/**
 * data-structure-typed
 * @author Kirk Qi
 * @copyright Copyright (c) 2022 Kirk Qi <qilinaus@gmail.com>
 * @license MIT License
 */
import { IterableElementBase } from '../base';
/**
 * 1. Complete Binary Tree: Heaps are typically complete binary trees, meaning every level is fully filled except possibly for the last level, which has nodes as far left as possible.
 * 2. Heap Properties: Each node in a heap follows a specific order property, which varies depending on the type of heap:
 * Max Heap: The value of each parent node is greater than or equal to the value of its children.
 * Min Heap: The value of each parent node is less than or equal to the value of its children.
 * 3. Root Node Access: In a heap, the largest element (in a max heap) or the smallest element (in a min heap) is always at the root of the tree.
 * 4. Efficient Insertion and Deletion: Due to its structure, a heap allows for insertion and deletion operations in logarithmic time (O(log n)).
 * 5. Managing Dynamic Data Sets: Heaps effectively manage dynamic data sets, especially when frequent access to the largest or smallest elements is required.
 * 6. Non-linear Search: While a heap allows rapid access to its largest or smallest element, it is less efficient for other operations, such as searching for a specific element, as it is not designed for these tasks.
 * 7. Efficient Sorting Algorithms: For example, heap sort. Heap sort uses the properties of a heap to sort elements.
 * 8. Graph Algorithms: Such as Dijkstra's shortest path algorithm and Prime's minimum-spanning tree algorithm, which use heaps to improve performance.
 * @example
 * // Use Heap to sort an array
 *     function heapSort(arr: number[]): number[] {
 *       const heap = new Heap<number>(arr, { comparator: (a, b) => a - b });
 *       const sorted: number[] = [];
 *       while (!heap.isEmpty()) {
 *         sorted.push(heap.poll()!); // Poll minimum element
 *       }
 *       return sorted;
 *     }
 *
 *     const array = [5, 3, 8, 4, 1, 2];
 *     console.log(heapSort(array)); // [1, 2, 3, 4, 5, 8]
 * @example
 * // Use Heap to solve top k problems
 *     function topKElements(arr: number[], k: number): number[] {
 *       const heap = new Heap<number>([], { comparator: (a, b) => b - a }); // Max heap
 *       arr.forEach(num => {
 *         heap.add(num);
 *         if (heap.size > k) heap.poll(); // Keep the heap size at K
 *       });
 *       return heap.toArray();
 *     }
 *
 *     const numbers = [10, 30, 20, 5, 15, 25];
 *     console.log(topKElements(numbers, 3)); // [15, 10, 5]
 * @example
 * // Use Heap to merge sorted sequences
 *     function mergeSortedSequences(sequences: number[][]): number[] {
 *       const heap = new Heap<{ value: number; seqIndex: number; itemIndex: number }>([], {
 *         comparator: (a, b) => a.value - b.value // Min heap
 *       });
 *
 *       // Initialize heap
 *       sequences.forEach((seq, seqIndex) => {
 *         if (seq.length) {
 *           heap.add({ value: seq[0], seqIndex, itemIndex: 0 });
 *         }
 *       });
 *
 *       const merged: number[] = [];
 *       while (!heap.isEmpty()) {
 *         const { value, seqIndex, itemIndex } = heap.poll()!;
 *         merged.push(value);
 *
 *         if (itemIndex + 1 < sequences[seqIndex].length) {
 *           heap.add({
 *             value: sequences[seqIndex][itemIndex + 1],
 *             seqIndex,
 *             itemIndex: itemIndex + 1
 *           });
 *         }
 *       }
 *
 *       return merged;
 *     }
 *
 *     const sequences = [
 *       [1, 4, 7],
 *       [2, 5, 8],
 *       [3, 6, 9]
 *     ];
 *     console.log(mergeSortedSequences(sequences)); // [1, 2, 3, 4, 5, 6, 7, 8, 9]
 * @example
 * // Use Heap to dynamically maintain the median
 *     class MedianFinder {
 *       private low: MaxHeap<number>; // Max heap, stores the smaller half
 *       private high: MinHeap<number>; // Min heap, stores the larger half
 *
 *       constructor() {
 *         this.low = new MaxHeap<number>([]);
 *         this.high = new MinHeap<number>([]);
 *       }
 *
 *       addNum(num: number): void {
 *         if (this.low.isEmpty() || num <= this.low.peek()!) this.low.add(num);
 *         else this.high.add(num);
 *
 *         // Balance heaps
 *         if (this.low.size > this.high.size + 1) this.high.add(this.low.poll()!);
 *         else if (this.high.size > this.low.size) this.low.add(this.high.poll()!);
 *       }
 *
 *       findMedian(): number {
 *         if (this.low.size === this.high.size) return (this.low.peek()! + this.high.peek()!) / 2;
 *         return this.low.peek()!;
 *       }
 *     }
 *
 *     const medianFinder = new MedianFinder();
 *     medianFinder.addNum(10);
 *     console.log(medianFinder.findMedian()); // 10
 *     medianFinder.addNum(20);
 *     console.log(medianFinder.findMedian()); // 15
 *     medianFinder.addNum(30);
 *     console.log(medianFinder.findMedian()); // 20
 *     medianFinder.addNum(40);
 *     console.log(medianFinder.findMedian()); // 25
 *     medianFinder.addNum(50);
 *     console.log(medianFinder.findMedian()); // 30
 * @example
 * // Use Heap for load balancing
 *     function loadBalance(requests: number[], servers: number): number[] {
 *       const serverHeap = new Heap<{ id: number; load: number }>([], { comparator: (a, b) => a.load - b.load }); // min heap
 *       const serverLoads = new Array(servers).fill(0);
 *
 *       for (let i = 0; i < servers; i++) {
 *         serverHeap.add({ id: i, load: 0 });
 *       }
 *
 *       requests.forEach(req => {
 *         const server = serverHeap.poll()!;
 *         serverLoads[server.id] += req;
 *         server.load += req;
 *         serverHeap.add(server); // The server after updating the load is re-entered into the heap
 *       });
 *
 *       return serverLoads;
 *     }
 *
 *     const requests = [5, 2, 8, 3, 7];
 *     console.log(loadBalance(requests, 3)); // [12, 8, 5]
 * @example
 * // Use Heap to schedule tasks
 *     type Task = [string, number];
 *
 *     function scheduleTasks(tasks: Task[], machines: number): Map<number, Task[]> {
 *       const machineHeap = new Heap<{ id: number; load: number }>([], { comparator: (a, b) => a.load - b.load }); // Min heap
 *       const allocation = new Map<number, Task[]>();
 *
 *       // Initialize the load on each machine
 *       for (let i = 0; i < machines; i++) {
 *         machineHeap.add({ id: i, load: 0 });
 *         allocation.set(i, []);
 *       }
 *
 *       // Assign tasks
 *       tasks.forEach(([task, load]) => {
 *         const machine = machineHeap.poll()!;
 *         allocation.get(machine.id)!.push([task, load]);
 *         machine.load += load;
 *         machineHeap.add(machine); // The machine after updating the load is re-entered into the heap
 *       });
 *
 *       return allocation;
 *     }
 *
 *     const tasks: Task[] = [
 *       ['Task1', 3],
 *       ['Task2', 1],
 *       ['Task3', 2],
 *       ['Task4', 5],
 *       ['Task5', 4]
 *     ];
 *     const expectedMap = new Map<number, Task[]>();
 *     expectedMap.set(0, [
 *       ['Task1', 3],
 *       ['Task4', 5]
 *     ]);
 *     expectedMap.set(1, [
 *       ['Task2', 1],
 *       ['Task3', 2],
 *       ['Task5', 4]
 *     ]);
 *     console.log(scheduleTasks(tasks, 2)); // expectedMap
 */
export class Heap extends IterableElementBase {
    /**
     * The constructor initializes a heap data structure with optional elements and options.
     * @param elements - The `elements` parameter is an iterable object that contains the initial
     * elements to be added to the heap.
     * It is an optional parameter, and if not provided, the heap will
     * be initialized as empty.
     * @param [options] - The `options` parameter is an optional object that can contain additional
     * configuration options for the heap.
     * In this case, it is used to specify a custom comparator
     * function for comparing elements in the heap.
     * The comparator function is used to determine the
     * order of elements in the heap.
     */
    constructor(elements = [], options) {
        super(options);
        if (options) {
            const { comparator } = options;
            if (comparator)
                this._comparator = comparator;
        }
        this.addMany(elements);
    }
    _elements = [];
    /**
     * The function returns an array of elements.
     * @returns The element array is being returned.
     */
    get elements() {
        return this._elements;
    }
    /**
     * Get the size (number of elements) of the heap.
     */
    get size() {
        return this.elements.length;
    }
    /**
     * Get the last element in the heap, which is not necessarily a leaf node.
     * @returns The last element or undefined if the heap is empty.
     */
    get leaf() {
        return this.elements[this.size - 1] ?? undefined;
    }
    /**
     * Static method that creates a binary heap from an array of elements and a comparison function.
     * @returns A new Heap instance.
     * @param elements
     * @param options
     */
    static heapify(elements, options) {
        return new Heap(elements, options);
    }
    /**
     * Time Complexity: O(log n)
     * Space Complexity: O(1)
     *
     * The add function pushes an element into an array and then triggers a bubble-up operation.
     * @param {E} element - The `element` parameter represents the element that you want to add to the
     * data structure.
     * @returns The `add` method is returning a boolean value, which is the result of calling the
     * `_bubbleUp` method with the index `this.elements.length - 1` as an argument.
     */
    add(element) {
        this._elements.push(element);
        return this._bubbleUp(this.elements.length - 1);
    }
    /**
     * Time Complexity: O(k log n)
     * Space Complexity: O(1)
     *
     * The `addMany` function iterates over elements and adds them to a collection, returning an array of
     * boolean values indicating success or failure.
     * @param {Iterable<E> | Iterable<R>} elements - The `elements` parameter in the `addMany` method is
     * an iterable containing elements of type `E` or `R`. The method iterates over each element in the
     * iterable and adds them to the data structure. If a transformation function `_toElementFn` is
     * provided, it transforms the element
     * @returns The `addMany` method returns an array of boolean values indicating whether each element
     * in the input iterable was successfully added to the data structure.
     */
    addMany(elements) {
        const ans = [];
        for (const el of elements) {
            if (this._toElementFn) {
                ans.push(this.add(this._toElementFn(el)));
                continue;
            }
            ans.push(this.add(el));
        }
        return ans;
    }
    /**
     * Time Complexity: O(log n)
     * Space Complexity: O(1)
     *
     * Remove and return the top element (the smallest or largest element) from the heap.
     * @returns The top element or undefined if the heap is empty.
     */
    poll() {
        if (this.elements.length === 0)
            return;
        const value = this.elements[0];
        const last = this.elements.pop();
        if (this.elements.length) {
            this.elements[0] = last;
            this._sinkDown(0, this.elements.length >> 1);
        }
        return value;
    }
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * Peek at the top element of the heap without removing it.
     * @returns The top element or undefined if the heap is empty.
     */
    peek() {
        return this.elements[0];
    }
    /**
     * Check if the heap is empty.
     * @returns True if the heap is empty, otherwise false.
     */
    isEmpty() {
        return this.size === 0;
    }
    /**
     * Reset the elements of the heap. Make the elements empty.
     */
    clear() {
        this._elements = [];
    }
    /**
     * Time Complexity: O(n)
     * Space Complexity: O(n)
     *
     * Clear and add elements of the heap
     * @param elements
     */
    refill(elements) {
        this._elements = elements;
        return this.fix();
    }
    /**
     * Time Complexity: O(n)
     * Space Complexity: O(1)
     *
     * Use a comparison function to check whether a binary heap contains a specific element.
     * @param element - the element to check.
     * @returns Returns true if the specified element is contained; otherwise, returns false.
     */
    has(element) {
        return this.elements.includes(element);
    }
    /**
     * Time Complexity: O(n)
     * Space Complexity: O(1)
     *
     * The `delete` function removes an element from an array-like data structure, maintaining the order
     * and structure of the remaining elements.
     * @param {E} element - The `element` parameter represents the element that you want to delete from
     * the array `this.elements`.
     * @returns The `delete` function is returning a boolean value. It returns `true` if the element was
     * successfully deleted from the array, and `false` if the element was not found in the array.
     */
    delete(element) {
        const index = this.elements.indexOf(element);
        if (index < 0)
            return false;
        if (index === 0) {
            this.poll();
        }
        else if (index === this.elements.length - 1) {
            this.elements.pop();
        }
        else {
            this.elements.splice(index, 1, this.elements.pop());
            this._bubbleUp(index);
            this._sinkDown(index, this.elements.length >> 1);
        }
        return true;
    }
    /**
     * Time Complexity: O(n)
     * Space Complexity: O(log n)
     *
     * Depth-first search (DFS) method, different traversal orders can be selected。
     * @param order - Traverse order parameter: 'IN' (in-order), 'PRE' (pre-order) or 'POST' (post-order).
     * @returns An array containing elements traversed in the specified order.
     */
    dfs(order = 'PRE') {
        const result = [];
        // Auxiliary recursive function, traverses the binary heap according to the traversal order
        const _dfs = (index) => {
            const left = 2 * index + 1, right = left + 1;
            if (index < this.size) {
                if (order === 'IN') {
                    _dfs(left);
                    result.push(this.elements[index]);
                    _dfs(right);
                }
                else if (order === 'PRE') {
                    result.push(this.elements[index]);
                    _dfs(left);
                    _dfs(right);
                }
                else if (order === 'POST') {
                    _dfs(left);
                    _dfs(right);
                    result.push(this.elements[index]);
                }
            }
        };
        _dfs(0); // Traverse starting from the root node
        return result;
    }
    /**
     * Time Complexity: O(n)
     * Space Complexity: O(n)
     *
     * Clone the heap, creating a new heap with the same elements.
     * @returns A new Heap instance containing the same elements.
     */
    clone() {
        return new Heap(this, { comparator: this.comparator, toElementFn: this.toElementFn });
    }
    /**
     * Time Complexity: O(n log n)
     * Space Complexity: O(n)
     *
     * Sort the elements in the heap and return them as an array.
     * @returns An array containing the elements sorted in ascending order.
     */
    sort() {
        const visitedNode = [];
        const cloned = new Heap(this, { comparator: this.comparator });
        while (cloned.size !== 0) {
            const top = cloned.poll();
            if (top !== undefined)
                visitedNode.push(top);
        }
        return visitedNode;
    }
    /**
     * Time Complexity: O(n log n)
     * Space Complexity: O(n)
     *
     * Fix the entire heap to maintain heap properties.
     */
    fix() {
        const results = [];
        for (let i = Math.floor(this.size / 2); i >= 0; i--)
            results.push(this._sinkDown(i, this.elements.length >> 1));
        return results;
    }
    /**
     * Time Complexity: O(n)
     * Space Complexity: O(n)
     *
     * The `filter` function creates a new Heap object containing elements that pass a given callback
     * function.
     * @param callback - The `callback` parameter is a function that will be called for each element in
     * the heap. It takes three arguments: the current element, the index of the current element, and the
     * heap itself. The callback function should return a boolean value indicating whether the current
     * element should be included in the filtered list
     * @param {any} [thisArg] - The `thisArg` parameter is an optional argument that specifies the value
     * to be used as `this` when executing the `callback` function. If `thisArg` is provided, it will be
     * passed as the `this` value to the `callback` function. If `thisArg` is
     * @returns The `filter` method is returning a new `Heap` object that contains the elements that pass
     * the filter condition specified by the `callback` function.
     */
    filter(callback, thisArg) {
        const filteredList = new Heap([], { toElementFn: this.toElementFn, comparator: this.comparator });
        let index = 0;
        for (const current of this) {
            if (callback.call(thisArg, current, index, this)) {
                filteredList.add(current);
            }
            index++;
        }
        return filteredList;
    }
    /**
     * Time Complexity: O(n)
     * Space Complexity: O(n)
     *
     * The `map` function creates a new heap by applying a callback function to each element of the
     * original heap.
     * @param callback - The `callback` parameter is a function that will be called for each element in
     * the heap. It takes three arguments: `el` (the current element), `index` (the index of the current
     * element), and `this` (the heap itself). The callback function should return a value of
     * @param comparator - The `comparator` parameter is a function that defines the order of the
     * elements in the heap. It takes two elements `a` and `b` as arguments and returns a negative number
     * if `a` should be placed before `b`, a positive number if `a` should be placed after
     * @param [toElementFn] - The `toElementFn` parameter is an optional function that converts the raw
     * element `RR` to the desired type `T`. It takes a single argument `rawElement` of type `RR` and
     * returns a value of type `T`. This function is used to transform the elements of the original
     * @param {any} [thisArg] - The `thisArg` parameter is an optional argument that allows you to
     * specify the value of `this` within the callback function. It is used to set the context or scope
     * in which the callback function will be executed. If `thisArg` is provided, it will be used as the
     * value of
     * @returns a new instance of the `Heap` class with the mapped elements.
     */
    map(callback, comparator, toElementFn, thisArg) {
        const mappedHeap = new Heap([], { comparator, toElementFn });
        let index = 0;
        for (const el of this) {
            mappedHeap.add(callback.call(thisArg, el, index, this));
            index++;
        }
        return mappedHeap;
    }
    _DEFAULT_COMPARATOR = (a, b) => {
        if (typeof a === 'object' || typeof b === 'object') {
            throw TypeError(`When comparing object types, a custom comparator must be defined in the constructor's options parameter.`);
        }
        if (a > b)
            return 1;
        if (a < b)
            return -1;
        return 0;
    };
    _comparator = this._DEFAULT_COMPARATOR;
    /**
     * The function returns the value of the _comparator property.
     * @returns The `_comparator` property is being returned.
     */
    get comparator() {
        return this._comparator;
    }
    /**
     * The function `_getIterator` returns an iterable iterator for the elements in the class.
     */
    *_getIterator() {
        for (const element of this.elements) {
            yield element;
        }
    }
    /**
     * Time Complexity: O(log n)
     * Space Complexity: O(1)
     *
     * Float operation to maintain heap properties after adding an element.
     * @param index - The index of the newly added element.
     */
    _bubbleUp(index) {
        const element = this.elements[index];
        while (index > 0) {
            const parent = (index - 1) >> 1;
            const parentItem = this.elements[parent];
            if (this.comparator(parentItem, element) <= 0)
                break;
            this.elements[index] = parentItem;
            index = parent;
        }
        this.elements[index] = element;
        return true;
    }
    /**
     * Time Complexity: O(log n)
     * Space Complexity: O(1)
     *
     * Sinking operation to maintain heap properties after removing the top element.
     * @param index - The index from which to start sinking.
     * @param halfLength
     */
    _sinkDown(index, halfLength) {
        const element = this.elements[index];
        while (index < halfLength) {
            let left = (index << 1) | 1;
            const right = left + 1;
            let minItem = this.elements[left];
            if (right < this.elements.length && this.comparator(minItem, this.elements[right]) > 0) {
                left = right;
                minItem = this.elements[right];
            }
            if (this.comparator(minItem, element) >= 0)
                break;
            this.elements[index] = minItem;
            index = left;
        }
        this.elements[index] = element;
        return true;
    }
}
export class FibonacciHeapNode {
    element;
    degree;
    left;
    right;
    child;
    parent;
    marked;
    /**
     * The constructor function initializes an object with an element and a degree, and sets the marked
     * property to false.
     * @param {E} element - The "element" parameter represents the value or data that will be stored in
     * the node of a data structure. It can be any type of data, such as a number, string, object, or
     * even another data structure.
     * @param [degree=0] - The degree parameter represents the degree of the element in a data structure
     * called a Fibonacci heap. The degree of a node is the number of children it has. By default, the
     * degree is set to 0 when a new node is created.
     */
    constructor(element, degree = 0) {
        this.element = element;
        this.degree = degree;
        this.marked = false;
    }
}
export class FibonacciHeap {
    /**
     * The constructor function initializes a FibonacciHeap object with an optional comparator function.
     * @param [comparator] - The `comparator` parameter is an optional argument that represents a
     * function used to compare elements in the FibonacciHeap. If a comparator function is provided, it
     * will be used to determine the order of elements in the heap. If no comparator function is
     * provided, a default comparator function will be used.
     */
    constructor(comparator) {
        this.clear();
        this._comparator = comparator || this._defaultComparator;
        if (typeof this.comparator !== 'function') {
            throw new Error('FibonacciHeap constructor: given comparator should be a function.');
        }
    }
    _root;
    /**
     * The function returns the root node of a Fibonacci heap.
     * @returns The method is returning either a FibonacciHeapNode object or undefined.
     */
    get root() {
        return this._root;
    }
    _size = 0;
    /**
     * The function returns the size of an object.
     * @returns The size of the object, which is a number.
     */
    get size() {
        return this._size;
    }
    _min;
    /**
     * The function returns the minimum node in a Fibonacci heap.
     * @returns The method is returning the minimum node of the Fibonacci heap, which is of type
     * `FibonacciHeapNode<E>`. If there is no minimum node, it will return `undefined`.
     */
    get min() {
        return this._min;
    }
    _comparator;
    /**
     * The function returns the comparator used for comparing elements.
     * @returns The `_comparator` property of the object.
     */
    get comparator() {
        return this._comparator;
    }
    /**
     * Get the size (number of elements) of the heap.
     * @returns {number} The size of the heap.  Returns 0 if the heap is empty. Returns -1 if the heap is invalid.
     */
    clear() {
        this._root = undefined;
        this._min = undefined;
        this._size = 0;
    }
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * Insert an element into the heap and maintain the heap properties.
     * @param element
     * @returns {FibonacciHeap<E>} FibonacciHeap<E> - The heap itself.
     */
    add(element) {
        return this.push(element);
    }
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * Insert an element into the heap and maintain the heap properties.
     * @param element
     * @returns {FibonacciHeap<E>} FibonacciHeap<E> - The heap itself.
     */
    push(element) {
        const node = this.createNode(element);
        node.left = node;
        node.right = node;
        this.mergeWithRoot(node);
        if (!this.min || this.comparator(node.element, this.min.element) <= 0) {
            this._min = node;
        }
        this._size++;
        return this;
    }
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * Peek at the top element of the heap without removing it.
     * @returns The top element or undefined if the heap is empty.
     * @protected
     */
    peek() {
        return this.min ? this.min.element : undefined;
    }
    /**
     * Time Complexity: O(n), where n is the number of elements in the linked list.
     * Space Complexity: O(1)
     *
     * Get the size (number of elements) of the heap.
     * @param {FibonacciHeapNode<E>} head - The head of the linked list.
     * @protected
     * @returns FibonacciHeapNode<E>[] - An array containing the elements of the linked list.
     */
    consumeLinkedList(head) {
        const elements = [];
        if (!head)
            return elements;
        let node = head;
        let flag = false;
        while (true) {
            if (node === head && flag)
                break;
            else if (node === head)
                flag = true;
            if (node) {
                elements.push(node);
                node = node.right;
            }
        }
        return elements;
    }
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * @param parent
     * @param node
     */
    mergeWithChild(parent, node) {
        if (!parent.child) {
            parent.child = node;
        }
        else {
            node.right = parent.child.right;
            node.left = parent.child;
            parent.child.right.left = node;
            parent.child.right = node;
        }
    }
    /**
     * Time Complexity: O(log n)
     * Space Complexity: O(1)
     *
     * Remove and return the top element (the smallest or largest element) from the heap.
     * @returns The top element or undefined if the heap is empty.
     */
    poll() {
        return this.pop();
    }
    /**
     * Time Complexity: O(log n)
     * Space Complexity: O(1)
     *
     * Remove and return the top element (the smallest or largest element) from the heap.
     * @returns The top element or undefined if the heap is empty.
     */
    pop() {
        if (this._size === 0)
            return undefined;
        const z = this.min;
        if (z.child) {
            const elements = this.consumeLinkedList(z.child);
            for (const node of elements) {
                this.mergeWithRoot(node);
                node.parent = undefined;
            }
        }
        this.removeFromRoot(z);
        if (z === z.right) {
            this._min = undefined;
            this._root = undefined;
        }
        else {
            this._min = z.right;
            this._consolidate();
        }
        this._size--;
        return z.element;
    }
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * merge two heaps. The heap that is merged will be cleared. The heap that is merged into will remain.
     * @param heapToMerge
     */
    merge(heapToMerge) {
        if (heapToMerge.size === 0) {
            return; // Nothing to merge
        }
        // Merge the root lists of the two heaps
        if (this.root && heapToMerge.root) {
            const thisRoot = this.root;
            const otherRoot = heapToMerge.root;
            const thisRootRight = thisRoot.right;
            const otherRootLeft = otherRoot.left;
            thisRoot.right = otherRoot;
            otherRoot.left = thisRoot;
            thisRootRight.left = otherRootLeft;
            otherRootLeft.right = thisRootRight;
        }
        // Update the minimum node
        if (!this.min || (heapToMerge.min && this.comparator(heapToMerge.min.element, this.min.element) < 0)) {
            this._min = heapToMerge.min;
        }
        // Update the size
        this._size += heapToMerge.size;
        // Clear the heap that was merged
        heapToMerge.clear();
    }
    /**
     * Create a new node.
     * @param element
     * @protected
     */
    createNode(element) {
        return new FibonacciHeapNode(element);
    }
    /**
     * Default comparator function used by the heap.
     * @param {E} a
     * @param {E} b
     * @protected
     */
    _defaultComparator(a, b) {
        if (a < b)
            return -1;
        if (a > b)
            return 1;
        return 0;
    }
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * Merge the given node with the root list.
     * @param node - The node to be merged.
     */
    mergeWithRoot(node) {
        if (!this.root) {
            this._root = node;
        }
        else {
            node.right = this.root.right;
            node.left = this.root;
            this.root.right.left = node;
            this.root.right = node;
        }
    }
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * Remove and return the top element (the smallest or largest element) from the heap.
     * @param node - The node to be removed.
     * @protected
     */
    removeFromRoot(node) {
        if (this.root === node)
            this._root = node.right;
        if (node.left)
            node.left.right = node.right;
        if (node.right)
            node.right.left = node.left;
    }
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * Remove and return the top element (the smallest or largest element) from the heap.
     * @param y
     * @param x
     * @protected
     */
    _link(y, x) {
        this.removeFromRoot(y);
        y.left = y;
        y.right = y;
        this.mergeWithChild(x, y);
        x.degree++;
        y.parent = x;
    }
    /**
     * Time Complexity: O(n log n)
     * Space Complexity: O(n)
     *
     * Remove and return the top element (the smallest or largest element) from the heap.
     * @protected
     */
    _consolidate() {
        const A = new Array(this._size);
        const elements = this.consumeLinkedList(this.root);
        let x, y, d, t;
        for (const node of elements) {
            x = node;
            d = x.degree;
            while (A[d]) {
                y = A[d];
                if (this.comparator(x.element, y.element) > 0) {
                    t = x;
                    x = y;
                    y = t;
                }
                this._link(y, x);
                A[d] = undefined;
                d++;
            }
            A[d] = x;
        }
        for (let i = 0; i < this._size; i++) {
            if (A[i] && this.comparator(A[i].element, this.min.element) <= 0) {
                this._min = A[i];
            }
        }
    }
}
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