class Queue {
    constructor() {
        this.q = [];
    }

    enqueue(x) {
        this.q.push(x);
    }

    dequeue() {
        return this.q.shift();
    }

    isEmpty() {
        return this.q.length == 0;
    }
}

class RankedTree {
    constructor() {
        this.root = null;
    }

    _getUnwrappedGraph() {
        let result = "";

        let q = new Queue();
        q.enqueue(this.root);

        let edges = [];
        while (!q.isEmpty()) {
            let node = q.dequeue();
            if (!q) {
                continue;
            }

            result += `"${node.toString()}" [label="${node.value}, ${node.rank}"];\n`;

            [node.left, node.right].filter(child => child).forEach(child => {
                edges.push([node, child]);
                q.enqueue(child);
            });
        }

        edges.forEach(vertices => {
            let [u, v] = vertices;
            result += `"${u.toString()}" -> "${v.toString()}" [label="${nodeDifference(v)}"]\n`;
        });

        return result;
    }

    toString() {
        return `digraph {\n${this._getUnwrappedGraph()}}\n`;
    }

    rank() {
        return nodeRank(this.root);
    }

    isCorrect() {
        return this.isCorrectNode(this.root);
    }

    search(value, node) {
        return nodeSearch(value, node || this.root);
    }

    insert(value) {
        let insertedNode = new Node(value);

        if (!this.root) {
            this.root = insertedNode;
            return;
        }

        let parent = findParentNode(value, this.root);
        if (!parent) {
            return;
        }

        insertedNode.parent = parent;

        if (value < parent.value) {
            parent.left = insertedNode;
        } else {
            parent.right = insertedNode;
        }

        this.insertRebalance(insertedNode);
    }

    transplant(u, v) {
        if (!u.parent) {
            this.root = v;
        } else if (u.parent.left === u) {
            u.parent.left = v;
        } else {
            u.parent.right = v;
        }

        if (v) {
            v.rank = u.rank;
            v.parent = u.parent;
        }
    }

    deleteNode(node) {
        if (!node) {
            return null;
        }

        let [y, parent] = [null, node.parent];

        if (!node.left) {
            y = node.right;
            this.transplant(node, node.right);
        } else if (!node.right) {
            y = node.left;
            this.transplant(node, node.left);
        } else {
            let successor = nodeMinimum(node.right);
            parent = successor.parent != node ? successor.parent : successor;

            if (successor.parent != node) {
                parent = successor.right ? successor.right : successor.parent;
                this.transplant(successor, successor.right);
                successor.right = node.right;
                successor.right.parent = successor;
            }

            this.transplant(node, successor);
            successor.left = node.left;
            node.left.parent = successor;
        }

        return [y, parent];
    }

    delete(value) {
        let node = this.root;
        while (node && node.value != value) {
            node = value < node.value ? node.left : node.right;
        }

        let toRebalance = this.deleteNode(node);
        if (toRebalance) {
            let [y, parent] = toRebalance;
            this.deleteRebalance(y, parent);
        }
    }

    /* abstract methods */
    isCorrectNode(node) {
        throw "not implemented!";
    }

    insertRebalance(node) {
        throw "not implemented!";
    }

    deleteRebalance(node, parent) {
        throw "not implemented!";
    }
}