Binary Tree

#include <iostream>
#include <vector>

struct Node{
    Node *lhs;
    Node *rhs;
    int val;

    Node(int v) : val(v){
        rhs = nullptr;
        lhs = nullptr;
    }
};

class BinaryTree{
public:
    BinaryTree();
    BinaryTree(std::vector<bool> v);
    void push(int val);
    bool empty();
    int top() const;
    size_t Size() const;
    void print(Node* p);
    void printFromHead();
    BinaryTree& operator=(const BinaryTree& rhs){
        Node* tmp = rhs.head;
        return copy(tmp);
    }

private:
    size_t size;
    Node *head;
    BinaryTree& copy(Node* rhs);
};

BinaryTree& BinaryTree::copy(Node* rhs){
    if(rhs == nullptr){
        return *this;
    }

    copy(rhs->rhs);
    copy(rhs->lhs);
    push(rhs->val);
}

BinaryTree::BinaryTree() {
    head = nullptr;
    size = 0;
}

BinaryTree::BinaryTree(std::vector<bool> v){
    for (int i = 0; i < v.size(); ++i) {
        push(v[i]);
    }
}

void BinaryTree::print(Node* p){
    std::cout << p->val << '\n';
    if(p->lhs != nullptr){
        print(p->lhs);
    }
    if(p->rhs != nullptr){
        print(p->rhs);
    }
}

void BinaryTree::printFromHead() {
    print(head);
}

void BinaryTree::push(int val){
    Node *tmp = new Node(val);
    if(head != nullptr){
        Node *last = head;
        while(last->lhs != nullptr || last->rhs != nullptr){
            if(last->rhs != nullptr){
                last = last->rhs;
            }else if(last->lhs != nullptr){
                last = last->lhs;
            }else{
                break;
            }
        }

        if(last->val >= val){
            last->lhs = tmp;
        }else{
            last->rhs = tmp;
        }
    }else{
        head = new Node(val);
    }
    size++;
}

bool BinaryTree::empty(){
    return head == nullptr;
}

size_t BinaryTree::Size() const{
    return size;
}

int BinaryTree::top() const{
    return  head->val;
}

int main() {
    std::cout << "First tree:\n";
    BinaryTree *bt = new BinaryTree();
    bt->push(12);
    bt->push(10);
    bt->push(111);
    bt->push(150);
    std::cout << bt->empty() << '\n';
    std::cout << bt->Size() << '\n';
    bt->printFromHead();
    std::cout << "Second, bitmask tree:\n";

    std::vector<bool> v = {1,0,1,0};
    BinaryTree bt2 = BinaryTree(v);
    bt2.printFromHead();

    std::cout << "Third tree\n";
    BinaryTree bt3 = bt2;
    bt3.printFromHead();
}