#include<vector>
#include<algorithm>

struct Heap {
    // The tree relationships are index based. For node i (0-based), its children are 2*i+1 and 2*i+2
    std::vector<int> _values;
    
    void push(int value) {  // Add `value` into the heap
        _values.push_back(value);
        int i = _values.size()-1;
        
        // Maintain the heap property
        while(i > 0 && _values[(i-1)/2] < _values[i]) {
            std::swap(_values[(i-1)/2], _values[i]);
            i = (i-1)/2;
        }
    }
    
    int top() {
        return _values[0];
    }
    
    void pop() {  // Remove the highest value element
        std::swap(_values[0], _values.back());
        _values.pop_back();
        
        // Restore the heap property
        int i=-1, ni = 0;
        while(i != ni) {
            i = ni;
            // Check if left child is larger than node i
            if(2*i+1 < (int)_values.size() && _values[2*i+1] > _values[ni]) {
                ni = 2*i+1;
            }
            // Check if right child is larger than node i and the left child
            if(2*i+2 < (int)_values.size() && _values[2*i+2] > _values[ni]) {
                ni = 2*i+2;
            }
            std::swap(_values[i], _values[ni]);  // ni will be the index of the largest child larger than node i
        }
    }
};

int main() {
    Heap heap;
    heap.push(5);
    int max_element = heap.top();
    heap.pop();
}