/**
 * data-structure-typed
 *
 * @author Pablo Zeng
 * @copyright Copyright (c) 2022 Pablo Zeng <zrwusa@gmail.com>
 * @license MIT License
 */
import type { VertexKey } from '../../types';
import { IGraph } from '../../interfaces';
import { AbstractEdge, AbstractGraph, AbstractVertex } from './abstract-graph';
export declare class UndirectedVertex<V = any> extends AbstractVertex<V> {
    /**
     * The constructor function initializes a vertex with an optional value.
     * @param {VertexKey} key - The `key` parameter is of type `VertexKey` and represents the identifier of the vertex. It is
     * used to uniquely identify the vertex within a graph or network.
     * @param {V} [value] - The "value" parameter is an optional parameter of type V. It is used to initialize the value of the
     * vertex. If no value is provided, the vertex will be initialized with a default value.
     */
    constructor(key: VertexKey, value?: V);
}
export declare class UndirectedEdge<E = number> extends AbstractEdge<E> {
    endpoints: [VertexKey, VertexKey];
    /**
     * The constructor function creates an instance of a class with two vertex IDs, an optional weight, and an optional
     * value.
     * @param {VertexKey} v1 - The first vertex ID of the edge.
     * @param {VertexKey} v2 - The parameter `v2` is a `VertexKey`, which represents the identifier of the second vertex in a
     * graph edge.
     * @param {number} [weight] - The weight parameter is an optional number that represents the weight of the edge.
     * @param {E} [value] - The "value" parameter is an optional parameter of type E. It is used to store a value associated
     * with the edge.
     */
    constructor(v1: VertexKey, v2: VertexKey, weight?: number, value?: E);
}
/**
 *
 */
export declare class UndirectedGraph<V = any, E = any, VO extends UndirectedVertex<V> = UndirectedVertex<V>, EO extends UndirectedEdge<E> = UndirectedEdge<E>> extends AbstractGraph<V, E, VO, EO> implements IGraph<V, E, VO, EO> {
    /**
     * The constructor initializes a new Map object to store edgeMap.
     */
    constructor();
    protected _edgeMap: Map<VO, EO[]>;
    get edgeMap(): Map<VO, EO[]>;
    set edgeMap(v: Map<VO, EO[]>);
    /**
     * The function creates a new vertex with an optional value and returns it.
     * @param {VertexKey} key - The `key` parameter is the unique identifier for the vertex. It is used to distinguish one
     * vertex from another in the graph.
     * @param [value] - The `value` parameter is an optional value that can be assigned to the vertex. If a value is provided,
     * it will be used as the value of the vertex. If no value is provided, the `key` parameter will be used as the value of
     * the vertex.
     * @returns The method is returning a new instance of the `UndirectedVertex` class, casted as type `VO`.
     */
    createVertex(key: VertexKey, value?: VO['value']): VO;
    /**
     * The function creates an undirected edge between two vertexMap with an optional weight and value.
     * @param {VertexKey} v1 - The parameter `v1` represents the first vertex of the edge.
     * @param {VertexKey} v2 - The parameter `v2` represents the second vertex of the edge.
     * @param {number} [weight] - The `weight` parameter is an optional number that represents the weight of the edge. If
     * no weight is provided, it defaults to 1.
     * @param [value] - The `value` parameter is an optional value that can be assigned to the edge. It can be of any type and
     * is used to store additional information or data associated with the edge.
     * @returns a new instance of the `UndirectedEdge` class, which is casted as type `EO`.
     */
    createEdge(v1: VertexKey, v2: VertexKey, weight?: number, value?: EO['value']): EO;
    /**
     * Time Complexity: O(|E|), where |E| is the number of edgeMap incident to the given vertex.
     * Space Complexity: O(1)
     *
     * The function `getEdge` returns the first edge that connects two endpoints, or undefined if no such edge exists.
     * @param {VO | VertexKey | undefined} v1 - The parameter `v1` represents a vertex or vertex ID. It can be of type `VO` (vertex
     * object), `undefined`, or `VertexKey` (a string or number representing the ID of a vertex).
     * @param {VO | VertexKey | undefined} v2 - The parameter `v2` represents a vertex or vertex ID. It can be of type `VO` (vertex
     * object), `undefined`, or `VertexKey` (vertex ID).
     * @returns an edge (EO) or undefined.
     */
    getEdge(v1: VO | VertexKey | undefined, v2: VO | VertexKey | undefined): EO | undefined;
    /**
     * Time Complexity: O(|E|), where |E| is the number of edgeMap incident to the given vertex.
     * Space Complexity: O(1)
     *
     * The function removes an edge between two vertexMap in a graph and returns the removed edge.
     * @param {VO | VertexKey} v1 - The parameter `v1` represents either a vertex object (`VO`) or a vertex ID (`VertexKey`).
     * @param {VO | VertexKey} v2 - VO | VertexKey - This parameter can be either a vertex object (VO) or a vertex ID
     * (VertexKey). It represents the second vertex of the edge that needs to be removed.
     * @returns the removed edge (EO) if it exists, or undefined if either of the endpoints (VO) does not exist.
     */
    deleteEdgeBetween(v1: VO | VertexKey, v2: VO | VertexKey): EO | undefined;
    /**
     * Time Complexity: O(E), where E is the number of edgeMap incident to the given vertex.
     * Space Complexity: O(1)
     *
     * The function `deleteEdge` deletes an edge between two endpoints in a graph.
     * @param {EO | VertexKey} edgeOrOneSideVertexKey - The parameter `edgeOrOneSideVertexKey` can be
     * either an edge object or a vertex key.
     * @param {VertexKey} [otherSideVertexKey] - The parameter `otherSideVertexKey` is an optional
     * parameter that represents the key of the vertex on the other side of the edge. It is used when the
     * `edgeOrOneSideVertexKey` parameter is a vertex key, and it specifies the key of the vertex on the
     * other side of the
     * @returns The `deleteEdge` function returns either the deleted edge object (EO) or `undefined`.
     */
    deleteEdge(edgeOrOneSideVertexKey: EO | VertexKey, otherSideVertexKey?: VertexKey): EO | undefined;
    /**
     * Time Complexity: O(1) - Constant time for Map operations.
     * Space Complexity: O(1) - Constant space, as it creates only a few variables.
     *
     * The `deleteVertex` function removes a vertex from a graph by its ID or by the vertex object itself.
     * @param {VO | VertexKey} vertexOrKey - The parameter `vertexOrKey` can be either a vertex object (`VO`) or a vertex ID
     * (`VertexKey`).
     * @returns The method is returning a boolean value.
     */
    deleteVertex(vertexOrKey: VO | VertexKey): boolean;
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * The function `degreeOf` returns the degree of a vertex in a graph, which is the number of edgeMap connected to that
     * vertex.
     * @param {VertexKey | VO} vertexOrKey - The parameter `vertexOrKey` can be either a `VertexKey` or a `VO`.
     * @returns The function `degreeOf` returns the degree of a vertex in a graph. The degree of a vertex is the number of
     * edgeMap connected to that vertex.
     */
    degreeOf(vertexOrKey: VertexKey | VO): number;
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * The function returns the edgeMap of a given vertex or vertex ID.
     * @param {VertexKey | VO} vertexOrKey - The parameter `vertexOrKey` can be either a `VertexKey` or a `VO`. A `VertexKey` is a
     * unique identifier for a vertex in a graph, while `VO` represents the type of the vertex.
     * @returns an array of edgeMap.
     */
    edgesOf(vertexOrKey: VertexKey | VO): EO[];
    /**
     * Time Complexity: O(|V| + |E|), where |V| is the number of vertexMap and |E| is the number of edgeMap.
     * Space Complexity: O(|E|)
     *
     * The function "edgeSet" returns an array of unique edgeMap from a set of edgeMap.
     * @returns The method `edgeSet()` returns an array of type `EO[]`.
     */
    edgeSet(): EO[];
    /**
     * Time Complexity: O(|V| + |E|), where |V| is the number of vertexMap and |E| is the number of edgeMap.
     * Space Complexity: O(|E|)
     *
     * The function "getNeighbors" returns an array of neighboring endpoints for a given vertex or vertex ID.
     * @param {VO | VertexKey} vertexOrKey - The parameter `vertexOrKey` can be either a vertex object (`VO`) or a vertex ID
     * (`VertexKey`).
     * @returns an array of vertexMap (VO[]).
     */
    getNeighbors(vertexOrKey: VO | VertexKey): VO[];
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * The function "getEndsOfEdge" returns the endpoints at the ends of an edge if the edge exists in the graph, otherwise
     * it returns undefined.
     * @param {EO} edge - The parameter "edge" is of type EO, which represents an edge in a graph.
     * @returns The function `getEndsOfEdge` returns an array containing two endpoints `[VO, VO]` if the edge exists in the
     * graph. If the edge does not exist, it returns `undefined`.
     */
    getEndsOfEdge(edge: EO): [VO, VO] | undefined;
    /**
     * The isEmpty function checks if the graph is empty.
     * @return True if the graph is empty and false otherwise
     */
    isEmpty(): boolean;
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * The clear function resets the vertex and edge maps to empty maps.
     */
    clear(): void;
    /**
     * The clone function creates a new UndirectedGraph object and copies the
     * vertexMap and edgeMap from this graph to the new one. This is done by
     * assigning each of these properties to their respective counterparts in the
     * cloned graph. The clone function returns a reference to this newly created,
     * cloned UndirectedGraph object.
     *
     * @return A new instance of the undirectedgraph class
     */
    clone(): UndirectedGraph<V, E, VO, EO>;
    /**
     *  Time Complexity: O(V + E)
     *  Space Complexity: O(V)
     *   Tarjan is an algorithm based on dfs,which is used to solve the connectivity problem of graphs.
     *  1. Tarjan can find the articulation points and bridges(critical edgeMap) of undirected graphs in linear time
     *
     * The function `tarjan` implements the Tarjan's algorithm to find bridges and cut vertices in a
     * graph.
     * @returns The function `tarjan()` returns an object with the following properties:
     */
    tarjan(): {
        dfnMap: Map<VO, number>;
        lowMap: Map<VO, number>;
        bridges: EO[];
        cutVertices: VO[];
    };
    /**
     * The function "getBridges" returns an array of bridges in a graph using the Tarjan's algorithm.
     * @returns The function `getBridges()` is returning the bridges found using the Tarjan's algorithm.
     */
    getBridges(): EO[];
    /**
     * The function "getCutVertices" returns an array of cut vertices using the Tarjan's algorithm.
     * @returns the cut vertices found using the Tarjan's algorithm.
     */
    getCutVertices(): VO[];
    /**
     * The function returns the dfnMap property of the result of the tarjan() function.
     * @returns the `dfnMap` property of the result of calling the `tarjan()` function.
     */
    getDFNMap(): Map<VO, number>;
    /**
     * The function returns the lowMap property of the result of the tarjan() function.
     * @returns the lowMap property of the result of calling the tarjan() function.
     */
    getLowMap(): Map<VO, number>;
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * The function adds an edge to the graph by updating the adjacency list with the vertexMap of the edge.
     * @param {EO} edge - The parameter "edge" is of type EO, which represents an edge in a graph.
     * @returns a boolean value.
     */
    protected _addEdge(edge: EO): boolean;
}