avl-tree-typed/src/data-structures/graph/undirected-graph.ts

Standard AVL tree

/**
 * data-structure-typed
 *
 * @author Pablo Zeng
 * @copyright Copyright (c) 2022 Pablo Zeng <zrwusa@gmail.com>
 * @license MIT License
 */

import type { GraphOptions, VertexKey } from '../../types';
import { IGraph } from '../../interfaces';
import { AbstractEdge, AbstractGraph, AbstractVertex } from './abstract-graph';
import { arrayRemove } from '../../utils';

export class UndirectedVertex<V = any> extends AbstractVertex<V> {
  constructor(key: VertexKey, value?: V) {
    super(key, value);
  }
}

export class UndirectedEdge<E = number> extends AbstractEdge<E> {
  endpoints: [VertexKey, VertexKey];

  constructor(v1: VertexKey, v2: VertexKey, weight?: number, value?: E) {
    super(weight, value);
    this.endpoints = [v1, v2];
  }
}

/**
 * Undirected graph implementation.
 * @template V - Vertex value type.
 * @template E - Edge value type.
 * @template VO - Concrete vertex class (extends AbstractVertex<V>).
 * @template EO - Concrete edge class (extends AbstractEdge<E>).
 * @remarks Time O(1), Space O(1)
 * @example examples will be generated by unit test
 */
export 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>
{
  /**
   * Construct an undirected graph with runtime defaults.
   * @param options - `GraphOptions<V>` (e.g. `vertexValueInitializer`, `defaultEdgeWeight`).
   * @remarks Time O(1), Space O(1)
   */
  constructor(options?: Partial<GraphOptions<V>>) {
    super(options);
    this._edgeMap = new Map<VO, EO[]>();
  }

  protected _edgeMap: Map<VO, EO[]>;

  get edgeMap(): Map<VO, EO[]> {
    return this._edgeMap;
  }

  set edgeMap(v: Map<VO, EO[]>) {
    this._edgeMap = v;
  }

  /**
   * Construct an undirected graph from keys with value initializer `v => v`.
   * @template K - Vertex key type.
   * @param keys - Iterable of vertex keys.
   * @returns UndirectedGraph with all keys added.
   * @remarks Time O(V), Space O(V)
   */
  static fromKeys<K extends VertexKey>(
    keys: Iterable<K>
  ): UndirectedGraph<K, any, UndirectedVertex<K>, UndirectedEdge<any>> {
    const g: UndirectedGraph<K, any, UndirectedVertex<K>, UndirectedEdge<any>> = new UndirectedGraph<K, any>({
      vertexValueInitializer: (k: VertexKey) => k as K
    });
    for (const k of keys) g.addVertex(k);
    return g;
  }

  /**
   * Construct an undirected graph from `[key, value]` entries.
   * @template V - Vertex value type.
   * @param entries - Iterable of `[key, value]` pairs.
   * @returns UndirectedGraph with all vertices added.
   * @remarks Time O(V), Space O(V)
   */
  static fromEntries<V>(
    entries: Iterable<[VertexKey, V]>
  ): UndirectedGraph<V, any, UndirectedVertex<V>, UndirectedEdge<any>> {
    const g: UndirectedGraph<V, any, UndirectedVertex<V>, UndirectedEdge<any>> = new UndirectedGraph<V, any>();
    for (const [k, v] of entries) g.addVertex(k, v);
    return g;
  }

  /**
   * Create an undirected vertex instance. Does not insert into the graph.
   * @param key - Vertex identifier.
   * @param value - Optional payload.
   * @returns Concrete vertex instance.
   * @remarks Time O(1), Space O(1)
   */
  createVertex(key: VertexKey, value?: VO['value']): VO {
    return new UndirectedVertex(key, value) as VO;
  }

  /**
   * Create an undirected edge instance. Does not insert into the graph.
   * @param v1 - One endpoint key.
   * @param v2 - The other endpoint key.
   * @param weight - Edge weight; defaults to `defaultEdgeWeight`.
   * @param value - Edge payload.
   * @returns Concrete edge instance.
   * @remarks Time O(1), Space O(1)
   */
  override createEdge(v1: VertexKey, v2: VertexKey, weight?: number, value?: EO['value']): EO {
    return new UndirectedEdge(v1, v2, weight ?? this.options.defaultEdgeWeight ?? 1, value) as EO;
  }

  /**
   * Get an undirected edge between two vertices, if present.
   * @param v1 - One vertex or key.
   * @param v2 - The other vertex or key.
   * @returns Edge instance or `undefined`.
   * @remarks Time O(1) avg, Space O(1)
   */
  getEdge(v1: VO | VertexKey | undefined, v2: VO | VertexKey | undefined): EO | undefined {
    let edgeMap: EO[] | undefined = [];

    if (v1 !== undefined && v2 !== undefined) {
      const vertex1: VO | undefined = this._getVertex(v1);
      const vertex2: VO | undefined = this._getVertex(v2);

      if (vertex1 && vertex2) {
        edgeMap = this._edgeMap.get(vertex1)?.filter(e => e.endpoints.includes(vertex2.key));
      }
    }

    return edgeMap ? edgeMap[0] || undefined : undefined;
  }

  /**
   * Delete a single undirected edge between two vertices.
   * @param v1 - One vertex or key.
   * @param v2 - The other vertex or key.
   * @returns Removed edge or `undefined`.
   * @remarks Time O(1) avg, Space O(1)
   */
  deleteEdgeBetween(v1: VO | VertexKey, v2: VO | VertexKey): EO | undefined {
    const vertex1: VO | undefined = this._getVertex(v1);
    const vertex2: VO | undefined = this._getVertex(v2);

    if (!vertex1 || !vertex2) {
      return undefined;
    }

    const v1Edges = this._edgeMap.get(vertex1);
    let removed: EO | undefined = undefined;
    if (v1Edges) {
      removed = arrayRemove<EO>(v1Edges, (e: EO) => e.endpoints.includes(vertex2.key))[0] || undefined;
    }
    const v2Edges = this._edgeMap.get(vertex2);
    if (v2Edges) {
      arrayRemove<EO>(v2Edges, (e: EO) => e.endpoints.includes(vertex1.key));
    }
    return removed;
  }

  /**
   * Delete an edge by instance or by a pair of keys.
   * @param edgeOrOneSideVertexKey - Edge instance or one endpoint vertex/key.
   * @param otherSideVertexKey - Required second endpoint when deleting by pair.
   * @returns Removed edge or `undefined`.
   * @remarks Time O(1) avg, Space O(1)
   */
  deleteEdge(edgeOrOneSideVertexKey: EO | VertexKey, otherSideVertexKey?: VertexKey): EO | undefined {
    let oneSide: VO | undefined, otherSide: VO | undefined;
    if (this.isVertexKey(edgeOrOneSideVertexKey)) {
      if (this.isVertexKey(otherSideVertexKey)) {
        oneSide = this._getVertex(edgeOrOneSideVertexKey);
        otherSide = this._getVertex(otherSideVertexKey);
      } else {
        return;
      }
    } else {
      oneSide = this._getVertex(edgeOrOneSideVertexKey.endpoints[0]);
      otherSide = this._getVertex(edgeOrOneSideVertexKey.endpoints[1]);
    }

    if (oneSide && otherSide) {
      return this.deleteEdgeBetween(oneSide, otherSide);
    } else {
      return;
    }
  }

  /**
   * Delete a vertex and remove it from all neighbor lists.
   * @param vertexOrKey - Vertex or key.
   * @returns `true` if removed; otherwise `false`.
   * @remarks Time O(deg), Space O(1)
   */
  deleteVertex(vertexOrKey: VO | VertexKey): boolean {
    let vertexKey: VertexKey;
    let vertex: VO | undefined;
    if (this.isVertexKey(vertexOrKey)) {
      vertex = this.getVertex(vertexOrKey);
      vertexKey = vertexOrKey;
    } else {
      vertex = vertexOrKey;
      vertexKey = this._getVertexKey(vertexOrKey);
    }

    /**
     * All neighbors connected via undirected edges.
     * @param vertexOrKey - Vertex or key.
     * @returns Array of neighbor vertices.
     * @remarks Time O(deg), Space O(deg)
     */
    const neighbors = this.getNeighbors(vertexOrKey);

    if (vertex) {
      neighbors.forEach(neighbor => {
        const neighborEdges = this._edgeMap.get(neighbor);
        if (neighborEdges) {
          const restEdges = neighborEdges.filter(edge => {
            return !edge.endpoints.includes(vertexKey);
          });
          this._edgeMap.set(neighbor, restEdges);
        }
      });
      this._edgeMap.delete(vertex);
    }

    return this._vertexMap.delete(vertexKey);
  }

  /**
   * Degree of a vertex (# of incident undirected edges).
   * @param vertexOrKey - Vertex or key.
   * @returns Non-negative integer.
   * @remarks Time O(1) avg, Space O(1)
   */
  degreeOf(vertexOrKey: VertexKey | VO): number {
    const vertex = this._getVertex(vertexOrKey);
    if (vertex) {
      return this._edgeMap.get(vertex)?.length || 0;
    } else {
      return 0;
    }
  }

  /**
   * Incident undirected edges of a vertex.
   * @param vertexOrKey - Vertex or key.
   * @returns Array of incident edges.
   * @remarks Time O(deg), Space O(deg)
   */
  edgesOf(vertexOrKey: VertexKey | VO): EO[] {
    const vertex = this._getVertex(vertexOrKey);
    if (vertex) {
      return this._edgeMap.get(vertex) || [];
    } else {
      return [];
    }
  }

  /**
   * Unique set of undirected edges across endpoints.
   * @returns Array of edges.
   * @remarks Time O(E), Space O(E)
   */
  edgeSet(): EO[] {
    const edgeSet: Set<EO> = new Set();
    this._edgeMap.forEach(edgeMap => {
      edgeMap.forEach(edge => {
        edgeSet.add(edge);
      });
    });
    return [...edgeSet];
  }

  getNeighbors(vertexOrKey: VO | VertexKey): VO[] {
    const neighbors: VO[] = [];
    const vertex = this._getVertex(vertexOrKey);
    if (vertex) {
      const neighborEdges = this.edgesOf(vertex);
      for (const edge of neighborEdges) {
        const neighbor = this._getVertex(edge.endpoints.filter(e => e !== vertex.key)[0]);
        if (neighbor) {
          neighbors.push(neighbor);
        }
      }
    }
    return neighbors;
  }

  /**
   * Resolve an edge's two endpoints to vertex instances.
   * @param edge - Edge instance.
   * @returns `[v1, v2]` or `undefined` if either endpoint is missing.
   * @remarks Time O(1), Space O(1)
   */
  getEndsOfEdge(edge: EO): [VO, VO] | undefined {
    if (!this.hasEdge(edge.endpoints[0], edge.endpoints[1])) {
      return undefined;
    }
    const v1 = this._getVertex(edge.endpoints[0]);
    const v2 = this._getVertex(edge.endpoints[1]);
    if (v1 && v2) {
      return [v1, v2];
    } else {
      return undefined;
    }
  }

  /**
   * Whether the graph has no vertices and no edges.
   * @remarks Time O(1), Space O(1)
   */
  isEmpty(): boolean {
    return this.vertexMap.size === 0 && this.edgeMap.size === 0;
  }

  /**
   * Remove all vertices and edges.
   * @remarks Time O(V + E), Space O(1)
   */
  clear() {
    this._vertexMap = new Map<VertexKey, VO>();
    this._edgeMap = new Map<VO, EO[]>();
  }

  /**
   * Deep clone as the same concrete class.
   * @returns A new graph of the same concrete class (`this` type).
   * @remarks Time O(V + E), Space O(V + E)
   */
  override clone(): this {
    return super.clone();
  }

  /**
   * Tarjan-based bridge and articulation point detection.
   * @returns `{ dfnMap, lowMap, bridges, cutVertices }`.
   * @remarks Time O(V + E), Space O(V + E)
   */
  tarjan(): { dfnMap: Map<VO, number>; lowMap: Map<VO, number>; bridges: EO[]; cutVertices: VO[] } {
    const dfnMap = new Map<VO, number>();
    const lowMap = new Map<VO, number>();
    const bridges: EO[] = [];
    const cutVertices: VO[] = [];

    let time = 0;

    const dfs = (vertex: VO, parent: VO | undefined) => {
      dfnMap.set(vertex, time);
      lowMap.set(vertex, time);
      time++;

      const neighbors = this.getNeighbors(vertex);
      let childCount = 0;

      for (const neighbor of neighbors) {
        if (!dfnMap.has(neighbor)) {
          childCount++;
          dfs(neighbor, vertex);
          lowMap.set(vertex, Math.min(lowMap.get(vertex)!, lowMap.get(neighbor)!));

          if (lowMap.get(neighbor)! > dfnMap.get(vertex)!) {
            // Found a bridge
            const edge = this.getEdge(vertex, neighbor);
            if (edge) {
              bridges.push(edge);
            }
          }

          if (parent !== undefined && lowMap.get(neighbor)! >= dfnMap.get(vertex)!) {
            // Found an articulation point
            cutVertices.push(vertex);
          }
        } else if (neighbor !== parent) {
          lowMap.set(vertex, Math.min(lowMap.get(vertex)!, dfnMap.get(neighbor)!));
        }
      }

      if (parent === undefined && childCount > 1) {
        // Special case for root in DFS tree
        cutVertices.push(vertex);
      }
    };

    for (const vertex of this.vertexMap.values()) {
      if (!dfnMap.has(vertex)) {
        dfs(vertex, undefined);
      }
    }

    return {
      dfnMap,
      lowMap,
      bridges,
      cutVertices
    };
  }

  /**
   * Get bridges discovered by `tarjan()`.
   * @returns Array of edges that are bridges.
   * @remarks Time O(B), Space O(1)
   */
  getBridges() {
    return this.tarjan().bridges;
  }

  /**
   * Get articulation points discovered by `tarjan()`.
   * @returns Array of cut vertices.
   * @remarks Time O(C), Space O(1)
   */
  getCutVertices() {
    return this.tarjan().cutVertices;
  }

  /**
   * DFN index map computed by `tarjan()`.
   * @returns Map from vertex to DFN index.
   * @remarks Time O(V), Space O(V)
   */
  getDFNMap() {
    return this.tarjan().dfnMap;
  }

  /**
   * LOW link map computed by `tarjan()`.
   * @returns Map from vertex to LOW value.
   * @remarks Time O(V), Space O(V)
   */
  getLowMap() {
    return this.tarjan().lowMap;
  }

  /**
   * Internal hook to attach an undirected edge into adjacency maps.
   * @param edge - Edge instance.
   * @returns `true` if both endpoints exist; otherwise `false`.
   * @remarks Time O(1) avg, Space O(1)
   */
  protected _addEdge(edge: EO): boolean {
    for (const end of edge.endpoints) {
      const endVertex = this._getVertex(end);
      if (endVertex === undefined) return false;
      if (endVertex) {
        const edgeMap = this._edgeMap.get(endVertex);
        if (edgeMap) {
          edgeMap.push(edge);
        } else {
          this._edgeMap.set(endVertex, [edge]);
        }
      }
    }
    return true;
  }
}