, class T>
auto map(FUNC func, const std::vector<T> &arg1, const std::vector<T> &arg2)
{
    int nvalues = std::min( arg1.size(), arg2.size() );

    auto result = std::vector<T>(nvalues);

    for (int i=0; i<nvalues; ++i)
    {
        result[i] = func(arg1[i], arg2[i]);
    }

    return result;
}

int sum(int x, int y)
{
    return x + y;
}

int difference(int x, int y)
{
    return x - y;
}

int multiply(int x, int y)
{
    return x * y;
}

template<class T>
void print_vector(const std::vector<T> &values)
{
    std::cout << "[";

    for (const T &value : values)
    {
        std::cout << " " << value;
    }

    std::cout << " ]" << std::endl;
}

int main(int argc, char **argv)
{
    auto a = std::vector<int>( { 1, 2, 3, 4, 5 } );
    auto b = std::vector<int>( { 6, 7, 8, 9, 10 } );

    auto result = map( sum, a, b );
    print_vector(result);

    result = map( difference, a, b );
    print_vector(result);

    result = map( multiply, a, b );
    print_vector(result);

    return 0;
}

Compile and run using the command

g++ --std=c++14 map.cpp -o map
./map

This should print out

[ 7 9 11 13 15 ]
[ -5 -5 -5 -5 -5 ]
[ 6 14 24 36 50 ]

Can you see how this works?

The map function takes as its first argument the function to be mapped. The other arguments are the two vectors of data for the mapping. The line

int nvalues = std::min( arg1.size(), arg2.size() );

works out the number of pairs of data that can be mapped, using the smallest size of the two vectors. The map function then loops through each of these pairs of data, calling func for each pair, and storing the result in the vector result. This is then returned at the end.

Because the map function calls the mapped function using the argument func, it can map any function that is passed to it, as long as that function accepts two arguments.

General Map

The mapping function we have just written is limited to functions have only two arguments. Mapping is very useful and common, and a general mapping function that can map functions with any number of arguments can be written easily using C++ 2014. We have written such a function and made it available in the file include/part1.h. The code for this general mapping function is below;

template<class FUNC, class... ARGS>
auto map(FUNC func, const std::vector<ARGS>&... args)
{
    typedef typename std::result_of<FUNC(ARGS...)>::type RETURN_TYPE;

    int nargs=detail::get_min_container_size(args...);

    std::vector<RETURN_TYPE> result(nargs);

    for (size_t i=0; i<nargs; ++i)
    {
        result[i] = func(args[i]...);
    }

    return result;
}

The difference between this general mapping function, and the one we have written before, is that we allow an arbitrary number of arguments to be passed, via the ... variadic template operator. Because the return type of the mapping function may be different from the type of the arguments, we use std::result_of to obtain the return type of the function, and assign this to RETURN_TYPE. This is used when creating the std::vector<RETURN_TYPE> that contains the results.

With this general mapping function, we can now solve more interesting problems.

For example, let us now look at a completely different function to map. The file include/part1.h defines a new Point class, and a function that can calculate the distance between two points, as seen here;

class Point
{
public:
    Point() : x(0), y(0), z(0)
    {}

    Point(float _x, float _y, float _z) : x(_x), y(_y), z(_z)
    {}

    float x, y, z;
};

float calc_distance(const Point &p1, const Point &p2)
{
    const float dx = p1.x - p2.x;
    const float dy = p1.y - p2.y;
    const float dz = p1.z - p2.z;

    return std::sqrt(dx*dx + dy*dy + dz*dz);
}

Edit your map.cpp file so that it contains the code;

#include "part1.h"

using namespace part1;

int main(int argc, char **argv)
{
    auto a = std::vector<Point>( { Point(1.0,1.0,1.0), Point(2.0,2.0,2.0), Point(3.0,3.0,3.0) } );
    auto b = std::vector<Point>( { Point(4.0,4.0,4.0), Point(5.0,5.0,5.0), Point(6.0,6.0,6.0) } );

    auto distances = map( calc_distance, a, b );

    print_vector(distances);

    return 0;
}

Compile and run this program using the command

g++ --std=c++14 -Iinclude map.cpp -o map
./map

(note that you have to use -Iinclude to tell the compiler the path to the include directory that contains part1.h)

This should result in the following being printed to the screen;

[ 5.19615 5.19615 5.19615 ]

Can you see how this has worked? The lines;

auto a = std::vector<Point>( { Point(1.0,1.0,1.0), Point(2.0,2.0,2.0), Point(3.0,3.0,3.0) } );
auto b = std::vector<Point>( { Point(4.0,4.0,4.0), Point(5.0,5.0,5.0), Point(6.0,6.0,6.0) } );

have created two vectors of Point objects. We then used the map function to use the calc_function to calculate distances between pairs of points in turn using this line.

auto distances = map( calc_distances, a, b );

These distances were printed using the print_vector function, which has also been provided for you in include/part1.h using this line

print_vector( distances );

Mapping functions with multiple arguments

One advantage of our new map function is that it knows how to handle multiple arguments. For example, let’s create a function that only maps a single argument. Edit your map.cpp function so that it contains;

#include "part1.h"

using namespace part1;

int square(int x)
{
    return x * x;
}

int main(int argc, char **argv)
{
    auto a = std::vector<int>( { 1, 2, 3, 4, 5, 6, 7, 8 } );

    auto result = map( square, a );

    print_vector( result );

    return 0;
}

Compile and run using the command

g++ --std=c++14 -Iinclude map.cpp -o map
./map

This should print out

[ 1 4 9 16 25 36 49 64 ]

The map function in include/part1.h can work with mapping functions that accept any number of arguments. If the mapping function accepts n arguments, then you must pass n+1 arguments to map, i.e. the mapped function, plus n vectors of arguments.

For example, edit your map.cpp and copy into it this code;

#include "part1.h"

using namespace part1;

int find_smallest(int x, int y, int z)
{
    return std::min( x, std::min(y,z) );
}

int main(int argc, char **argv)
{
    auto a = std::vector<int>( { 1, 2, 3, 4, 5 } );
    auto b = std::vector<int>( { 5, 4, 3, 2, 1 } );
    auto c = std::vector<int>( { 1, 2, 1, 2, 1 } );

    auto result = map( find_smallest, a, b, c );

    print_vector( result );

    return 0;
}

Compile and run using

g++ --std=c++14 -Iinclude map.cpp -o map
./map

This should print

[ 1 2 1 2 1 ]

Is this what you expect?

Exercise

You should see that there is a directory called shakespeare that contains the full text of many of Shakespeare’s plays.

You should also see that there is a header file called include/filecounter.h that contains two functions;

count_lines : this counts the number of lines in the passed file,
get_arguments : this converts the arguments passed to a program into a vector of strings

Your task is to write a C++ program, called countlines.cpp, that will count the total number of lines in each of these Shakespeare plays in the directory shakespeare, e.g. by using the command line call

g++ --std=c++14 -Iinclude countlines.cpp -o countlines
./countlines shakespeare/*

Use the map function defined in include/part1.h to count the number of lines in each Shakespeare play, printing the result as a list.

If you get stuck or want some inspiration, a possible answer is given here.

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