std::stable_sort - cppreference.com
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    std::stable_sort

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    C++
     
    Algorithm library
    Constrained algorithms and algorithms on ranges (C++20)
    Constrained algorithms, e.g. ranges::copy, ranges::sort, ...
    Non-modifying sequence operations    
    Batch operations
    (C++17)
    Search operations
    Modifying sequence operations
    Copy operations
    (C++11)
    (C++11)
    (C++11)
    Swap operations
    Transformation operations
    Generation operations
    Removing operations
    Order-changing operations
    (until C++17)(C++11)
    (C++20)(C++20)
    Sampling operations
    (C++17)

    Sorting and related operations
    Partitioning operations
    (C++11)    
    (C++11)

    Sorting operations
    Binary search operations
    (on partitioned ranges)
    Set operations (on sorted ranges)
    Merge operations (on sorted ranges)
    Heap operations
    Minimum/maximum operations
    (C++11)
    (C++17)
    Lexicographical comparison operations
    (C++20)
    Permutation operations


     
    Defined in header <algorithm> 
    template< class RandomIt >
void stable_sort( RandomIt first, RandomIt last );
    		(1) (constexpr since C++26) 
    template< class RandomIt, class Compare >
void stable_sort( RandomIt first, RandomIt last, Compare comp );
    		(2) (constexpr since C++26) 
    template< class ExecutionPolicy, class RandomIt >
void stable_sort( ExecutionPolicy&& policy,
                  RandomIt first, RandomIt last );
    		(3) (since C++17) 
    template< class ExecutionPolicy, class RandomIt, class Compare >
void stable_sort( ExecutionPolicy&& policy,
                  RandomIt first, RandomIt last, Compare comp );
    		(4) (since C++17)

    Sorts the elements in the target range [first, last). The order of equivalent elements is guaranteed to be preserved.

    1) Elements are sorted with respect to operator<(until C++20)std::less{}(since C++20).
    2) Elements are sorted with respect to comp.
    3,4) Same as (1,2), but executed according to policy.
    These overloads participate in overload resolution only if the value of the following expression is true:

    std::is_execution_policy_v<std::decay_t<ExecutionPolicy>>

    		(until C++20)

    std::is_execution_policy_v<std::remove_cvref_t<ExecutionPolicy>>

    		(since C++20)

    If any of the following conditions is satisfied, the behavior is undefined:

    (until C++11)
    (since C++11)

    Parameters

    first, last - the pair of iterators defining the target range
    comp - comparison function object (i.e. an object that satisfies the requirements of Compare) which returns ​true if the first argument is less than (i.e. is ordered before) the second.

    The signature of the comparison function should be equivalent to the following:

    bool cmp(const Type1& a, const Type2& b);

    While the signature does not need to have const&, the function must not modify the objects passed to it and must be able to accept all values of type (possibly const) Type1 and Type2 regardless of value category (thus, Type1& is not allowed, nor is Type1 unless for Type1 a move is equivalent to a copy(since C++11)).
    The types Type1 and Type2 must be such that an object of type RandomIt can be dereferenced and then implicitly converted to both of them. ​

    policy - the execution policy to use
    Type requirements
    -
    RandomIt must meet the requirements of LegacyRandomAccessIterator.
    -
    Compare must meet the requirements of Compare.

    Complexity

    Given N as last - first:

    1,3) 𝓞(N·log2(N)) comparisons using operator<(until C++20)std::less{}(since C++20) (or only 𝓞(N·log(N)) comparisons if enough extra memory is available).
    2,4) 𝓞(N·log2(N)) applications of the comparator comp (or only 𝓞(N·log(N)) comparisons if enough extra memory is available).

    Exceptions

    3,4) During the execution process:
    • If the temporary memory resources required for parallelization are not available, std::bad_alloc is thrown.
    • If an uncaught exception is thrown while accessing objects via an algorithm argument, the behavior is determined by the execution policy (for standard policies, std::terminate is invoked).

    Notes

    This function attempts to allocate a temporary buffer equal in size to the sequence to be sorted. If the allocation fails, the less efficient algorithm is chosen.

    Feature-test macro Value Std Feature
    __cpp_lib_constexpr_algorithms 202306L (C++26) constexpr stable sorting, overloads (1,2)

    Possible implementation

    See also the implementations in libstdc++ and libc++.

    Example

    Run this code
    #include <algorithm>
#include <array>
#include <iostream>
#include <string>
#include <vector>
 
struct Employee
{
    int age;
    std::string name; // Does not participate in comparisons
};
 
bool operator<(const Employee& lhs, const Employee& rhs)
{
    return lhs.age < rhs.age;
}

#if __cpp_lib_constexpr_algorithms >= 202306L
consteval auto get_sorted()
{
    auto v = std::array{3, 1, 4, 1, 5, 9};
    std::stable_sort(v.begin(), v.end());
    return v;
}
static_assert(std::ranges::is_sorted(get_sorted()));
#endif

int main()
{
    std::vector<Employee> v{{108, "Zaphod"}, {32, "Arthur"}, {108, "Ford"}};
    
    std::stable_sort(v.begin(), v.end());
    
    for (const Employee& e : v)
        std::cout << e.age << ", " << e.name << '\n';
}

    Output: 

    32, Arthur
108, Zaphod
108, Ford

    See also