function balanceFactor(node) {
    if (!node) {
        return 0;
    }

    let [left, right] = [nodeRank(node.left), nodeRank(node.right)];
    return right - left;
}

function updateRank(node) {
    let [left, right] = [nodeRank(node.left), nodeRank(node.right)];
    node.rank = 1 + Math.max(left, right);
}

class AVLTree extends RankedTree {
    isCorrectNode(node, recursive) {
        if (!node) {
            return true;
        }

        let differences = nodeDifferences(node).sort();
        if (
            (!differences.equals([1, 1]) && !differences.equals([1, 2])) ||
            node.rank != 1 + Math.max(...differences)
        ) {
            return false;
        }

        recursive = recursive ?? true;
        return (
            !recursive ||
            (this.isCorrectNode(node.left) && this.isCorrectNode(node.right))
        );
    }

    fix0Child(x, y, z, rotatingAroundRoot, rotateLeft, rotateRight) {
        let newRoot = x.parent;

        if (!y || nodeDifference(y) == 2) {
            newRoot = rotateRight(z);
            if (rotatingAroundRoot) {
                this.root = newRoot;
            }
            this.record("Fixing 0-child by single rotation: by z", z);

            z.demote();
            this.record("Fixing 0-child by single rotation: demoting z", z);
        } else if (nodeDifference(y) == 1) {
            rotateLeft(x);
            this.record(
                "Fixing 0-child by double-rotation: first rotation by x",
                x
            );

            newRoot = rotateRight(z);
            if (rotatingAroundRoot) {
                this.root = newRoot;
            }
            this.record(
                "Fixing 0-child by double-rotation: second rotation by z",
                z
            );

            y.promote();
            this.record("Fixing 0-child by double-rotation: promoting y", y);

            x.demote();
            this.record("Fixing 0-child by double-rotation: demoting x", x);

            z.demote();
            this.record("Fixing 0-child by double-rotation: demoting z", z);
        }
    }

    insertRebalance(x) {
        let diffs = nodeDifferences(x.parent).sort();
        while (x.parent && diffs.equals([0, 1])) {
            x.parent.promote();
            this.record(
                "Insertion rebalance: promoting (0, 1) parent",
                x.parent
            );

            x = x.parent;
            diffs = nodeDifferences(x.parent).sort();
        }

        if (!x.parent) {
            return;
        }

        let rotatingAroundRoot = x.parent.parent == null;

        let rankDifference = nodeDifference(x);
        if (rankDifference != 0) {
            return;
        }

        let xParent = x.parent;

        if (rankDifference == 0 && x.parent.left === x) {
            this.fix0Child(
                x,
                x.right,
                xParent,
                rotatingAroundRoot,
                rotateLeft,
                rotateRight
            );
        } else if (rankDifference == 0 && x.parent.right === x) {
            this.fix0Child(
                x,
                x.left,
                xParent,
                rotatingAroundRoot,
                rotateRight,
                rotateLeft
            );
        }
    }

    deleteRotate(x, y, leaning, rotatingAroundRoot, rotateLeft, rotateRight) {
        let newRoot = x;

        let factor = balanceFactor(y);
        switch (factor) {
            case 0:
            case leaning:
                newRoot = rotateLeft(x);
                break;
            default:
                rotateRight(y);
                this.record("AVL deletion, fixing by double-rotation: by y", y);

                newRoot = rotateLeft(x);
                break;
        }
        if (rotatingAroundRoot) {
            this.root = newRoot;
        }
        this.record("AVL deletion, fixing by rotation by x", x);

        [newRoot.left, newRoot.right, newRoot]
            .filter((x) => x)
            .forEach((n) => {
                updateRank(n);
                this.record("Updating rank of nodes affected by rotations", n);
            });

        return factor == 0;
    }

    deleteFixup(y, parent) {
        let x = y ? y : parent;

        let factor = balanceFactor(x);
        switch (factor) {
            case 0:
                updateRank(x);
                this.record(
                    "Updating rank of node affected by the propagation of delete",
                    x
                );

                return false;
            case -1:
            case 1:
                return true;
        }

        let rotatingAroundRoot = x.parent == null;
        let [z, leaning, toLeft, toRight] = [
            x.left,
            -1,
            rotateRight,
            rotateLeft,
        ];
        if (factor == 2) {
            [z, leaning, toLeft, toRight] = [
                x.right,
                1,
                rotateLeft,
                rotateRight,
            ];
        }

        return this.deleteRotate(
            x,
            z,
            leaning,
            rotatingAroundRoot,
            toLeft,
            toRight
        );
    }

    deleteRebalance(node, parent) {
        while (node || parent) {
            this.deleteFixup(node, parent);
            [node, parent] = [parent, parent ? parent.parent : null];
        }
    }
}