How to orderly traverse a Boost.Heap Priority Queue and update a given element?

Question

I'm looking for a good data structure that can maintain its elements sorted. Currently I'm trying Boost.Heap.

I frequently need to orderly traverse the data structure and when reaching an element based on some property, update its priority. Boost.Heap priority queues provide ordered and non-ordered iterators. Element updates occurs through a node handle, a handle can be obtained from a ordinary non-ordered iterator, but not directly from a ordered one as in the following example:

#include <iostream>
#include <algorithm>
#include <boost/heap/fibonacci_heap.hpp>

using namespace boost::heap;

int main()
{
    fibonacci_heap<int> fib_heap;

    fib_heap.push(1);
    fib_heap.push(2);
    fib_heap.push(3);

    for(auto i = fib_heap.ordered_begin(); i != fib_heap.ordered_end(); ++i)
    {
        // no viable conversion here
        auto h = fibonacci_heap<int>::s_handle_from_iterator(i);

        if(*h == 2) // dumb test
        {
            fib_heap.increase(h, *h + 2);
            break;
        }
    }

    std::for_each(fib_heap.ordered_begin(), fib_heap.ordered_end(),
    [](const int &e)
    {
        std::cout << e << std::endl;
    });
}

How can I orderly traverse the queue and update an element in the traversal?

Note that I leave traversal after the update.

(Suggestions of alternative libraries for such purpose are welcome)

Answer 1

If I find no better alternative, I'll need to save the handle inside each corresponding element for later usage (c++1y code):

#include <iostream>
#include <algorithm>
#include <boost/heap/fibonacci_heap.hpp>

using namespace boost::heap;

template<typename T>
struct heap_data
{
    typedef typename fibonacci_heap<heap_data>::handle_type handle_t;
    handle_t handle;
    T data;

    heap_data(const T &data_) : data(data_) {}

    bool operator<(heap_data const & rhs) const
    {
        return data < rhs.data;
    }
};

void setup_handle(fibonacci_heap<heap_data<int>>::handle_type &&handle)
{
    (*handle).handle = handle;
}

int main()
{
    fibonacci_heap<heap_data<int>> heap;

    setup_handle(heap.emplace(1));
    setup_handle(heap.emplace(2));
    setup_handle(heap.emplace(3));

    std::find_if(heap.ordered_begin(), heap.ordered_end(),
    [&heap](const heap_data<int> &e)
    {
        if(e.data == 2)
        {
            const_cast<heap_data<int> &>(e).data += 2;
            heap.increase(e.handle);
            return true;
        }
        return false;
    });

    std::for_each(heap.ordered_begin(), heap.ordered_end(),
    [](const heap_data<int> &e)
    {
        std::cout << e.data << std::endl;
    });
}

Answer 2

Your requirements are not very clear to me. But how about std::multimap or std::multiset? Update operations are O(log n). I think traversal should be O(n) (BST traversal), but it's not documented in my standard C++ references (cppreference.com, cplusplus.com). Looks like boost::heap traversal is amortized O(n log n).