why it isn't possible to sort a std::map directly using std::sort based upon its value field

Question

I've already seen lot of solutions for sorting a std::map based on its value. But I want to know why it's not possible to sort it directly using std::sort like the code I've written.

#include <iostream>
#include <map>
#include <algorithm>


void print_values(const std::map<size_t, size_t>& map_data) {
    for(const auto& my_pair : map_data)
        std::cout << my_pair.first << " : " << my_pair.second << "\n";
    std::cout << std::endl;
}

bool compare(const std::pair<size_t, size_t>& a, const std::pair<size_t, size_t>& b) {
    return a.second > b.second;
}

int32_t main(int32_t argc, char* argv[]) {
    std::map<size_t, size_t> coins_count;
    coins_count.insert(std::make_pair(1, 2));
    coins_count.insert(std::make_pair(2, 3));
    coins_count.insert(std::make_pair(3, 4));
    coins_count.insert(std::make_pair(4, 2));
    coins_count.insert(std::make_pair(5, 3));
    coins_count.insert(std::make_pair(6, 1));
    coins_count.insert(std::make_pair(7, 2));
    
    print_values(coins_count);
    
    std::sort(coins_count.begin(), coins_count.end(), compare);
    
    print_values(coins_count);

    return EXIT_SUCCESS;
}

Answer 1

std::map is implemented as some flavor of binary search tree sorted by key. That means that a std::map must always be sorted by key, using the comparison function defined for the map at construction time, for element lookup to function properly.

Answer 2

The map itself is always sorted by key. So you can only sort some other thing, that could refer to map elements.

You could sort an array of map iterators:

std::vector<decltype(coins_count)::iterator> vec;
for (auto i = coins_count.begin(), end = coins_count.end(); i != end; ++i) {
    vec.push_back(i);
}
std::sort(vec.begin(), vec.end(),
    [](auto& a, auto& b) { return a->second < b->second; }
);    
for(auto&& i : vec) {
    std::cout << i->first << " : " << i->second << "\n";
}

Alternatively you could sort an array of map keys:

std::vector<decltype(coins_count)::key_type> vec;
for(auto&& i : coins_count) {
    vec.push_back(i.first);
}
std::sort(vec.begin(), vec.end(),
    [&coins_count](auto& a, auto& b) {
        return coins_count.at(a) < coins_count.at(b);
    }
);
for(auto&& i : vec) {
    std::cout << i << " : " << coins_count.at(i) << "\n";
}

Code will output:

6 : 1
1 : 2
4 : 2
7 : 2
2 : 3
5 : 3
3 : 4

Answer 3

The elements of a map are always maintained in a sorted manner, by definition.

You can define this ordering yourself using a template argument, but you cannot manually change the order of elements yourself with std::sort (and this call will fail even if no elements would have been swapped).