splay_operation.h

// A node of the tree
class Node {
  public:
    int key;
    Node* left;
    Node* right;
    Node* parent;

    // Constructor
    Node(int key, Node* parent=nullptr, Node* left=nullptr, Node* right=nullptr) {
        this->key = key;
        this->parent = parent;
        this->left = left;
        this->right = right;
        if (left) left->parent = this;
        if (right) right->parent = this;
    }
};

// Binary tree
class Tree {
  public:
    // Pointer to root of the tree; nullptr if the tree is empty.
    Node* root;

    Tree(Node* root=nullptr) {
        this->root = root;
    }

    // Rotate the given `node` up. Perform a single rotation of the edge
    // between the node and its parent, choosing left or right rotation
    // appropriately.
    virtual void rotate(Node* node) {
        if (node->parent) {
            if (node->parent->left == node) {
                if (node->right) node->right->parent = node->parent;
                node->parent->left = node->right;
                node->right = node->parent;
            } else {
                if (node->left) node->left->parent = node->parent;
                node->parent->right = node->left;
                node->left = node->parent;
            }
            if (node->parent->parent) {
                if (node->parent->parent->left == node->parent)
                    node->parent->parent->left = node;
                else
                    node->parent->parent->right = node;
            } else {
                root = node;
            }

            Node* original_parent = node->parent;
            node->parent = node->parent->parent;
            original_parent->parent = node;
        }
    }

    // Look up the given key in the tree, returning the
    // the node with the requested key or nullptr.
    Node* lookup(int key) {
        // TODO: Utilize splay suitably.
        Node* node = root;
        while (node) {
            if (node->key == key) {
                return node;
            }
            if (key < node->key)
                node = node->left;
            else