/**
 * data-structure-typed
 *
 * @author Pablo Zeng
 * @copyright Copyright (c) 2022 Pablo Zeng <zrwusa@gmail.com>
 * @license MIT License
 */
import type { VertexKey } from '../../types';
import { AbstractEdge, AbstractGraph, AbstractVertex } from './abstract-graph';
import { IGraph } from '../../interfaces';
export declare class DirectedVertex<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 data structure.
     * @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 DirectedEdge<E = any> extends AbstractEdge<E> {
    src: VertexKey;
    dest: VertexKey;
    /**
     * The constructor function initializes the source and destination vertexMap of an edge, along with an optional weight
     * and value.
     * @param {VertexKey} src - The `src` parameter is the source vertex ID. It represents the starting point of an edge in
     * a graph.
     * @param {VertexKey} dest - The `dest` parameter represents the destination vertex of an edge. It is of type
     * `VertexKey`, which is likely a unique identifier for a vertex in a graph.
     * @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 represents the value associated with
     * the edge.
     */
    constructor(src: VertexKey, dest: VertexKey, weight?: number, value?: E);
}
/**
 *
 */
export declare class DirectedGraph<V = any, E = any, VO extends DirectedVertex<V> = DirectedVertex<V>, EO extends DirectedEdge<E> = DirectedEdge<E>> extends AbstractGraph<V, E, VO, EO> implements IGraph<V, E, VO, EO> {
    /**
     * The constructor function initializes an instance of a class.
     */
    constructor();
    protected _outEdgeMap: Map<VO, EO[]>;
    get outEdgeMap(): Map<VO, EO[]>;
    set outEdgeMap(v: Map<VO, EO[]>);
    protected _inEdgeMap: Map<VO, EO[]>;
    get inEdgeMap(): Map<VO, EO[]>;
    set inEdgeMap(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 of type `VertexKey`, which
     * could be a number or a string depending on how you want to identify your vertexMap.
     * @param [value] - The 'value' parameter is an optional value that can be assigned to the vertex. If a value is provided,
     * it will be assigned to the 'value' property of the vertex. If no value is provided, the 'value' property will be
     * assigned the same value as the 'key' parameter
     * @returns a new instance of a DirectedVertex object, casted as type VO.
     */
    createVertex(key: VertexKey, value?: V): VO;
    /**
     * The function creates a directed edge between two vertexMap with an optional weight and value.
     * @param {VertexKey} src - The source vertex ID of the edge. It represents the starting point of the edge.
     * @param {VertexKey} dest - The `dest` parameter is the identifier of the destination vertex for 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 a DirectedEdge object, casted as type EO.
     */
    createEdge(src: VertexKey, dest: VertexKey, weight?: number, value?: E): EO;
    /**
     * Time Complexity: O(|V|) where |V| is the number of vertexMap
     * Space Complexity: O(1)
     *
     * The `getEdge` function retrieves an edge between two vertexMap based on their source and destination IDs.
     * @param {VO | VertexKey | undefined} srcOrKey - The source vertex or its ID. It can be either a vertex object or a vertex ID.
     * @param {VO | VertexKey | undefined} destOrKey - The `destOrKey` parameter in the `getEdge` function represents the
     * destination vertex of the edge. It can be either a vertex object (`VO`), a vertex ID (`VertexKey`), or `undefined` if the
     * destination is not specified.
     * @returns the first edge found between the source and destination vertexMap, or undefined if no such edge is found.
     */
    getEdge(srcOrKey: VO | VertexKey | undefined, destOrKey: VO | VertexKey | undefined): EO | undefined;
    /**
     * Time Complexity: O(|E|) where |E| is the number of edgeMap
     * Space Complexity: O(1)
     *
     * The function removes an edge between two vertexMap in a graph and returns the removed edge.
     * @param {VO | VertexKey} srcOrKey - The source vertex or its ID.
     * @param {VO | VertexKey} destOrKey - The `destOrKey` parameter represents the destination vertex or its ID.
     * @returns the removed edge (EO) if it exists, or undefined if either the source or destination vertex does not exist.
     */
    deleteEdgeSrcToDest(srcOrKey: VO | VertexKey, destOrKey: VO | VertexKey): EO | undefined;
    /**
     * Time Complexity: O(E) where E is the number of edgeMap
     * Space Complexity: O(1)
     *
     * The `deleteEdge` function removes an edge from a graph and returns the removed edge.
     * @param {EO | VertexKey} edgeOrSrcVertexKey - The `edge` parameter can be either an `EO` object (edge object) or
     * a `VertexKey` (key of a vertex).
     * @param {VertexKey} [destVertexKey] - The `destVertexKey` parameter is an optional parameter that
     * represents the key of the destination vertex of the edge. It is used to specify the destination
     * vertex when the `edge` parameter is a vertex key. If `destVertexKey` is not provided, the function
     * assumes that the `edge`
     * @returns the removed edge (EO) or undefined if no edge was removed.
     */
    deleteEdge(edgeOrSrcVertexKey: EO | VertexKey, destVertexKey?: 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(|E|) where |E| is the number of edgeMap
     * Space Complexity: O(1)
     *
     * The function removes edgeMap between two vertexMap and returns the removed edgeMap.
     * @param {VertexKey | VO} v1 - The parameter `v1` can be either a `VertexKey` or a `VO`. A `VertexKey` represents the
     * unique identifier of a vertex in a graph, while `VO` represents the actual vertex object.
     * @param {VertexKey | VO} v2 - The parameter `v2` represents either a `VertexKey` or a `VO` object. It is used to specify
     * the second vertex in the edge that needs to be removed.
     * @returns an array of removed edgeMap (EO[]).
     */
    deleteEdgesBetween(v1: VertexKey | VO, v2: VertexKey | VO): EO[];
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * The function `incomingEdgesOf` returns an array of incoming edgeMap 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 The method `incomingEdgesOf` returns an array of edgeMap (`EO[]`).
     */
    incomingEdgesOf(vertexOrKey: VO | VertexKey): EO[];
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * The function `outgoingEdgesOf` returns an array of outgoing edgeMap from a given vertex or vertex ID.
     * @param {VO | VertexKey} vertexOrKey - The parameter `vertexOrKey` can accept either a vertex object (`VO`) or a vertex ID
     * (`VertexKey`).
     * @returns The method `outgoingEdgesOf` returns an array of edgeMap (`EO[]`).
     */
    outgoingEdgesOf(vertexOrKey: VO | VertexKey): EO[];
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * The function "degreeOf" returns the total degree of a vertex, which is the sum of its out-degree and in-degree.
     * @param {VertexKey | VO} vertexOrKey - The parameter `vertexOrKey` can be either a `VertexKey` or a `VO`.
     * @returns The sum of the out-degree and in-degree of the specified vertex or vertex ID.
     */
    degreeOf(vertexOrKey: VertexKey | VO): number;
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * The function "inDegreeOf" returns the number of incoming edgeMap for a given vertex.
     * @param {VertexKey | VO} vertexOrKey - The parameter `vertexOrKey` can be either a `VertexKey` or a `VO`.
     * @returns The number of incoming edgeMap of the specified vertex or vertex ID.
     */
    inDegreeOf(vertexOrKey: VertexKey | VO): number;
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * The function `outDegreeOf` returns the number of outgoing edgeMap from a given vertex.
     * @param {VertexKey | VO} vertexOrKey - The parameter `vertexOrKey` can be either a `VertexKey` or a `VO`.
     * @returns The number of outgoing edgeMap from the specified vertex or vertex ID.
     */
    outDegreeOf(vertexOrKey: VertexKey | VO): number;
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * The function "edgesOf" returns an array of both outgoing and incoming edgeMap of a given vertex or vertex ID.
     * @param {VertexKey | VO} vertexOrKey - The parameter `vertexOrKey` can be either a `VertexKey` or a `VO`.
     * @returns The function `edgesOf` returns an array of edgeMap.
     */
    edgesOf(vertexOrKey: VertexKey | VO): EO[];
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * The function "getEdgeSrc" returns the source vertex of an edge, or undefined if the edge does not exist.
     * @param {EO} e - The parameter "e" is of type EO, which represents an edge in a graph.
     * @returns either a vertex object (VO) or undefined.
     */
    getEdgeSrc(e: EO): VO | undefined;
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * The function "getEdgeDest" returns the destination vertex of an edge.
     * @param {EO} e - The parameter "e" is of type "EO", which represents an edge in a graph.
     * @returns either a vertex object of type VO or undefined.
     */
    getEdgeDest(e: EO): VO | undefined;
    /**
     * Time Complexity: O(|E|) where |E| is the number of edgeMap
     * Space Complexity: O(1)
     *
     * The function `getDestinations` returns an array of destination vertexMap connected to a given vertex.
     * @param {VO | VertexKey | undefined} vertex - The `vertex` parameter represents the starting vertex from which we want to
     * find the destinations. It can be either a `VO` object, a `VertexKey` value, or `undefined`.
     * @returns an array of vertexMap (VO[]).
     */
    getDestinations(vertex: VO | VertexKey | undefined): VO[];
    /**
     * Time Complexity: O(|V| + |E|) where |V| is the number of vertexMap and |E| is the number of edgeMap
     * Space Complexity: O(|V|)
     *
     * The `topologicalSort` function performs a topological sort on a graph and returns an array of vertexMap or vertex IDs
     * in the sorted order, or undefined if the graph contains a cycle.
     * @param {'vertex' | 'key'} [propertyName] - The `propertyName` parameter is an optional parameter that specifies the
     * property to use for sorting the vertexMap. It can have two possible values: 'vertex' or 'key'. If 'vertex' is
     * specified, the vertexMap themselves will be used for sorting. If 'key' is specified, the ids of
     * @returns an array of vertexMap or vertex IDs in topological order. If there is a cycle in the graph, it returns undefined.
     */
    topologicalSort(propertyName?: 'vertex' | 'key'): Array<VO | VertexKey> | undefined;
    /**
     * Time Complexity: O(|E|) where |E| is the number of edgeMap
     * Space Complexity: O(|E|)
     *
     * The `edgeSet` function returns an array of all the edgeMap in the graph.
     * @returns The `edgeSet()` method returns an array of edgeMap (`EO[]`).
     */
    edgeSet(): EO[];
    /**
     * Time Complexity: O(|E|) where |E| is the number of edgeMap
     * Space Complexity: O(1)
     *
     * The function `getNeighbors` returns an array of neighboring vertexMap of a given vertex or vertex ID in a graph.
     * @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 source and destination vertexMap of an edge if it 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 vertexMap `[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 A boolean value
     */
    isEmpty(): boolean;
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * The clear function resets the vertex map, in-edge map, and out-edge map.
     */
    clear(): void;
    /**
     * The clone function creates a new DirectedGraph object with the same vertices and edges as the original.
     *
     * @return A new instance of the directedgraph class
     */
    clone(): DirectedGraph<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.
     *  Tarjan can find the SSC(strongly connected components), articulation points, and bridges of directed graphs.
     *
     * The function `tarjan` implements the Tarjan's algorithm to find strongly connected components in a
     * graph.
     * @returns The function `tarjan()` returns an object with three properties: `dfnMap`, `lowMap`, and
     * `SCCs`.
     */
    tarjan(): {
        dfnMap: Map<VO, number>;
        lowMap: Map<VO, number>;
        SCCs: Map<number, VO[]>;
    };
    /**
     * Time Complexity: O(V + E) - Depends on the implementation (Tarjan's algorithm).
     * Space Complexity: O(V) - Depends on the implementation (Tarjan's algorithm).
     *
     * The function returns a map that associates each vertex object with its corresponding depth-first
     * number.
     * @returns A Map object with keys of type VO and values of type number.
     */
    getDFNMap(): Map<VO, number>;
    /**
     * The function returns a Map object that contains the low values of each vertex in a Tarjan
     * algorithm.
     * @returns The method `getLowMap()` is returning a `Map` object with keys of type `VO` and values of
     * type `number`.
     */
    getLowMap(): Map<VO, number>;
    /**
     * The function "getSCCs" returns a map of strongly connected components (SCCs) using the Tarjan
     * algorithm.
     * @returns a map where the keys are numbers and the values are arrays of VO objects.
     */
    getSCCs(): Map<number, VO[]>;
    /**
     * Time Complexity: O(1)
     * Space Complexity: O(1)
     *
     * The function `_addEdge` adds an edge to a graph if the source and destination vertexMap exist.
     * @param {EO} edge - The parameter `edge` is of type `EO`, which represents an edge in a graph. It is the edge that
     * needs to be added to the graph.
     * @returns a boolean value. It returns true if the edge was successfully added to the graph, and false if either the
     * source or destination vertex does not exist in the graph.
     */
    protected _addEdge(edge: EO): boolean;
}