Using comparator to sort set of unique pairs with different criterias for uniqueness and less than

Question

First of all I've tried to search for similar questions but I didn't find any response explaining what could my problem be.

The problem is the following: Given a set of N nodes with coordinates (x,y,z) sort them using a 4th value F as fast as possible.

I want to use a std::set with a custom comparator for this purpose because it has O(log(N)) complexity. I know I could also try a std::vector and a call to std::sort on std::vector but in theory is a slower operation.

Why this? Because I'm constantly inserting elements in the set, changing the F value (it means I change the value and to reorder the element in the container I erase and re-insert it) and I want to take the element with the less F value (that's the element at the front of the container).

But let's go with the std::set problem.

The coordinates define the uniqueness property, following the strict weak ordering rules,it means that a and b are the considered the same object if

!comp(a,b) && !comp(b,a)

The problem is related to define a uniqueness criteria based on the coordinates and a sorting criteria based on the F value. I don't want the set to store two elements with the same coordiantes, but I want it to be allow to store two elements with different coordinates but same F value

The comparator should also satisfais the following three properties:

1. Irreflexivity x < x false
2. Assymetry x < y true implies y < x false
3. Transitivy x < y && y < z implies x < z true

So knowing all these properties I've been working around with the following example implementation:

Some definitions

class Node;
struct NodeComparator;
using NodePair = std::pair<Node *, int>;
using NodeSet  = std::set<NodePair, NodeComparator>;

Here I'm using pointers for convenience

Class Node

class Node
{

public:
    Node()
    {
    }
    Node(int _x, int _y, int _z, int _val) : x(_x), y(_y), z(_z), value(_val)
    {
    }

    int x, y, z;
    int value;

    friend inline std::ostream &operator<<(std::ostream &os, const Node &dt)
    {
        os << "[" << dt.x << ", " << dt.y << ", " << dt.z << "], [" << dt.value << "]";
        return os;
    }
    friend bool operator==(const Node &_lhs, const Node &_rhs){
        if( _lhs.x == _rhs.x &&
            _lhs.y == _rhs.y &&
            _lhs.z == _rhs.z ){
                return true;
            }
        return false;
    }
};

Here the operator << is overloaded only for debugging purposes

The comparator

struct NodeComparator
{
    bool operator()(const NodePair &_lhs, const NodePair &_rhs) const
    {
        if( _lhs.first == nullptr || _rhs.first == nullptr )
            return false;
        /*
        This first check implements uniqueness. 
        If _lhs == _rhs --> comp(_lhs,_rhs) == false && comp(_rhs, _lhs) == false
        So ( !comp(l,r) && !comp(r,l) ) == true
        */
        if( *_lhs.first == *_rhs.first) 
            return false;
        
        int ret = _lhs.second - _rhs.second;
        return ret < 0;
    }
};

I guess one problem could be the case of two nodes with different coordinates but same F value

Full example with concrete cases

Ìn this example I use the above classes to insert/find/erase some elements, but has it is show on the output, it's not behaving as expected:

#include <iostream>
#include <set>
#include <vector>
#include <algorithm>
#include <tuple>

class Node;
struct NodeComparator;
using NodePair = std::pair<Node *, int>;
using NodeSet  = std::set<NodePair, NodeComparator>;
class Node
{

public:
    Node()
    {
    }
    Node(int _x, int _y, int _z, int _val) : x(_x), y(_y), z(_z), value(_val)
    {
    }

    int x, y, z;
    int value;

    friend inline std::ostream &operator<<(std::ostream &os, const Node &dt)
    {
        os << "[" << dt.x << ", " << dt.y << ", " << dt.z << "], [" << dt.value << "]";
        return os;
    }
};

struct NodeComparator
{
    bool operator()(const NodePair &_lhs, const NodePair &_rhs) const
    {
        /*
        This first check implements uniqueness. 
        If _lhs == _rhs --> comp(_lhs,_rhs) == false && comp(_rhs, _lhs) == false
        So ( !comp(l,r) && !comp(r,l) ) == true
        */
        if(_lhs == _rhs) 
            return false;
        
        int ret = _lhs.second - _rhs.second;
        return ret < 0;
    }
};
int main(int argc, char **argv)
{
    Node n1(0, 2, 4, 12), 
         n2(2, 4, 5, 25), 
         n3(0, 1, 4, 34), 
         n4(0, 1, 4, 20), 
         n5(0, 1, 5, 20),
         n6(0, 2, 4, 112);

    NodeSet set;

    set.insert({&n1, n1.value});
    set.insert({&n2, n2.value});
    set.insert({&n3, n3.value});
    set.insert({&n4, n4.value}); //Should not be inserted because it already exists n3 with same coords
    set.insert({&n5, n5.value});

    //Try to insert multiple times a previously inserted node (n1 coords is == n6 coords)
    //It should not be inserted because it already exists one node with the same coords (n1)
    set.insert({&n6, n6.value});
    set.insert({&n6, n6.value});
    set.insert({&n6, n6.value});
    set.insert({&n6, n6.value});
    set.insert({&n6, 0});
    set.insert({&n6, 1});

    if (set.find({&n4, n4.value}) != set.end())
        std::cout << "Found n4" << std::endl;
    
    auto it = set.erase({&n4, 20});
    std::cout << "It value (elements erased): " << it << std::endl;

    if (set.find({&n4, n4.value}) != set.end())
        std::cout << "Found n4 after removal" << std::endl;
    
    std::cout << "Final Set content: " << std::endl;
    for (auto &it : set)
        std::cout << *it.first << std::endl;


    return 0;
}

To compile it with C++11 or above: g++ -o main main.cpp

Output:

Found n4
It value (elements erased): 1
Final Set content: 
[0, 2, 4], [12]
[2, 4, 5], [25]
[0, 1, 4], [34]
[0, 2, 4], [112]

**Expected Output: ** Correspond to elements n1, n5, n2, n3 ordered from the one with less F (n1) to the one with the higher F (n3).

Final Set content: 
[0, 2, 4], [12]
[0, 1, 5], [20]
[2, 4, 5], [25]
[0, 1, 4], [34]

I would appreciate a lot any help or ideas and alternatives of implementation. Thanks

Answer 1

Unfortunately, your requirements cannot be fulfilled by one std::set alone. The std::set uses the same comparator for sorting and uniqueness. The comparator has no state, meaning, you cannot compare one time with the first and the next time with a second condition. That will not work.

So, you need to use 2 containers, like first a std::unordered_set using a comparator for equal coordinates and the a second container for the sorting, like a std::multiset..

You could also use a std::unordered_map in conjunction with a std::multiset.

Or you create your own container as a class and try to optimize performance.

Let me show you an example using the combination of std::unordered_set and std::multiset. It will be fast, because the std::unordered_set uses hashes.

#include <iostream>
#include <unordered_set>
#include <set>
#include <array>
#include <vector>

using Coordinate = std::array<int, 3>;

struct Node {
    Coordinate coordinate{};
    int value{};
    bool operator == (const Node& other) const { return coordinate == other.coordinate; }
    friend std::ostream& operator << (std::ostream& os, const Node& n) {
        return os << "[" << n.coordinate[0] << ", " << n.coordinate[1] << ", " << n.coordinate[2] << "], [" << n.value << "]"; }
};
struct CompareOnSecond { bool operator ()(const Node& n1, const Node& n2)const { return n1.value < n2.value; } };
struct Hash {size_t operator()(const Node& n) const {return n.coordinate[0] ^ n.coordinate[1] ^ n.coordinate[2];} };

using UniqueNodes = std::unordered_set<Node, Hash>;
using Sorter = std::multiset<Node, CompareOnSecond>;

int main() {
    // a vector with some test nodes
    std::vector<Node> testNodes{
    { {{0, 2, 4}}, 12 },
    { {{2, 4, 5}}, 25 },
    { {{0, 1, 4}}, 34 },
    { {{0, 1, 4}}, 20 },
    { {{0, 1, 5}}, 20 },
    { {{0, 2, 4}}, 112 } };

    // Here we will store the unique nodes
    UniqueNodes uniqueNodes{};
    for (const Node& n : testNodes) uniqueNodes.insert(n);

    // And now, do the sorting
    Sorter sortedNodes(uniqueNodes.begin(), uniqueNodes.end());

    // Some test functions
    std::cout << "\nSorted unique nodes:\n";
    for (const Node& n : sortedNodes) std::cout << n << '\n';

    // find a node
    if (sortedNodes.find({ {{0, 1, 4}}, 20 }) != sortedNodes.end())
        std::cout << "\nFound n4\n";

    // Erase a node
    auto it = sortedNodes.erase({ {{0, 1, 4}}, 20 });
    std::cout << "It value (elements erased): " << it << '\n';

    // Was it really erased?
    if (sortedNodes.find({ {{0, 1, 4}}, 20 }) != sortedNodes.end())
        std::cout << "\nFound n4 after removal\n";

    // Show final result
    std::cout << "\nFinal Set content:\n";
    for (const Node& n : sortedNodes) std::cout << n << '\n';
}

Answer 2

Finally, thanks to suggestions and comments of the users I implemented a solution using Boost multi index with 2 index. One hashed unique index and one ordered-non-unique index. Despite this I marked the answer above as accepted because is the most standard solution.

#include <iostream>
#include <boost/multi_index_container.hpp>
#include <boost/multi_index/ordered_index.hpp>
#include <boost/multi_index/identity.hpp>
#include <boost/multi_index/member.hpp>
#include <boost/multi_index/hashed_index.hpp>
#include <boost/multi_index/key_extractors.hpp>

using namespace ::boost;
using namespace ::boost::multi_index;

struct IndexByCost {};
struct IndexByWorldPosition {};

class Node
{

public:
    Node(int _val, int _i) : value(_val), index(_i) {}

    int value; //NON UNIQUE
    unsigned int index; //UNIQUE

    friend inline std::ostream &operator<<(std::ostream &os, const Node &dt)
    {
        os << dt.index << ": [" << dt.value << "]";
        return os;
    }

};

using MagicalMultiSet = boost::multi_index_container<
  Node*, // the data type stored
  boost::multi_index::indexed_by< // list of indexes
    boost::multi_index::hashed_unique<  //hashed index wo
      boost::multi_index::tag<IndexByWorldPosition>, // give that index a name
      boost::multi_index::member<Node, unsigned int, &Node::index> // what will be the index's key
    >,
    boost::multi_index::ordered_non_unique<  //ordered index over 'i1'
      boost::multi_index::tag<IndexByCost>, // give that index a name
      boost::multi_index::member<Node, int, &Node::value> // what will be the index's key
    >
  >
>;

int main(int argc, char const *argv[])
{
    
    MagicalMultiSet container;

    Node n1{24, 1};
    Node n2{12, 2};
    Node n3{214,3};
    Node n4{224,4};
    Node n5{221,5};
    Node n6{221,6};

    auto & indexByCost          = container.get<IndexByCost>();
    auto & indexByWorldPosition = container.get<IndexByWorldPosition>();

    indexByCost.insert(&n1);
    indexByCost.insert(&n2);
    indexByCost.insert(&n3);
    indexByCost.insert(&n4);
    indexByCost.insert(&n5);

    for(auto &it: indexByCost)
        std::cout << *it << std::endl;
    
    auto it = indexByCost.begin();
    std::cout << "Best Node " << **it << std::endl;

    indexByCost.erase(indexByCost.begin());

    it = indexByCost.begin();
    std::cout << "Best Node After erasing the first one: " << **it << std::endl;

    std::cout << "What if we modify the value of the nodes?" << std::endl;
    n2.value = 1;
    std::cout << "Container view from index by world position" << std::endl;
    for(auto &it: indexByWorldPosition)
        std::cout << *it << std::endl;
    
    auto found = indexByWorldPosition.find(2);
    if(found != indexByWorldPosition.end() )
        std::cout << "Okey found n2 by index" << std::endl;

    found = indexByWorldPosition.find(1);
    if(found != indexByWorldPosition.end() )
        std::cout << "Okey found n1 by index" << std::endl;
    
    std::cout << "Imagine we update the n1 cost" << std::endl;
    n1.value = 10000;
    indexByWorldPosition.erase(found);
    indexByWorldPosition.insert(&n1);

    std::cout << "Container view from index by cost " << std::endl;

    for(auto &it: indexByCost)
        std::cout << *it << std::endl;
    
    return 0;
}