AVL tree

#include <SFML/Graphics.hpp>
#include<iostream>
#include<string>
#include<cstdlib>
#include<conio.h>
#include<vector>
#include<iomanip>
using namespace sf;


struct node {
    int         key;
    uint8_t     height;

    node*       left;
    node*       right;

    node(int k, node* leftC = nullptr, node* rightC = nullptr) :
            key(k), left(leftC), right(rightC), height(1) {}

};


class AVL_Tree {
public:
    AVL_Tree(node* _root) : root(_root) {}

    node* insert(int k)
    {
        root = insert(root, k);
    }

    void search(int k) {
        root = find(root, k);
    }

private:

    node* find(node* v, int k) {
        if (v == nullptr)
            return nullptr;
        else if (k < v->key) {
            return find(v->left, k);
        }
        else if (k > v->key) {
            return find(v->right, k);
        }
        else
            return v;
    }

    node* insert(node* v, int k) // вставка ключа k в дерево с корнем p
    {
        if (!v) return new node(k);
        if (k < v->key)
            v->left = insert(v->left, k);
        else
            v->right = insert(v->right, k);
        return balance(v);
    }
    uint8_t getHeight(node* v) {
        return (v ? v->height : 0);
    }

    int balanceFactor(node* v) {
        return getHeight(v->right) - getHeight(v->left);
    }

    void fixHeight(node* v) {
        uint8_t hl = getHeight(v->left);
        uint8_t hr = getHeight(v->right);

        v->height = (hl > hr ? hl : hr) + 1;
    }

    node* rotateRight(node* v) {
        node* q = v->left;

        v->left = q->right;
        q->right = v;

        fixHeight(v); fixHeight(q);

        return q;
    }

    node* rotateLeft(node* v) {
        node* q = v->right;

        v->right = q->left;
        q->left = v;

        fixHeight(v); fixHeight(q);

        return q;
    }

    node* balance(node* v)
    {
        fixHeight(v);
        if (balanceFactor(v) == 2)
        {
            if (balanceFactor(v->right) < 0)
                v->right = rotateRight(v->right);
            return rotateLeft(v);
        }
        if (balanceFactor(v) == -2)
        {
            if (balanceFactor(v->left) > 0)
                v->left = rotateLeft(v->left);
            return rotateRight(v);
        }
        return v;
    }

    node* root;

};