Why does priority_queue in STL not follow strict weak ordering?

i Have been playing around with STL containers and the compare function/functors they supports, however i found priority_queue doesn't follow the usual strict weak ordering , i am trying to understand what might be the reason but not able to figure it out, any pointers would be helpful.

It also mentioned in this blog that priority_queue doesnt follow strict weak ordering. enter link description here

#include "STL.h"
#include "queue"
#include "vector"
#include "iostream"
#include "functional"
using namespace std;

typedef bool(*func)(const int& val1 , const int& val2);

bool strict_weak_order_function(const int& val1 , const int& val2){
    return val1 > val2;
}

bool comparer_function(const int& val1 , const int& val2){
    return !strict_weak_order_function(val1 , val2);
}

struct Compaper_functor{
    bool operator()(const int& val1 , const int& val2){
        return !strict_weak_order_function(val1 , val2);
    }
};


void runPriorityQueue(void){
    //priority_queue<int , vector<int> , func > pq(comparer_function);
    priority_queue<int , vector<int> , Compaper_functor > pq;
    int size;
    cin >> size;
    while(size--){
        int val;
        cin >> val;
        pq.push(val);
    }
    while(!pq.empty()){
        cout <<'\n'<< pq.top() << '\n';
        pq.pop();
    }
}

The problem is that the negation of your strict_weak_order (that uses >) is <= and that is not a strict weak order. A strict weak order R has to satisfy x R x == false for all x. However, R equal to <= yields (x <= x) == true.

You need to reverse the order of arguments (which corresponds to <) instead.

bool comparer_function(const int& val1 , const int& val2){
    return strict_weak_order_function(val2 , val1);
}

struct Compaper_functor{
    bool operator()(const int& val1 , const int& val2){
        return strict_weak_order_function(val2 , val1);
    }
};

Note however that a std::priority_queue has a std::less as default comparator, but that gives a max-heap (i.e. [5, 4, 3, 2, 1] output from the same input), so to get a min-heap (i.e. with output [1, 2, 3, 4, 5] from input [5, 4, 3, 2, 1]) you need to pass std::greater, see e.g. this:

#include <queue>
#include <iostream>

int main()
{
    auto const v  = std::vector<int> { 5, 4, 3, 2, 1 };

    // prints 5 through 1
    for (auto p = std::priority_queue<int> { v.begin(), v.end()  }; !p.empty(); p.pop())
        std::cout << p.top() << ',';
    std::cout << '\n';

    // prints 1 through 5
    for (auto p = std::priority_queue<int, std::vector<int>, std::greater<int>> { v.begin(), v.end()  }; !p.empty(); p.pop())
        std::cout << p.top() << ',';
    std::cout << '\n';
}

Live Example