import { BinaryTreeNode } from 'src/tree/binaryTreeNode';
import { CompareFn } from '..';
import { Heap } from './heap';
/**
 * A skew heap is a heap implemented as a binary tree
 * ([source](https://en.wikipedia.org/wiki/Skew_heap)).
 *
 * A skew heap is a self-adjusting heap which attempts to maintain balance
 * by unconditionally swapping all nodes in the merge path when merging two heaps. Every
 * operation that modifies the heap (e.g. push, pop, merge) is considered a merge and is done
 * by using a skew heap merge.
 *
 * Skew heaps can merge more quickly than binary heaps. This can seem contradictory, since
 * skew heaps have no structural constraints and no guarantee that the height of the tree is
 * logarithmic (i.e. balanced). However, amortized complexity analysis can demonstrate that
 * all operations on a skew heap can be done in O(log(n). More specifically, the
 * amortized complexity is known to be log<sub>φ</sub>(n) where φ is the golden ratio. This is
 * approximately 1.44*log<sub>2</sub>(n).
 *
 * #### Complexity
 *
 * | Property | Average  | Worst |
 * | :------- | :------  | :---- |
 * | Space    | O(n)     | O(n)
 * | Push     | O(log n) | O(log n)
 * | Peek     | O(1)	 | O(1)
 * | Pop      | O(log n) | O(log n)
 * | Search   | O(n)     | O(n)
 */
export declare class SkewHeap<T> implements Heap<T> {
    /**
     * The function to determine the order of elements.
     */
    protected compare: CompareFn<T>;
    /**
     * The number of elements in the list.
     */
    protected length: number;
    /**
     * The node at the "top" of the heap.
     */
    protected root: BinaryTreeNode<T> | undefined;
    /**
     * Instantiate a heap.
     *
     * @param compareFn - The function to determine the order of elements.
     * @param elements - A set of elements to initialize the heap with.
     */
    constructor(compareFn: CompareFn<T>, elements?: Iterable<T>);
    addAll(elements: Iterable<T>): number;
    clear(): void;
    comparator(): CompareFn<T>;
    contains(element: T): boolean;
    delete(element: T): boolean;
    merge(heap: Heap<T>): this;
    peek(): T | undefined;
    pop(): T | undefined;
    push(value: T): number;
    pushPop(value: T): T;
    replace(value: T): T | undefined;
    get size(): number;
    sorted(): Iterable<T>;
    /**
     * Receive an iterator through the list.
     *
     * **Note:** Unexpected behavior can occur if the collection is modified during iteration.
     *
     * @returns An iterator through the list
     */
    [Symbol.iterator](): Iterator<T>;
    update(curElement: T, newElement: T): boolean;
}