Is It Possible to Set a std::function out of Class which need to Access private class member in C++

I'm writing a Priority Queue, here is my code

#include <iostream>
#include<vector>
#include <functional>

template <class T>
class MaxPQ
{
public:
    MaxPQ(size_t size): container(size)
    {
    }

    MaxPQ(std::vector<T>& Raw)
    {
        //hard-code set it inside of class
        //this->setWrapper([=](size_t x, size_t y) -> bool { return this->container[x] < this->container[y]; });

        container.clear();
        for (const auto& val : Raw)
        {
            this->insert(val);
        }
    }

    MaxPQ(): container(0)
    {
    }

    ~MaxPQ()
    {
        container.clear();
    }

    void setWrapper(std::function<bool(size_t, size_t)> input)
    {
        compare_wrapper = input;
    }

    void insert(T newEle)
    {
        container.push_back(newEle);
        swim(container.size() - 1);
    }

    T delMax()
    {
        T result = max();
        swapByIndex(0, container.size() - 1);
        container.erase(container.end());
        sink(0);
        return result;
    }

    inline T max()
    {
        return container[0];
    }

    void swapByIndex(size_t Left, size_t Right)
    {
        using std::swap;
        swap(container[Left], container[Right]);
    }


    inline size_t left(size_t parent)
    {
        return parent * 2 + 1;
    }

    inline size_t right(size_t parent)
    {
        return parent * 2 + 2;
    }

    inline size_t parent(size_t child)
    {
        return (child - 1) >= 0 ? (child - 1) / 2 : -1;
    }

    void print()
    {
        using std::cout;
        for (const auto& val : container)
            cout << val << " ";
        cout << std::endl;
    }

private:
    std::vector<T> container;
    std::function<bool(size_t, size_t)> compare_wrapper;

    void swim(size_t targetIndex)
    {
        while (targetIndex > 0 && compare_wrapper(parent(targetIndex), targetIndex))
        {
            swapByIndex(parent(targetIndex), targetIndex);
            targetIndex = parent(targetIndex);
        }
    }

    void sink(size_t targetIndex)
    {
        while (left(targetIndex) < container.size())
        {
            size_t maxIndex = left(targetIndex);
            if (right(targetIndex) < container.size() && compare_wrapper(maxIndex, right(targetIndex)))
            {
                maxIndex = right(targetIndex);
            }
            if (compare_wrapper(maxIndex, targetIndex))
            {
                break;
            }
            swapByIndex(targetIndex, maxIndex);
            targetIndex = maxIndex;
        }
    }
};


int main()
{
    std::vector<int> temp{1, 8, 0, 9, 12, 4};
    auto myPQ = new MaxPQ<int>(temp);
    myPQ->setWrapper([=](size_t x, size_t y) -> bool
    {
//error here, trying to access private member `container`
        return myPQ->container[x] < myPQ->container[y];
    }); //set it out of class
    myPQ->print();
}

all code works pretty fine when I hard-code compare to bool less(int,int)() bool less(int,int)() is a private (because there is no need to let other call it) member function which will access private member container but others may want to custom the function I guess it looks like a function come from outside, but can act like a member function (which could access private member)

so How could I do so(to set such wrapper function by using lambda function or std::function), where should I write the setWrapper funtion, and where should I call it

is this a good design?

how does std::for_each set its function wrapper?

I'm new to STL, I may have some term or concept wrong, and English is not my first language, please forgive me.

thanks in advance