cocos-engine/cocos/rendering/custom/graph.ts

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export const enum directional {
    undirected = 0,
    directed = 1,
    bidirectional = 2,
}

export const enum parallel {
    disallow = 0,
    allow = 1,
}

export const enum traversal {
    none = 0,
    incidence = 1 << 0,
    bidirectional = 1 << 1,
    adjacency = 1 << 2,
    vertex_list = 1 << 3,
    edge_list = 1 << 4,
}

//--------------------------------------------------------------------------
// Vertex
//--------------------------------------------------------------------------
export interface Vertex {
    nullVertex (): Vertex | null;
}

//--------------------------------------------------------------------------
// Vertex Descriptor
//--------------------------------------------------------------------------
export type vertex_descriptor = number | Vertex;

//--------------------------------------------------------------------------
// Edge
//--------------------------------------------------------------------------
export interface Edge {
    getProperty (): unknown;
    source: vertex_descriptor;
    target: vertex_descriptor;
}

//--------------------------------------------------------------------------
// Edge Descriptor
//--------------------------------------------------------------------------
export class ED {
    constructor (source: vertex_descriptor, target: vertex_descriptor) {
        this.source = source;
        this.target = target;
    }
    equals (rhs: ED): boolean {
        return this.source === rhs.source
            && this.target === rhs.target;
    }
    source: vertex_descriptor;
    target: vertex_descriptor;
}

// Edge Descriptor with Property
export class EPD {
    constructor (source: vertex_descriptor, target: vertex_descriptor, edge: Edge) {
        this.source = source;
        this.target = target;
        this.edge = edge;
    }
    equals (rhs: EPD): boolean {
        return this.edge === rhs.edge;
    }
    source: vertex_descriptor;
    target: vertex_descriptor;
    readonly edge: Edge;
}

// Edge Descriptor
export type edge_descriptor = ED | EPD;

//--------------------------------------------------------------------------
// OutEdge
//--------------------------------------------------------------------------
// OutEdge
export class OutE {
    constructor (target: vertex_descriptor) {
        this.target = target;
    }
    equals (rhs: OutE): boolean {
        return this.target === rhs.target;
    }
    target: vertex_descriptor;
}

// OutEdge(Property)
export class OutEP {
    constructor (target: vertex_descriptor, edge: Edge) {
        this.target = target;
        this.edge = edge;
    }
    equals (rhs: OutEP): boolean {
        return this.target === rhs.target;
    }
    getProperty (): unknown {
        return this.edge.getProperty();
    }
    target: vertex_descriptor;
    readonly edge: Edge;
}

//--------------------------------------------------------------------------
// OutEdge Iterator
//--------------------------------------------------------------------------
export class OutEI implements IterableIterator<ED> {
    constructor (iterator: IterableIterator<OutE>, source: vertex_descriptor) {
        this.iterator = iterator;
        this.source = source;
    }
    [Symbol.iterator] (): OutEI {
        return this;
    }
    next (): IteratorResult<ED> {
        const res = this.iterator.next();
        if (res.done) {
            return { value: undefined, done: true };
        } else {
            return { value: new ED(this.source, res.value.target), done: false };
        }
    }
    readonly iterator: IterableIterator<OutE>;
    readonly source: vertex_descriptor;
}

// OutEdge(Property) Iterator
export class OutEPI implements IterableIterator<EPD> {
    constructor (iterator: IterableIterator<OutEP>, source: vertex_descriptor) {
        this.iterator = iterator;
        this.source = source;
    }
    [Symbol.iterator] (): OutEPI {
        return this;
    }
    next (): IteratorResult<EPD> {
        const res = this.iterator.next();
        if (res.done) {
            return { value: undefined, done: true };
        } else {
            return { value: new EPD(this.source, res.value.target, res.value.edge), done: false };
        }
    }
    readonly iterator: IterableIterator<OutEP>;
    readonly source: vertex_descriptor;
}

// OutEdge Iterator
export type out_edge_iterator = OutEI | OutEPI;

//--------------------------------------------------------------------------
// InEdge Iterator
//--------------------------------------------------------------------------
// InEdge Iterator
export class InEI implements IterableIterator<ED> {
    constructor (iterator: IterableIterator<OutE>, source: vertex_descriptor) {
        this.iterator = iterator;
        this.source = source;
    }
    [Symbol.iterator] (): InEI {
        return this;
    }
    next (): IteratorResult<ED> {
        const res = this.iterator.next();
        if (res.done) {
            return { value: undefined, done: true };
        } else {
            return { value: new ED(res.value.target, this.source), done: false };
        }
    }
    readonly iterator: IterableIterator<OutE>;
    readonly source: vertex_descriptor;
}

// InEdge(Property) Iterator
export class InEPI implements IterableIterator<EPD> {
    constructor (iterator: IterableIterator<OutEP>, source: vertex_descriptor) {
        this.iterator = iterator;
        this.source = source;
    }
    [Symbol.iterator] (): InEPI {
        return this;
    }
    next (): IteratorResult<EPD> {
        const res = this.iterator.next();
        if (res.done) {
            return { value: undefined, done: true };
        } else {
            return { value: new EPD(res.value.target, this.source, res.value.edge), done: false };
        }
    }
    readonly iterator: IterableIterator<OutEP>;
    readonly source: vertex_descriptor;
}

// InEdge Iterator
export type in_edge_iterator = InEI | InEPI;

//--------------------------------------------------------------------------
// Graph
//--------------------------------------------------------------------------
export interface Graph {
    readonly directed_category: directional;
    readonly edge_parallel_category: parallel;
    readonly traversal_category: traversal;

    nullVertex (): vertex_descriptor | null;
}

//--------------------------------------------------------------------------
// IncidenceGraph
//--------------------------------------------------------------------------
export interface IncidenceGraph extends Graph {
    edge (u: vertex_descriptor, v: vertex_descriptor): boolean;
    source (e: edge_descriptor): vertex_descriptor;
    target (e: edge_descriptor): vertex_descriptor;
    outEdges (v: vertex_descriptor): out_edge_iterator;
    outDegree (v: vertex_descriptor): number;
}

//--------------------------------------------------------------------------
// BidirectionalGraph
//--------------------------------------------------------------------------
export interface BidirectionalGraph extends IncidenceGraph {
    inEdges (v: vertex_descriptor): in_edge_iterator;
    inDegree (v: vertex_descriptor): number;
    degree (v: vertex_descriptor): number;
}

//--------------------------------------------------------------------------
// AdjacencyGraph
//--------------------------------------------------------------------------
// Adjacency Iterator
export class AdjI implements IterableIterator<vertex_descriptor> {
    constructor (graph: IncidenceGraph, iterator: OutEI) {
        this.graph = graph;
        this.iterator = iterator;
    }
    [Symbol.iterator] (): AdjI {
        return this;
    }
    next (): IteratorResult<vertex_descriptor> {
        const res = this.iterator.next();
        if (res.done) {
            return { value: undefined, done: true };
        } else {
            return { value: this.graph.target(res.value), done: false };
        }
    }
    readonly graph: IncidenceGraph;
    readonly iterator: OutEI;
}

export class AdjPI implements IterableIterator<vertex_descriptor> {
    constructor (graph: IncidenceGraph, iterator: OutEPI) {
        this.graph = graph;
        this.iterator = iterator;
    }
    [Symbol.iterator] (): AdjPI {
        return this;
    }
    next (): IteratorResult<vertex_descriptor> {
        const res = this.iterator.next();
        if (res.done) {
            return { value: undefined, done: true };
        } else {
            return { value: this.graph.target(res.value), done: false };
        }
    }
    readonly graph: IncidenceGraph;
    readonly iterator: OutEPI;
}

// Adjacency Iterator
export type adjacency_iterator = AdjI | AdjPI;

// AdjacencyGraph
export interface AdjacencyGraph extends Graph {
    adjacentVertices (v: vertex_descriptor): adjacency_iterator;
}

//--------------------------------------------------------------------------
// VertexListGraph
//--------------------------------------------------------------------------
export interface VertexListGraph extends Graph {
    vertices (): IterableIterator<vertex_descriptor>;
    numVertices (): number;
}

//--------------------------------------------------------------------------
// EdgeListGraph
//--------------------------------------------------------------------------
export interface EdgeListGraph extends Graph {
    edges (): IterableIterator<edge_descriptor>;
    numEdges (): number;
    source (e: edge_descriptor): vertex_descriptor;
    target (e: edge_descriptor): vertex_descriptor;
}

//--------------------------------------------------------------------------
// MutableGraph
//--------------------------------------------------------------------------
export interface MutableGraph extends Graph {
    addVertex (...args): vertex_descriptor;
    clearVertex (v: vertex_descriptor): void;
    removeVertex (v: vertex_descriptor): void;
    addEdge (u: vertex_descriptor, v: vertex_descriptor, p?: unknown): edge_descriptor | null;
    removeEdges (u: vertex_descriptor, v: vertex_descriptor): void;
    removeEdge (e: edge_descriptor): void;
}

//--------------------------------------------------------------------------
// PropertyMap
//--------------------------------------------------------------------------
export interface PropertyMap {
    get (x: vertex_descriptor | edge_descriptor): unknown;
}

export interface MutableVertexPropertyMap<T> extends PropertyMap {
    put (x: vertex_descriptor, value: T): void;
}

//--------------------------------------------------------------------------
// PropertyGraph
//--------------------------------------------------------------------------
export interface PropertyGraph extends Graph {
    get (tag: string): PropertyMap;
}

//--------------------------------------------------------------------------
// NamedGraph
//--------------------------------------------------------------------------
export interface NamedGraph extends Graph {
    vertexName (v: vertex_descriptor): string;
    vertexNameMap (): PropertyMap;
}

//--------------------------------------------------------------------------
// ComponentGraph
//--------------------------------------------------------------------------
export interface ComponentGraph extends Graph {
    readonly components: string[];
    component (id: number, v: vertex_descriptor): unknown;
    componentMap (id: number): unknown; // should be PropertyMap
}

//--------------------------------------------------------------------------
// PolymorphicGraph
//--------------------------------------------------------------------------
export interface PolymorphicGraph extends Graph {
    holds (id: number, v: vertex_descriptor): boolean;
    id (v: vertex_descriptor): number;
    object (v: vertex_descriptor): unknown;
    value (id: number, v: vertex_descriptor): unknown;
    tryValue(id: number, v: vertex_descriptor): unknown;
    visitVertex (visitor: unknown, v: vertex_descriptor): void;
}

//--------------------------------------------------------------------------
// ReferenceGraph
//--------------------------------------------------------------------------
export type reference_descriptor = ED | EPD;
export type child_iterator = OutEI | OutEPI;
export type parent_iterator = InEI | InEPI;

export interface ReferenceGraph extends Graph {
    reference (u: vertex_descriptor, v: vertex_descriptor): boolean;
    parent (e: reference_descriptor): vertex_descriptor;
    child (e: reference_descriptor): vertex_descriptor;
    parents (v: vertex_descriptor): parent_iterator;
    children (v: vertex_descriptor): child_iterator;
    numParents (v: vertex_descriptor): number;
    numChildren (v: vertex_descriptor): number;
    getParent (v: vertex_descriptor): vertex_descriptor | null;
    isAncestor (ancestor: vertex_descriptor, descendent: vertex_descriptor): boolean;
}

//--------------------------------------------------------------------------
// MutableReferenceGraph
//--------------------------------------------------------------------------
export interface MutableReferenceGraph extends ReferenceGraph {
    addReference (u: vertex_descriptor, v: vertex_descriptor, p?: unknown): reference_descriptor | null;
    removeReference (e: reference_descriptor): void;
    removeReferences (u: vertex_descriptor, v: vertex_descriptor): void;
}

//--------------------------------------------------------------------------
// ParentGraph
//--------------------------------------------------------------------------
export interface ParentGraph extends ReferenceGraph, NamedGraph {
    locateChild (v: vertex_descriptor | null, name: string): vertex_descriptor | null;
}

//--------------------------------------------------------------------------
// AddressableGraph
//--------------------------------------------------------------------------
export interface AddressableGraph extends ParentGraph {
    addressable (absPath: string): boolean;
    locate (absPath: string): vertex_descriptor | null;
    locateRelative (path: string, start?: vertex_descriptor | null): vertex_descriptor | null;
    path (v: vertex_descriptor): string;
}

//--------------------------------------------------------------------------
// UuidGraph
//--------------------------------------------------------------------------
export interface UuidGraph<Key> extends Graph {
    contains (key: Key): boolean;
    vertex (key: Key): vertex_descriptor;
    find (key: Key): vertex_descriptor | null;
}

//--------------------------------------------------------------------------
// Help Functions
//--------------------------------------------------------------------------
export function reindexEdgeList (el: (OutE|OutEP)[], u: number): void {
    for (const e of el) {
        if (e.target as number > u) {
            --(e.target as number);
        }
    }
}

export function removeAllEdgesFromList (edges: Set<Edge>, el: OutEP[], v: vertex_descriptor): void {
    const sz = el.length;
    for (let i = 0; i !== sz; ++i) {
        const oe = el[i];
        if (oe.target === v) {
            // NOTE: Wihtout this skip, this loop will double-delete
            // properties of loop edges. This solution is based on the
            // observation that the incidence edges of a vertex with a loop
            // are adjacent in the out edge list. This *may* actually hold
            // for multisets also.
            const skip = (i + 1 !== sz && oe.edge === el[i + 1].edge);
            edges.delete(oe.edge);
            if (skip) {
                ++i;
            }
        }
    }
}

export function getPath (g: ReferenceGraph & NamedGraph, v: vertex_descriptor | null): string {
    if (v === g.nullVertex()) {
        return '';
    }
    const paths: string[] = [];
    for (; v !== g.nullVertex(); v = g.getParent(v as vertex_descriptor)) {
        paths.push(g.vertexName(v as vertex_descriptor));
    }
    let path = '';
    for (let i = paths.length; i-- > 0;) {
        path += '/';
        path += paths[i];
    }
    return path;
}

export function findRelative (g: ParentGraph, v: vertex_descriptor | null, path: string): vertex_descriptor | null {
    const pseudo = g.nullVertex();
    const names = path.split('/');

    if (names.length === 0) { // empty string
        return v;
    }

    let curr = v;
    let start = 0;
    if (names[0] === '') { // absolute path
        // reset v to pseudo root
        curr = pseudo;
        // skip pseudo root
        ++start;
    }
    // locating begins
    for (let i = start; i !== names.length; ++i) {
        const name = names[i];
        if (name === '') { // empty name, do nothing
            continue;
        }
        if (name === '.') { // current node, do nothing
            continue;
        }
        if (name === '..') { // parent node
            if (curr === pseudo) {
                // current node is pseudo already, return not found
                return pseudo;
            }
            curr = g.getParent(curr as vertex_descriptor);
            continue;
        }
        curr = g.locateChild(curr, name);
        if (curr === pseudo) { // child not found
            return pseudo;
        }
    }
    return curr;
}

//=======================================================================
// DFS
// Based on boost/graph/depth_first_search.hpp
//=======================================================================

//=======================================================================
// Copyright 1997, 1998, 1999, 2000 University of Notre Dame.
// Copyright 2003 Bruce Barr
// Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek
//
// Distributed under the Boost Software License, Version 1.0. (See
// accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
//=======================================================================

export interface TerminatorFunc {
    terminate (v: vertex_descriptor, g: IncidenceGraph): boolean;
}

class NoTermination implements TerminatorFunc {
    terminate (v: vertex_descriptor, g: IncidenceGraph): boolean {
        return false;
    }
}

function getDefaultStartingVertex (g: IncidenceGraph & VertexListGraph): vertex_descriptor | null {
    const iter = g.vertices();
    const v = iter.next();
    if (v.done) {
        return g.nullVertex();
    } else {
        return v.value;
    }
}

export interface GraphVisitor {
    // 0. before dfs
    initializeVertex (v: vertex_descriptor, g: IncidenceGraph): void;
    // 1. dfs starting vertex (usually the root)
    startVertex (v: vertex_descriptor, g: IncidenceGraph): void;
    // 2. vertex discovered
    discoverVertex (v: vertex_descriptor, g: IncidenceGraph): void;
    // 3. edge discovered
    examineEdge (e: edge_descriptor, g: IncidenceGraph): void;
    // 4(a). is tree edge
    treeEdge (e: edge_descriptor, g: IncidenceGraph): void;
    // 4(b). is back edge
    backEdge (e: edge_descriptor, g: IncidenceGraph): void;
    // 4(c). is forward or cross edge
    forwardOrCrossEdge (e: edge_descriptor, g: IncidenceGraph): void;
    // 5. edge finished
    finishEdge (e: edge_descriptor, g: IncidenceGraph): void;
    // 6. vertex finished
    finishVertex (v: vertex_descriptor, g: IncidenceGraph): void;
}

export enum GraphColor {
    WHITE,
    GRAY,
    GREEN,
    RED,
    BLACK,
}

class VertexInfo {
    constructor (
        v: vertex_descriptor,
        e: edge_descriptor | null,
        iter: out_edge_iterator | null,
    ) {
        this.v = v;
        this.e = e;
        this.iter = iter;
    }
    v: vertex_descriptor;
    e: edge_descriptor | null;
    iter: out_edge_iterator | null;
}

function depthFirstVisitImpl (
    g: IncidenceGraph,
    u: vertex_descriptor,
    visitor: GraphVisitor,
    color: MutableVertexPropertyMap<GraphColor>,
    func: TerminatorFunc,
): void {
    let srcE: edge_descriptor | null = null;
    let ei: out_edge_iterator | null = null;
    const stack = new Array<VertexInfo>();

    color.put(u, GraphColor.GRAY);
    visitor.discoverVertex(u, g);

    ei = g.outEdges(u);
    if (func.terminate(u, g)) {
        // If this vertex terminates the search, we push empty range
        stack.push(new VertexInfo(u, null, null));
    } else {
        stack.push(new VertexInfo(u, null, ei));
    }

    while (stack.length) {
        const back = stack.pop()!;
        u = back.v;
        srcE = back.e;
        ei = back.iter;
        // finish_edge has to be called here, not after the
        // loop. Think of the pop as the return from a recursive call.
        if (srcE !== null) {
            visitor.finishEdge(srcE, g);
        }
        if (ei) { // has out edges
            for (let ev = ei.next(); !ev.done; ev = ei.next()) {
                const e = ev.value;
                const v = e.target;
                visitor.examineEdge(e, g);
                const vColor = color.get(v);
                if (vColor === GraphColor.WHITE) {
                    visitor.treeEdge(e, g);
                    srcE = e;
                    stack.push(new VertexInfo(u, srcE, ei));
                    u = v;
                    color.put(u, GraphColor.GRAY);
                    visitor.discoverVertex(u, g);
                    ei = g.outEdges(u);
                    if (func.terminate(u, g)) {
                        break;
                    }
                } else {
                    if (vColor === GraphColor.GRAY) {
                        visitor.backEdge(e, g);
                    } else {
                        visitor.forwardOrCrossEdge(e, g);
                    }
                    visitor.finishEdge(e, g);
                }
            }
        }
        color.put(u, GraphColor.BLACK);
        visitor.finishVertex(u, g);
    }
}

export function depthFirstSearch (
    g: IncidenceGraph & VertexListGraph,
    visitor: GraphVisitor,
    color: MutableVertexPropertyMap<GraphColor>,
    startVertex: vertex_descriptor | null = null,
): void {
    // get start vertex
    startVertex = startVertex || getDefaultStartingVertex(g);
    // graph is empty, do nothing
    if (startVertex === null || g.numVertices() === 0) {
        return;
    }
    // initialize vertex and color map
    for (const u of g.vertices()) {
        color.put(u, GraphColor.WHITE);
        visitor.initializeVertex(u, g);
    }
    // start DFS
    const terminator = new NoTermination();
    // try starting from startVertex
    if (startVertex !== getDefaultStartingVertex(g)) {
        visitor.startVertex(startVertex, g);
        depthFirstVisitImpl(g, startVertex, visitor, color, terminator);
    }
    // try starting from each vertex
    for (const u of g.vertices()) {
        // if vertex is not visited, start DFS
        if (color.get(u) === GraphColor.WHITE) {
            visitor.startVertex(u, g);
            depthFirstVisitImpl(g, u, visitor, color, terminator);
        }
    }
}

export function depthFirstVisit (
    g: IncidenceGraph,
    u: vertex_descriptor,
    visitor: GraphVisitor,
    color: MutableVertexPropertyMap<GraphColor>,
    func: TerminatorFunc = new NoTermination(),
): void {
    visitor.startVertex(u, g);
    depthFirstVisitImpl(g, u, visitor, color, func);
}

export class DefaultVisitor implements GraphVisitor {
    initializeVertex (v: vertex_descriptor, g: IncidenceGraph): void {
        // do nothing
    }
    startVertex (v: vertex_descriptor, g: IncidenceGraph): void {
        // do nothing
    }
    discoverVertex (v: vertex_descriptor, g: IncidenceGraph): void {
        // do nothing
    }
    examineEdge (e: edge_descriptor, g: IncidenceGraph): void {
        // do nothing
    }
    treeEdge (e: edge_descriptor, g: IncidenceGraph): void {
        // do nothing
    }
    backEdge (e: edge_descriptor, g: IncidenceGraph): void {
        // do nothing
    }
    forwardOrCrossEdge (e: edge_descriptor, g: IncidenceGraph): void {
        // do nothing
    }
    finishEdge (e: edge_descriptor, g: IncidenceGraph): void {
        // do nothing
    }
    finishVertex (v: vertex_descriptor, g: IncidenceGraph): void {
        // do nothing
    }
}

export class ReferenceGraphView <BaseGraph extends ReferenceGraph & VertexListGraph>
implements IncidenceGraph, VertexListGraph {
    constructor (g: BaseGraph) {
        this.g = g;
        this.directed_category = directional.directed;
        this.edge_parallel_category = parallel.allow;
        this.traversal_category = traversal.incidence | traversal.vertex_list;
    }
    nullVertex (): vertex_descriptor | null {
        return this.g.nullVertex();
    }
    edge (u: vertex_descriptor, v: vertex_descriptor): boolean {
        return this.g.reference(u, v);
    }
    source (e: edge_descriptor): vertex_descriptor {
        return this.g.parent(e);
    }
    target (e: edge_descriptor): vertex_descriptor {
        return this.g.child(e);
    }
    outEdges (v: vertex_descriptor): out_edge_iterator {
        return this.g.children(v);
    }
    outDegree (v: vertex_descriptor): number {
        return this.g.numChildren(v);
    }
    vertices (): IterableIterator<vertex_descriptor> {
        return this.g.vertices();
    }
    numVertices (): number {
        return this.g.numVertices();
    }
    readonly directed_category: directional;
    readonly edge_parallel_category: parallel;
    readonly traversal_category: traversal;
    g: BaseGraph;
}