Pythonic Operators on STL Set Algorithms

 

Table of Contents

Introduction


Ever since I started working with Python and that have gotten me into alot thinking how to redesign my libraries to be pythonic, if I were to implement them from scratch again. In this first article of the series, I want to introduce Python’s wonderful and intuitive operators for working with set algebra into C++ world. These operators are nothing more than syntatic-sugar to reduce the amount of code to write.

Table of Python Set Operators

PythonSetOperators

 

Set Intersection

set_intersection2

C++ Reference: std::set_intersection

  • Commutative

set_intersection is an algorithm that produces a set of elements which are common to both sets. It is commutative, meaning that even the 2 sets are switched places, the algorithm returns the same result.

void intersection_example()
{
    std::vector v1{ 1,2,3,4,5,6,7,8 };
    std::vector v2{         5,  7,  9,10 };
    std::sort(v1.begin(), v1.end());
    std::sort(v2.begin(), v2.end());

    std::vector v_intersection;

    std::set_intersection(v1.begin(), v1.end(),
        v2.begin(), v2.end(),
        std::back_inserter(v_intersection));

    for (int n : v_intersection)
        std::cout << n << ' ';
}

Output

5 7

This is the example using & operator to do intersection.

void intersection_example()
{
    std::vector v1{ 1,2,3,4,5,6,7,8 };
    std::vector v2{         5,  7,  9,10 };

    std::vector v_intersection = s(v1) & s(v2);

    for (int n : v_intersection)
        std::cout << n << ' ';
}

I skip showing the output of the operator example as it is the same.

s is a function, not class. If s is to be a class, to instantiate it, a container type would have to be specified (See below).

std::vector v_intersection = s(v1) & s(v2);

In order to make use of automatic type deduction, s has to be a function that does nothing but returns the wrapper class.

#include 
#include 

template
struct wrapper
{
    wrapper(T& container) : cont(container) {}
    T& cont;
};

template
wrapper s(T& s_cont)
{
    return wrapper(s_cont);
}

The & operator function checks whether to sort the container. Since std::sort only works with random access iterators, so we cannot use this function with STL list and slist which has non-random access iterators. In my 15 years of work, I have not seen a single use of list in any codebase.

template
T operator&(wrapper& left, wrapper& right)
{
    T& c1 = left.cont;
    T& c2 = right.cont;
    if (!std::is_sorted(c1.begin(), c1.end()))
        std::sort(c1.begin(), c1.end());
    if (!std::is_sorted(c2.begin(), c2.end()))
        std::sort(c2.begin(), c2.end());

    T v_intersection;

    std::set_intersection(c1.begin(), c1.end(),
        c2.begin(), c2.end(),
        std::back_inserter(v_intersection));

    return std::move(v_intersection);
}

All set algorithm precondition requires the ranges to be sorted, hence this is_sorted check.

Set Union

set_union2

C++ Reference: std::set_union

  • Commutative

set_union is an algorithm that produces a set of elements from both sets. For the elements appearing in intersection, it always picks them from the 1st set, not 2nd set.

void union_example()
{
    std::vector v1 = { 1, 2, 3, 4, 5 };
    std::vector v2 = {       3, 4, 5, 6, 7 };
    std::sort(v1.begin(), v1.end());
    std::sort(v2.begin(), v2.end());

    std::vector dest1;

    std::set_union(v1.begin(), v1.end(),
        v2.begin(), v2.end(),
        std::back_inserter(dest1));

    for (const auto &i : dest1) {
        std::cout << i << ' ';
    }
    std::cout << '\n';
}

Output

1 2 3 4 5 6 7

The code required to write is much lesser therefore the code is more concise.

void union_example()
{
    std::vector v1 = { 1, 2, 3, 4, 5 };
    std::vector v2 = {       3, 4, 5, 6, 7 };

    std::vector dest1 = s(v1) | s(v2);

    for (int n : dest1)
        std::cout << n << ' ';
}

The | operator is almost similar to & operator except that algorithm is different.

template
T operator|(wrapper& left, wrapper& right)
{
    T& c1 = left.cont;
    T& c2 = right.cont;
    if (!std::is_sorted(c1.begin(), c1.end()))
        std::sort(c1.begin(), c1.end());
    if (!std::is_sorted(c2.begin(), c2.end()))
        std::sort(c2.begin(), c2.end());

    T dest1;

    std::set_union(c1.begin(), c1.end(),
        c2.begin(), c2.end(),
        std::back_inserter(dest1));

    return std::move(dest1);
}

Set Difference

set_difference2

C++ Reference: std::set_difference

  • Non-Commutative

set_difference returns the elements in 1st set which is not in 2nd set and is represented by minus operator in Python. For obvious reason, the results is different when the arguments are swapped place. set_difference is non-commutative like minus operation.

void set_difference_example() 
{
    std::vector v1{ 1, 2, 5, 5, 5,    9 };
    std::vector v2{    2, 5,       7 };
    std::sort(v1.begin(), v1.end());
    std::sort(v2.begin(), v2.end());

    std::vector diff;

    std::set_difference(v1.begin(), v1.end(), v2.begin(), v2.end(),
        std::inserter(diff, diff.begin()));

    for (auto i : v1) std::cout << i << ' ';
    std::cout << "minus ";
    for (auto i : v2) std::cout << i << ' ';
    std::cout << "is: ";

    for (auto i : diff) std::cout << i << ' ';
    std::cout << '\n';
}

Output

1 2 5 5 5 9 minus 2 5 7 is: 1 5 5 9

This is example with minus operator.

void set_difference_example()
{
    std::vector v1{ 1, 2, 5, 5, 5, 9 };
    std::vector v2{    2, 5,       7 };

    std::vector diff = s(v1) - s(v2);

    for (auto i : v1) std::cout << i << ' ';
    std::cout << "minus ";
    for (auto i : v2) std::cout << i << ' ';
    std::cout << "is: ";

    for (auto i : diff) std::cout << i << ' ';
    std::cout << '\n';
}

The code for minus operator is shown below.

template
T operator-(wrapper& left, wrapper& right)
{
    T& c1 = left.cont;
    T& c2 = right.cont;
    if (!std::is_sorted(c1.begin(), c1.end()))
        std::sort(c1.begin(), c1.end());
    if (!std::is_sorted(c2.begin(), c2.end()))
        std::sort(c2.begin(), c2.end());

    T diff;

    std::set_difference(c1.begin(), c1.end(),
        c2.begin(), c2.end(),
        std::back_inserter(diff));

    return std::move(diff);
}

Set Symmetric Difference

set_sym_difference2

C++ Reference: std::set_symmetric_difference

  • Commutative

set_symmetric_difference computes the elements in either set but not both.

void set_symmetric_difference_example()
{
    std::vector v1{ 1,2,3,4,5,6,7,8 };
    std::vector v2{         5,  7,  9,10 };
    std::sort(v1.begin(), v1.end());
    std::sort(v2.begin(), v2.end());

    std::vector v_symDifference;

    std::set_symmetric_difference(
        v1.begin(), v1.end(),
        v2.begin(), v2.end(),
        std::back_inserter(v_symDifference));

    for (int n : v_symDifference)
        std::cout << n << ' ';
}

Output

1 2 3 4 6 8 9 10

set_symmetric_difference is represented by logical exclusive or operator.

void set_symmetric_difference_example()
{
    std::vector v1{ 1,2,3,4,5,6,7,8 };
    std::vector v2{         5,  7,  9,10 };

    std::vector v_symDifference = s(v1) ^ s(v2);

    for (int n : v_symDifference)
        std::cout << n << ' ';
}

The code for logical exclusive or operator is shown below.

template
T operator^(wrapper& left, wrapper& right)
{
    T& c1 = left.cont;
    T& c2 = right.cont;
    if (!std::is_sorted(c1.begin(), c1.end()))
        std::sort(c1.begin(), c1.end());
    if (!std::is_sorted(c2.begin(), c2.end()))
        std::sort(c2.begin(), c2.end());

    T v_symDifference;

    std::set_symmetric_difference(c1.begin(), c1.end(),
        c2.begin(), c2.end(),
        std::back_inserter(v_symDifference));

    return std::move(v_symDifference);
}

Superset and Subset

set_superset2

C++ Reference: std::includes

  • Non-Commutative

STL includes can be used to find out whether a set is a superset(returns a boolean). To check if it is subset, just switch the 2 sets.

void is_superset_example()
{
    std::vector v1{ 'a', 'b', 'c', 'f', 'h', 'x' };
    std::vector v2{ 'a', 'b', 'c' };
    std::vector v3{ 'a', 'c' };
    std::vector v4{ 'g' };
    std::vector v5{ 'a', 'c', 'g' };
    std::sort(v1.begin(), v1.end());
    std::sort(v2.begin(), v2.end());
    std::sort(v3.begin(), v3.end());
    std::sort(v4.begin(), v4.end());
    std::sort(v5.begin(), v5.end());

    for (auto i : v1) std::cout << i << ' ';
    std::cout << "\nincludes:\n" << std::boolalpha;

    for (auto i : v2) std::cout << i << ' ';
    std::cout << ": " 
              << std::includes(v1.begin(), v1.end(), v2.begin(), v2.end()) << '\n';
    for (auto i : v3) std::cout << i << ' ';
    std::cout << ": " 
              << std::includes(v1.begin(), v1.end(), v3.begin(), v3.end()) << '\n';
    for (auto i : v4) std::cout << i << ' ';
    std::cout << ": " 
              << std::includes(v1.begin(), v1.end(), v4.begin(), v4.end()) << '\n';
    for (auto i : v5) std::cout << i << ' ';
    std::cout << ": " 
              << std::includes(v1.begin(), v1.end(), v5.begin(), v5.end()) << '\n';

    auto cmp_nocase = [](char a, char b) {
        return std::tolower(a) < std::tolower(b);
    };

    std::vector v6{ 'A', 'B', 'C' };
    for (auto i : v6) std::cout << i << ' ';
    std::cout << ": (case-insensitive) "
        << std::includes(v1.begin(), v1.end(), v6.begin(), v6.end(), cmp_nocase)
        << '\n';
}

Output

a b c f h x
includes:
a b c : true
a c : true
g : false
a c g : false
A B C : (case-insensitive) true

The >= operator example is below. The <= operator example is not shown in this article.

void is_superset_example()
{
    std::vector v1{ 'a', 'b', 'c', 'f', 'h', 'x' };
    std::vector v2{ 'a', 'b', 'c' };
    std::vector v3{ 'a', 'c' };
    std::vector v4{ 'g' };
    std::vector v5{ 'a', 'c', 'g' };

    for (auto i : v1) std::cout << i << ' ';
    std::cout << "\nincludes:\n" << std::boolalpha;

    for (auto i : v2) std::cout << i << ' ';
    std::cout << ": " <= s(v2)) << '\n';
    for (auto i : v3) std::cout << i << ' ';
    std::cout << ": " <= s(v3)) << '\n';
    for (auto i : v4) std::cout << i << ' ';
    std::cout << ": " <= s(v4)) << '\n';
    for (auto i : v5) std::cout << i << ' ';
    std::cout << ": " <= s(v5)) << '\n';

    auto cmp_nocase = [](char a, char b) {
        return std::tolower(a) < std::tolower(b);
    };

    std::vector v6{ 'A', 'B', 'C' };
    for (auto i : v6) std::cout << i << ' ';
    std::cout << ": (case-insensitive) "
        << std::includes(v1.begin(), v1.end(), v6.begin(), v6.end(), cmp_nocase)
        << '\n';
}

User cannot opt for use of a custom comparator in the >= and <= overloaded operators at the moment, as shown in the case-insensitive example. In this situation, includes has to be called directly.

// Returns true if left is superset of right?
template
bool operator>=(wrapper& left, wrapper& right)
{
    T& c1 = left.cont;
    T& c2 = right.cont;

    if (!std::is_sorted(c1.begin(), c1.end()))
        std::sort(c1.begin(), c1.end());
    if (!std::is_sorted(c2.begin(), c2.end()))
        std::sort(c2.begin(), c2.end());

    return std::includes(
        c1.begin(), c1.end(),
        c2.begin(), c2.end());
}

// Returns true if left is subset of right?
template
bool operator<=(wrapper& left, wrapper& right)
{
    T& c1 = left.cont;
    T& c2 = right.cont;

    if (!std::is_sorted(c1.begin(), c1.end()))
        std::sort(c1.begin(), c1.end());
    if (!std::is_sorted(c2.begin(), c2.end()))
        std::sort(c2.begin(), c2.end());

    return std::includes(
        c2.begin(), c2.end(),
        c1.begin(), c1.end());
}

“I have no use for all these!”

Before you are quick to exclaim that you have no use for these set algorithms, I like to show to you a typical selection example where you can use this. Imagine you are writing a subject enrollment website for college students. On the form, there are currently selected subjects which the student added, and the available subject dropdown which student can pick. It makes sense to remove subject from available dropdown after addition because you do not want the student to accidentally add the same subject twice. One way to compute leftover subjects available for selection, is to just subtract the selected set from the complete set of subjects with minus operator introduced in this article.

Article source code is hosted at Github

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