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Associative containers place a strict weak ordering requirement on their key comparison predicates [ISO/IEC 14882-2014]. A strict weak ordering has the following properties:

• For for all x: x < x == false (irreflexivity)
• For for all x, y: if x < y then !(y < x) (asymmetry)
• For for all x, y, z: if x < y && y < z then x < z (transitivity)

Providing an invalid ordering predicate for an associative container (eg e.g., sets, maps, multisets, and multimaps), or as a comparison criterion with the sorting algorithms, can result in erratic behavior or infinite loops [Meyers 01]. When an ordering predicate is required for an associative container or a generic standard template library algorithm, the predicate must meet the requirements for inducing a strict weak ordering.

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In this noncompliant code example, the std::set object is created with a comparator that does not adhere to the strict weak ordering requirement. Specifically, it fails to return false for equivalent values. As a result, the behavior of iterating over the results from std::set::equal_range results in unspecified behavior:.

#include <functional>
#include <iostream>
#include <set>

void f() {
  std::set<int, std::less_equal<int>> s{5, 10, 20};  
  for (auto r = s.equal_range(10); r.first != r.second; ++r.first) {
    std::cout << *r.first << std::endl;
  }
}

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This compliant solution uses the default comparator with std::set instead of providing an invalid one:.

#include <iostream>
#include <set>

void f() {
  std::set<int> s{5, 10, 20};  
  for (auto r = s.equal_range(10); r.first != r.second; ++r.first) {
    std::cout << *r.first << std::endl;
  }
}

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This compliant solution uses std::tie() to properly implement the strict weak ordering operator< predicate:.

#include <iostream>
#include <set>
#include <tuple>
 
class S {
  int i, j;
 
public:
  S(int i, int j) : i(i), j(j) {}
  
  friend bool operator<(const S &lhs, const S &rhs) {
    return std::tie(lhs.i, lhs.j) < std::tie(rhs.i, rhs.j);
  }
  
  friend std::ostream &operator<<(std::ostream &os, const S& o) {
    os << "i: " << o.i << ", j: " << o.j;
    return os;
  }
};

void f() {
  std::set<S> t{S(1, 1), S(1, 2), S(2, 1)};  
  for (auto v : t) {
    std::cout << v << std::endl;
  }
}

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