Relational Operators

These are non-member functions.

Method
Multimap
Compares the values in the multimap
template <class K, size_t M, class T, class C, class A> bool operator==(const front<K, M, T, C, A> &lhs, const front<K, M, T, C, A> &rhs);
template <class K, size_t M, class T, class C, class A> bool operator!=(const front<K, M, T, C, A> &lhs, const front<K, M, T, C, A> &rhs);
FrontContainer
Front-Front Comparison
template <typename K, size_t M, typename T, typename C> bool operator<(const front<K, M, T, C> &lhs, const front<K, M, T, C> &rhs);
template <typename K, size_t M, typename T, typename C> bool operator>(const front<K, M, T, C> &lhs, const front<K, M, T, C> &rhs)
template <typename K, size_t M, typename T, typename C> bool operator<=(const front<K, M, T, C> &lhs, const front<K, M, T, C> &rhs)
template <typename K, size_t M, typename T, typename C> bool operator>=(const front<K, M, T, C> &lhs, const front<K, M, T, C> &rhs)
Front-Point Comparison
template <typename K, size_t M, typename T, typename C> bool operator<(const front<K, M, T, C> &lhs, const typename front<K, M, T, C>::key_type &rhs)
template <typename K, size_t M, typename T, typename C> bool operator>(const front<K, M, T, C> &lhs, const typename front<K, M, T, C>::key_type &rhs)
template <typename K, size_t M, typename T, typename C> bool operator<=(const front<K, M, T, C> &lhs, const typename front<K, M, T, C>::key_type &rhs)
template <typename K, size_t M, typename T, typename C> bool operator>=(const front<K, M, T, C> &lhs, const typename front<K, M, T, C>::key_type &rhs)
template <typename K, size_t M, typename T, typename C> bool operator<(const typename front<K, M, T, C>::key_type &lhs, const front<K, M, T, C> &rhs)
template <typename K, size_t M, typename T, typename C> bool operator>(const typename front<K, M, T, C>::key_type &lhs, const front<K, M, T, C> &rhs)
template <typename K, size_t M, typename T, typename C> bool operator<=(const typename front<K, M, T, C>::key_type &lhs, const front<K, M, T, C> &rhs)
template <typename K, size_t M, typename T, typename C> bool operator>=(const typename front<K, M, T, C>::key_type &lhs, const front<K, M, T, C> &rhs)

Parameters

• lhs, rhs - fronts or key_types whose contents to compare

Return value

• operator==, operator!=: true if the internal contents of the fronts are equal, false otherwise.
• operator<, operator>, operator<=, operator>=: true if front lhs (or a front containing only lhs as a point) dominates rhs

Complexity

• operator==, operator!=: \(O(mn)\)
• operator<, operator>, operator<=, operator>=: \(O(m n \log n)\) for fronts and \(O(m \log n)\) for points

\[ O(1) \]

Notes

In addition to the equality and inequality operators defined for spatial containers, the front contains includes relational operators.

In the context of fronts, operator< return true if the front lhs dominates the front rhs. When one of these parameters is a point, we treat this point as if it were front with a single point.

Info

Although these operators could be defined in other ways, the operators operator<, operator>, operator<=, operator>= as defined here are are later useful for pareto::archive containers, which need to sort fronts by their dominance relationships.

Example

C++

front<double, 3, unsigned> pf3(pf);
if (pf == pf3) {
    std::cout << "The fronts have the same elements" << std::endl;
} else {
    if (pf.size() != pf3.size()) {
        std::cout << "The fronts do not have the same elements" << std::endl;
    } else {
        std::cout << "The fronts might not have the same elements"
                  << std::endl;
    }
}

front<double, 3, unsigned> pf4(pf.begin(), pf.end());
if (pf == pf4) {
    std::cout << "The fronts have the same elements" << std::endl;
} else {
    if (pf.size() != pf4.size()) {
        std::cout << "The fronts do not have the same elements" << std::endl;
    } else {
        std::cout << "The fronts might not have the same elements"
                  << std::endl;
    }
}

if (pf_star < pf) {
    std::cout << "pf* dominates pf" << std::endl;
} else {
    std::cout << "pf* does not dominate pf" << std::endl;
}

Python

pf3 = pareto.front(pf)
if pf == pf3:
    print('The containers have the same elements')
else:
    if len(pf) != len(pf3):
        print('The containers do not have the same elements')
    else:
        print('The containers might not have the same elements')
        # You need a for loop after here to make sure

pf4 = pareto.front()
for [k, v] in pf:
    pf4[k] = v

if pf == pf4:
    print('The containers have the same elements')
else:
    if len(pf) != len(pf4):
        print('The containers do not have the same elements')
    else:
        print('The containers might not have the same elements')
        # You need a for loop after here to make sure

if pf_star < pf:
    print('pf* dominates pf')
else:
    print('pf* does not dominate pf')

Output

The fronts have the same elements
The fronts do not have the same elements
pf* dominates pf