@haragei/dag/dist/index.mjs.map

A Directed Acyclic Graph (DAG) library with online cycle detection and topological ordering.

{"version":3,"file":"index.mjs","sources":["../src/errors.ts","../src/internal/order.ts","../src/internal/priority-queue.ts","../src/internal/union.ts","../src/dag.ts"],"sourcesContent":["/**\n * Error thrown when a cycle would be introduced in a DAG.\n */\nexport class CycleError extends Error {\n    public constructor() {\n        super('Cycle detected');\n        this.name = 'CycleError';\n    }\n}\n","import type { Node } from './node';\n\n/**\n * Compares two Node<T> objects by order.\n *\n * @param lhs - The left hand-side operand.\n * @param rhs - The right hand-side operand.\n * @return Negative number if 'lhs' is less than 'rhs', positive number if\n * `lhs` is greater than `rhs`, or 0 if they have equal order.\n */\nexport function byOrder<T>(lhs: Node<T>, rhs: Node<T>): -1 | 0 | 1 {\n    return byValue(lhs.order, rhs.order);\n}\n\n/**\n * Compares two numbers by value.\n *\n * @param lhs - The left hand-side operand.\n * @param rhs - The right hand-side operand.\n * @return Negative number if 'lhs' is less than 'rhs', positive number if\n * `lhs` is greater than `rhs`, or 0 if they are equal.\n */\nexport function byValue(lhs: number, rhs: number): -1 | 0 | 1 {\n    return lhs < rhs ? -1 : lhs == rhs ? 0 : +1;\n}\n","/**\n * A simple priority queue based on a sorted array.\n */\nexport class PriorityQueue<T> {\n    #data: T[];\n    #priorities: number[];\n\n    /**\n     * Creates a new, empty priority queue.\n     */\n    public constructor() {\n        this.#data = [];\n        this.#priorities = [];\n    }\n\n    /**\n     * Enqueues an item with the given priority.\n     *\n     * The priority is in ascending order, where lower values have higher priority.\n     *\n     * @param item - Item to insert to the queue.\n     * @param priority - Item priority to use to re-prioritize the queue.\n     */\n    public enqueue(item: T, priority: number): void {\n        const { length } = this.#data;\n\n        this.#data.push(item);\n        this.#priorities.push(priority);\n\n        if (length > 0 && this.#priorities[length - 1]! > priority) {\n            let lo = 0,\n                hi = length;\n\n            while (lo < hi) {\n                const mid = lo + Math.trunc((hi - lo) / 2);\n                if (this.#priorities[mid]! < priority) {\n                    lo = mid + 1;\n                } else {\n                    hi = mid;\n                }\n            }\n\n            if (lo < length) {\n                this.#data.copyWithin(lo + 1, lo, length);\n                this.#data[lo] = item;\n\n                this.#priorities.copyWithin(lo + 1, lo, length);\n                this.#priorities[lo] = priority;\n            }\n        }\n    }\n\n    /**\n     * Returns iterator over all queue items in priority order.\n     *\n     * @returns Queue item iterator in priority order.\n     */\n    [Symbol.iterator](): Iterator<T> {\n        return this.#data[Symbol.iterator]();\n    }\n\n    /**\n     * Returns an array containing all queue items in priority order.\n     *\n     * @return Queue items in priority order.\n     */\n    public toArray(): T[] {\n        return this.#data.slice(0);\n    }\n}\n","/**\n * Combines two sets into a new set.\n *\n * @param a - The first set.\n * @param b - The second set.\n * @return A new set that contains all elements from both input sets.\n */\nexport function union<T>(a: Set<T>, b: Set<T>): Set<T> {\n    if ('union' in a) {\n        return a.union(b);\n    }\n\n    const result = new Set<T>(a);\n    for (const item of b) {\n        result.add(item);\n    }\n\n    return result;\n}\n","import { CycleError } from './errors';\nimport type { Node } from './internal/node';\nimport { byOrder, byValue } from './internal/order';\nimport { PriorityQueue } from './internal/priority-queue';\nimport { union } from './internal/union';\n\n/**\n * Represents a set of nodes that can be processed in parallel as defined by\n * their relationship to each other in the graph.\n */\nexport type ParallelCollection<T> = Set<T | SerialCollection<T>>;\n\n/**\n * Represents a list of nodes that must be processed sequentially as defined by\n * their relationship to each other in the graph.\n */\nexport type SerialCollection<T> = (T | Set<T>)[];\n\n/**\n * A Directed Acyclic Graph structure with online cycle detection and topological ordering.\n */\nexport class DAG<T> {\n    /**\n     * The internal state of the graph.\n     */\n    #nodes: Map<T, Node<T>>;\n\n    /**\n     * a topological order of the nodes in the graph.\n     */\n    #order: T[];\n\n    /**\n     * Creates a new DAG with optional initial nodes.\n     *\n     * @param initialNodes - An optional iterable of initial nodes to populate the graph with.\n     */\n    public constructor(initialNodes?: Iterable<T>) {\n        this.#nodes = new Map();\n        this.#order = [];\n\n        if (initialNodes) {\n            for (const node of initialNodes) {\n                this.#ensureNodeExists(node);\n            }\n        }\n    }\n\n    /**\n     * Returns a list of all nodes in the graph in a topological order.\n     *\n     * **Note:** for every `U -> V` directed edge, `U` will appear\n     * before `V` in a topological order.\n     *\n     * @return An array of all graph nodes in a topological order.\n     */\n    public get order(): T[] {\n        return this.#order.slice(0);\n    }\n\n    /**\n     * Returns the number of nodes in the graph.\n     *\n     * @return Number of nodes in the graph\n     */\n    public get size(): number {\n        return this.#nodes.size;\n    }\n\n    /**\n     * Iterates over all nodes in the graph in a topological order.\n     *\n     * @alias keys\n     * @return An iterator over all nodes in the graph.\n     */\n    [Symbol.iterator](): IterableIterator<T> {\n        return this.#order[Symbol.iterator]();\n    }\n\n    /**\n     * Iterates over all nodes in the graph in a topological order.\n     *\n     * @return An iterator over all nodes in the graph.\n     */\n    keys(): IterableIterator<T> {\n        return this.#order[Symbol.iterator]();\n    }\n\n    /**\n     * Creates a new, independent copy of this DAG.\n     *\n     * @return Clone of this DAG.\n     */\n    public copy(): DAG<T> {\n        const clone = new DAG<T>();\n\n        clone.#order = this.#order.slice(0);\n        clone.#nodes = new Map();\n\n        for (const [id, node] of this.#nodes) {\n            clone.#nodes.set(id, {\n                id,\n                order: node.order,\n                incoming: new Set(node.incoming),\n                outgoing: new Set(node.outgoing),\n            });\n        }\n\n        return clone;\n    }\n\n    /**\n     * Removes all nodes (and their edges) from the graph.\n     *\n     * @return This DAG.\n     */\n    public clear(): this {\n        this.#nodes.clear();\n        this.#order.splice(0, this.#order.length);\n        return this;\n    }\n\n    /**\n     * Adds a node to the graph.\n     * If the node already exists, this is a no-op.\n     *\n     * @param node - The node to add.\n     * @return This DAG.\n     */\n    public add(node: T): this {\n        this.#ensureNodeExists(node);\n        return this;\n    }\n\n    /**\n     * Checks if a specific node exists in the graph.\n     *\n     * @param node - The node to check.\n     * @return `true` if the node exists, `false` otherwise.\n     */\n    public has(node: T): boolean {\n        return this.#nodes.has(node);\n    }\n\n    /**\n     * Removes a specified node from the graph.\n     * If such node doesn't exist, this is a no-op.\n     *\n     * **Note:** This also removes all edges from or to the specified node.\n     *\n     * @param node - The node to remove.\n     * @return This DAG.\n     */\n    public delete(node: T): this {\n        const state = this.#nodes.get(node);\n\n        if (state) {\n            const index = state.order;\n            const last = this.#order.length - 1;\n\n            for (let i = index; i < last; i++) {\n                this.#order[i] = this.#order[i + 1]!;\n                this.#nodes.get(this.#order[i]!)!.order = i;\n            }\n\n            this.#order.pop();\n\n            for (const id of state.incoming) {\n                this.#nodes.get(id)!.outgoing.delete(node);\n            }\n            for (const id of state.outgoing) {\n                this.#nodes.get(id)!.incoming.delete(node);\n            }\n\n            this.#nodes.delete(node);\n        }\n\n        return this;\n    }\n\n    /**\n     * Tries to add a directed edge to the graph.\n     *\n     * If any of the nodes doesn't already exist, it will be added.\n     *\n     * If inserting the given edge would introduce a cycle no changes\n     * are made to the graph and CycleError is thrown.\n     *\n     * Adding an edge from a node to that same node (i.e. `from` and `to` are\n     * the same) is considered a cycle and such edge cannot be added.\n     *\n     * @param from - The \"source\" node.\n     * @param to - The \"target\" node.\n     * @return This DAG.\n     */\n    public addEdge(from: T, to: T): this {\n        if (from == to) {\n            throw new CycleError();\n        }\n\n        this.#addEdge(from, to);\n\n        return this;\n    }\n\n    /**\n     * Tries to add a directed edge to the graph.\n     *\n     * If any of the nodes doesn't already exist, it will be added.\n     *\n     * If inserting the given edge would introduce a cycle no changes\n     * are made to the graph and `false` is returned.\n     *\n     * Adding an edge from a node to that same node (i.e. `from` and `to` are\n     * the same) is considered a cycle and such edge cannot be added.\n     *\n     * @param from - The \"source\" node.\n     * @param to - The \"target\" node.\n     * @return `true` if the edge was added, `false` otherwise.\n     */\n    public tryAddEdge(from: T, to: T): boolean {\n        try {\n            this.addEdge(from, to);\n            return true;\n        } catch {\n            return false;\n        }\n    }\n\n    /**\n     * Checks if a specific (directed) edge exists in the graph.\n     *\n     * @param from - The \"source\" node.\n     * @param to - The \"target\" node.\n     * @return `true` if the edge exists, `false` otherwise.\n     */\n    public hasEdge(from: T, to: T): boolean {\n        const node = this.#nodes.get(from);\n        return node !== undefined && node.outgoing.has(to);\n    }\n\n    /**\n     * Removes a specified edge from the graph.\n     * If such edge doesn't exist, this is a no-op.\n     *\n     * **Note:** this removes a directed edge. If an edge A -> B exists,\n     * it will not be removed with a removeEdge(B, A) call.\n     *\n     * @param from - The \"source\" node.\n     * @param to - The \"target\" node.\n     * @return This DAG.\n     */\n    public deleteEdge(from: T, to: T): this {\n        if (this.hasEdge(from, to)) {\n            this.#nodes.get(from)!.outgoing.delete(to);\n            this.#nodes.get(to)!.incoming.delete(from);\n        }\n\n        return this;\n    }\n\n    /**\n     * Removes all outgoing edges from a given node.\n     * If such node doesn't exist, this is a no-op.\n     *\n     * @param node - The node to remove outgoing edges from.\n     * @return This DAG.\n     */\n    public deleteOutgoingEdgesOf(node: T): this {\n        return this.#deleteAllEdges('outgoing', node);\n    }\n\n    /**\n     * Removes all incoming edges to a given node.\n     * If such node doesn't exist, this is a no-op.\n     *\n     * @param node - The node to remove incoming edges to.\n     * @return This DAG.\n     */\n    public deleteIncomingEdgesOf(node: T): this {\n        return this.#deleteAllEdges('incoming', node);\n    }\n\n    /**\n     * Returns the given nodes in a topological order.\n     *\n     * In a case that a node does not exist in the graph, it is pushed to the end of the array.\n     *\n     * @param nodes - The nodes to sort.\n     * @return An array of the given nodes in a topological order.\n     */\n    public getNodeOrder(...nodes: T[]): T[] {\n        return this.sortNodes(nodes);\n    }\n\n    /**\n     * Sorts the given array of nodes, in place by their topological order.\n     *\n     * In a case that a node does not exist in the graph, it is pushed to the end of the array.\n     *\n     * @param nodes - The nodes to sort.\n     * @return The input array of nodes, sorted in a topological order.\n     */\n    public sortNodes(nodes: T[]): T[] {\n        return nodes.sort((lhsId, rhsId) => {\n            const lhs = this.#nodes.get(lhsId);\n            if (!lhs) {\n                return +1;\n            }\n\n            const rhs = this.#nodes.get(rhsId);\n            if (!rhs) {\n                return -1;\n            }\n\n            return byValue(lhs.order, rhs.order);\n        });\n    }\n\n    /**\n     * Returns (an unordered) set of all immediate predecessors of the given nodes.\n     *\n     * @param nodes - The nodes to get immediate predecessors of.\n     * @return An unordered set of all immediate predecessors of the given nodes.\n     */\n    public getImmediatePredecessorsOf(...nodes: T[]): Set<T> {\n        return this.#getImmediate('incoming', ...nodes);\n    }\n\n    /**\n     * Returns an iterable of all immediate predecessors of the given nodes which\n     * iterates over them in a topological order.\n     *\n     * @param nodes - The nodes to get immediate predecessors of.\n     * @return A topologically ordered iterable of all immediate predecessors of the given nodes.\n     */\n    public getOrderedImmediatePredecessorsOf(...nodes: T[]): Iterable<T> {\n        return this.#toOrderedIterable(this.getImmediatePredecessorsOf(...nodes));\n    }\n\n    /**\n     * Returns (an unordered) set of all predecessors of the given nodes.\n     *\n     * @param nodes - The nodes to get predecessors of.\n     * @return An unordered set of all predecessors of the given nodes.\n     */\n    public getPredecessorsOf(...nodes: T[]): Set<T> {\n        return this.#getReachable('incoming', ...nodes);\n    }\n\n    /**\n     * Returns an iterable of all predecessors of the given nodes which\n     * iterates over them in a topological order.\n     *\n     * @param nodes - The nodes to get predecessors of.\n     * @return A topologically ordered iterable of all predecessors of the given nodes.\n     */\n    public getOrderedPredecessorsOf(...nodes: T[]): Iterable<T> {\n        return this.#toOrderedIterable(this.getPredecessorsOf(...nodes));\n    }\n\n    /**\n     * Returns (an unordered) set of all immediate successors of the given nodes.\n     *\n     * @param nodes - The nodes to get immediate successors of.\n     * @return An unordered set of all immediate successors of the given nodes.\n     */\n    public getImmediateSuccessorsOf(...nodes: T[]): Set<T> {\n        return this.#getImmediate('outgoing', ...nodes);\n    }\n\n    /**\n     * Returns an iterable of all immediate successors of the given nodes which\n     * iterates over them in a topological order.\n     *\n     * @param nodes - The nodes to get immediate successors of.\n     * @return A topologically ordered iterable of all immediate successors of the given nodes.\n     */\n    public getOrderedImmediateSuccessorsOf(...nodes: T[]): Iterable<T> {\n        return this.#toOrderedIterable(this.getImmediateSuccessorsOf(...nodes));\n    }\n\n    /**\n     * Returns (an unordered) set of all successors of the given nodes.\n     *\n     * @param nodes - The nodes to get successors of.\n     * @return An unordered set of all successors of the given nodes.\n     */\n    public getSuccessorsOf(...nodes: T[]): Set<T> {\n        return this.#getReachable('outgoing', ...nodes);\n    }\n\n    /**\n     * Returns an iterable of all successors of the given nodes which\n     * iterates over them in a topological order.\n     *\n     * @param nodes - The nodes to get successors of.\n     * @return A topologically ordered iterable of all successors of the given nodes.\n     */\n    public getOrderedSuccessorsOf(...nodes: T[]): Iterable<T> {\n        return this.#toOrderedIterable(this.getSuccessorsOf(...nodes));\n    }\n\n    /**\n     * Checks whether a directed path between two nodes exists in the graph.\n     *\n     * If A is directly connected to B, `hasPath(A, B)` is exactly the same as `hasEdge(A, B)`.\n     * On the other hand, if only the edges `A -> B` and `A -> C` exists in the\n     * graph, a `hasPath(A, C)` returns `true`, while `hasEdge(A, C)` returns `false`.\n     *\n     *\n     * @param from - The \"source\" node.\n     * @param to - The \"target\" node.\n     * @return `true` if a directed path exists, `false` otherwise.\n     */\n    public hasPath(from: T, to: T): boolean {\n        if (from == to) {\n            return false;\n        }\n\n        const fromNode = this.#nodes.get(from);\n        const toNode = this.#nodes.get(to);\n\n        if (!fromNode || !toNode || fromNode.order > toNode.order) {\n            return false;\n        }\n\n        if (fromNode.outgoing.has(to)) {\n            return true;\n        }\n\n        const queue = [from];\n        const visited = new Set(queue);\n\n        while (queue.length > 0) {\n            for (const successor of this.#nodes.get(queue.shift()!)!.outgoing) {\n                if (successor == to) {\n                    return true;\n                }\n\n                if (!visited.has(successor)) {\n                    visited.add(successor);\n                    queue.push(successor);\n                }\n            }\n        }\n\n        return false;\n    }\n\n    /**\n     * Merges two nodes if such action would not introduce a cycle.\n     *\n     * \"Merging\" of A and B is performed by making:\n     *   - all immediate predecessors of B be immediate predecessors of A, and\n     *   - all immediate successors of B be immediate successors of A.\n     *\n     * After that remapping, node B gets removed from the graph.\n     *\n     * **Note:** This method is a no-op if either A or B is absent in the graph.\n     *\n     * If there is a path between A and B (in either direction), a CycleError\n     * gets thrown, and the graph is not changed.\n     *\n     * @param a - The first node to merge.\n     * @param b - The second node to merge.\n     * @return This DAG.\n     */\n    public mergeNodes(a: T, b: T): this {\n        if (a == b) {\n            return this;\n        }\n\n        const nodeA = this.#nodes.get(a);\n        const nodeB = this.#nodes.get(b);\n\n        if (nodeA && nodeB) {\n            if (this.hasPath(a, b) || this.hasPath(b, a)) {\n                throw new CycleError();\n            }\n\n            for (const predecessor of nodeB.incoming) {\n                this.addEdge(predecessor, a);\n            }\n\n            for (const successor of nodeB.outgoing) {\n                this.addEdge(a, successor);\n            }\n\n            this.delete(b);\n        }\n\n        return this;\n    }\n\n    /**\n     * Tries to merge two nodes if such action would not introduce a cycle.\n     *\n     * \"Merging\" of A and B is performed by making:\n     *   - all immediate predecessors of B be immediate predecessors of A, and\n     *   - all immediate successors of B be immediate successors of A.\n     *\n     * After that remapping, node B gets removed from the graph.\n     *\n     * **Note:** This method is a no-op if either A or B is absent in the graph.\n     *\n     * If there is a path between A and B (in either direction), the merging would\n     * introduce a cycle so this function returns `false`, and the graph is not changed.\n     *\n     * @param a - The first node to merge.\n     * @param b - The second node to merge.\n     * @return True if the nodes were successfully merged, or if\n     * at least one of the given nodes is not present in the graph.\n     */\n    tryMergeNodes(a: T, b: T): boolean {\n        try {\n            this.mergeNodes(a, b);\n            return true;\n        } catch {\n            return false;\n        }\n    }\n\n    /**\n     * Returns an array of node arrays, where each inner array represents a subgraph.\n     *\n     * The nodes in each subgraph are topologically ordered.\n     *\n     * @return An array of independent subgraphs.\n     */\n    subGraphs(): T[][] {\n        const result: T[][] = [];\n\n        if (this.#order.length == 0) {\n            return result;\n        }\n\n        const visited = new Set<T>();\n\n        for (const id of this.#order) {\n            if (visited.has(id)) {\n                continue;\n            }\n\n            const subGraph = new PriorityQueue<T>();\n            const stack = [id];\n\n            while (stack.length > 0) {\n                const id = stack.pop()!;\n\n                if (visited.has(id)) {\n                    continue;\n                }\n\n                const node = this.#nodes.get(id)!;\n\n                visited.add(id);\n                subGraph.enqueue(id, node.order);\n\n                for (const successor of node.outgoing) {\n                    if (!visited.has(successor)) {\n                        stack.push(successor);\n                    }\n                }\n            }\n\n            result.push(subGraph.toArray());\n        }\n\n        return result;\n    }\n\n    /**\n     * Returns a set of all subgraphs in the graph.\n     *\n     * Each subgraph is represented either as a single node, or as an array which\n     * is meant to be processed sequentially and its items are either a single node\n     * or a Set of nodes that can be processed in parallel.\n     *\n     * @example\n     * ```typescript\n     * const dag = new DAG<string>(['Z']);\n     * dag.addEdge('A', 'B');\n     * dag.addEdge('A', 'C');\n     * dag.addEdge('B', 'D');\n     * dag.addEdge('C', 'D');\n     * dag.addEdge('X', 'Y');\n     *\n     * console.log(dag.parallelize());\n     * // Set(3) { [ 'A', Set(2) { 'B', 'C' }, 'D' ], [ 'X', 'Y' ], 'Z' }\n     *```\n     *\n     * @return A set of all subgraphs in the graph, parallelized.\n     */\n    parallelize(): ParallelCollection<T> {\n        const result: ParallelCollection<T> = new Set();\n\n        for (const subGraph of this.subGraphs()) {\n            result.add(this.#parallelize(subGraph));\n        }\n\n        return result;\n    }\n\n    /**\n     * Returns a list of all nodes in the given subgraph, ordered topologically.\n     * The list is meant to be processed sequentially and its items are either\n     * a single node or a Set of nodes that can be processed in parallel.\n     *\n     * @param subGraph - The subgraph to parallelize.\n     * @return The parallelized subgraph.\n     */\n    #parallelize(subGraph: ReadonlyArray<T>): SerialCollection<T> | T {\n        if (subGraph.length == 1) {\n            return subGraph[0]!;\n        }\n\n        const levels: Map<T, number> = new Map();\n        const groups: Set<T>[] = [];\n\n        for (const nodeId of subGraph) {\n            const node = this.#nodes.get(nodeId);\n            if (!node) {\n                continue;\n            }\n\n            const level = Math.max(\n                0,\n                ...Array.from(node.incoming, (id) => (levels.get(id) || 0) + 1),\n            );\n\n            levels.set(nodeId, level);\n            if (groups.length <= level) {\n                groups.push(new Set<T>());\n            }\n            groups[level]!.add(nodeId);\n        }\n\n        return groups.map((group) => (group.size == 1 ? Array.from(group)[0]! : group));\n    }\n\n    /**\n     * Adds a node to the graph and returns it.\n     * If the node already exists, it is returned unchanged.\n     *\n     * @param id - The node to add.\n     * @returns The Node state object.\n     */\n    #ensureNodeExists(id: T): Node<T> {\n        let node = this.#nodes.get(id);\n        if (node) {\n            return node;\n        }\n\n        node = {\n            id,\n            order: this.#order.length,\n            incoming: new Set(),\n            outgoing: new Set(),\n        };\n\n        this.#nodes.set(id, node);\n        this.#order.push(id);\n\n        return node;\n    }\n\n    /**\n     * Tries to add a directed edge to the graph.\n     *\n     * If any of the nodes doesn't already exist, it will be added.\n     *\n     * If inserting the given edge would introduce a cycle no changes\n     * are made to the graph and CycleError is thrown.\n     *\n     * @param from - The \"source\" node.\n     * @param to - The \"target\" node.\n     */\n    #addEdge(from: T, to: T): void {\n        if (this.hasEdge(from, to)) {\n            return;\n        }\n\n        //\n        // This function implements the PK algorithm for incremental\n        // topological ordering as presented in the paper:\n        //\n        //\t\tPEARCE, David J.; KELLY, Paul HJ. A dynamic algorithm for\n        //\t\ttopologically sorting directed acyclic graphs.\n        //\t\tLecture notes in computer science, 2004, 3059: 383-398.\n        //\n        //\t\thttps://citeseerx.ist.psu.edu/document?doi=388da0bed2a1658a34de39b28921de48f353b2ed\n        //\n\n        // N.B. intentionally reversing direction\n        const u = this.#ensureNodeExists(to);\n        const v = this.#ensureNodeExists(from);\n\n        if (u.order < v.order) {\n            const successors = this.#findSuccessors(u, v.order);\n            const predecessors = this.#findPredecessors(v, u.order);\n\n            successors.sort(byOrder);\n            predecessors.sort(byOrder);\n\n            const totalPredecessors = predecessors.length;\n            const totalAffected = totalPredecessors + successors.length;\n\n            const topology = new Array<number>(totalAffected);\n\n            let i = 0;\n            for (const { order } of successors) {\n                topology[i++] = order;\n            }\n            for (const { order } of predecessors) {\n                topology[i++] = order;\n            }\n\n            topology.sort(byValue);\n\n            for (i = 0; i < totalPredecessors; i++) {\n                const index = topology[i]!;\n                const predecessor = predecessors[i]!;\n                this.#order[index] = predecessor.id;\n                predecessor.order = index;\n            }\n            for (i = totalPredecessors; i < totalAffected; i++) {\n                const index = topology[i]!;\n                const successor = successors[i - totalPredecessors]!;\n                this.#order[index] = successor.id;\n                successor.order = index;\n            }\n        }\n\n        u.incoming.add(from);\n        v.outgoing.add(to);\n    }\n\n    /**\n     * Removes all edges from a given node in the given direction (i.e. incoming or outgoing).\n     * If such node doesn't exist, this is a no-op.\n     *\n     * @param direction - The direction of the edges to remove.\n     * @param node - The node whose incoming edges to remove.\n     * @return This DAG.\n     */\n    #deleteAllEdges(direction: 'incoming' | 'outgoing', node: T): this {\n        const state = this.#nodes.get(node);\n\n        if (state) {\n            const reversed = direction == 'incoming' ? 'outgoing' : 'incoming';\n\n            for (const from of state[direction]) {\n                this.#nodes.get(from)![reversed].delete(node);\n            }\n\n            state[direction].clear();\n        }\n\n        return this;\n    }\n\n    /**\n     * Returns all successors of the given node, such that their current topological\n     * order is less than the given one. These nodes will need to be reordered.\n     *\n     * @param startNode - The node whose successors to return.\n     * @param order - The order to constrain the successor set with.\n     * @return The unordered list of successors nodes.\n     */\n    #findSuccessors(startNode: Node<T>, order: number): Node<T>[] {\n        const result: Node<T>[] = [];\n        const visited = new Set<T>();\n        const stack = [startNode];\n\n        while (stack.length > 0) {\n            const node = stack.pop()!;\n\n            if (visited.has(node.id)) {\n                continue;\n            }\n\n            visited.add(node.id);\n            result.push(node);\n\n            for (const id of node.outgoing) {\n                const successor = this.#nodes.get(id)!;\n\n                if (successor.order == order) {\n                    throw new CycleError();\n                }\n                if (!visited.has(id) && successor.order < order) {\n                    stack.push(successor);\n                }\n            }\n        }\n\n        return result;\n    }\n\n    /**\n     * Returns all predecessors of the given node, such that their current topological\n     * order is greater than the given one. These nodes will need to be reordered.\n     *\n     * @param startNode - The node whose predecessors to return.\n     * @param order - The order to constrain the predecessor set with.\n     * @return The unordered list of predecessors nodes.\n     */\n    #findPredecessors(startNode: Node<T>, order: number): Node<T>[] {\n        const result: Node<T>[] = [];\n        const visited = new Set<T>();\n        const stack = [startNode];\n\n        while (stack.length > 0) {\n            const node = stack.pop()!;\n\n            if (visited.has(node.id)) {\n                continue;\n            }\n\n            visited.add(node.id);\n            result.push(node);\n\n            for (const id of node.incoming) {\n                const predecessor = this.#nodes.get(id)!;\n\n                if (!visited.has(id) && predecessor.order >= order) {\n                    stack.push(predecessor);\n                }\n            }\n        }\n\n        return result;\n    }\n\n    /**\n     * Returns (an unordered) set of all immediate neighbors of the given nodes.\n     *\n     * @param direction - The direction of the edges to traverse.\n     * @param nodes - Nodes whose immediate neighbors to return.\n     * @return An unordered set of all immediate neighbors of the given nodes.\n     */\n    #getImmediate(direction: 'incoming' | 'outgoing', ...nodes: T[]): Set<T> {\n        let results = new Set<T>();\n\n        for (const id of nodes) {\n            const node = this.#nodes.get(id);\n            if (node) {\n                results = union(results, node[direction]);\n            }\n        }\n\n        for (const id of nodes) {\n            results.delete(id);\n        }\n\n        return results;\n    }\n\n    /**\n     * Returns (an unordered) set of all nodes reachable from the given nodes.\n     *\n     * @param direction - The direction of the edges to traverse.\n     * @param nodes - Nodes whose reachable nodes to return.\n     * @return An unordered set of all reachable nodes of the given nodes..\n     */\n    #getReachable(direction: 'incoming' | 'outgoing', ...nodes: T[]): Set<T> {\n        const results = new Set(nodes);\n        const queue = nodes.slice(0);\n\n        while (queue.length > 0) {\n            const node = this.#nodes.get(queue.shift()!);\n            if (!node) {\n                continue;\n            }\n\n            for (const id of node[direction]) {\n                if (!results.has(id)) {\n                    results.add(id);\n                    queue.push(id);\n                }\n            }\n        }\n\n        for (const id of nodes) {\n            results.delete(id);\n        }\n\n        return results;\n    }\n\n    /**\n     * Returns a new iterable which iterates over the nodes\n     * in the given iterable in topological order.\n     *\n     * **Note:** This function assumes that all nodes\n     * in the given iterable are present in the graph.\n     *\n     * @param ids - An iterable of node ids.\n     * @returns Iterable over the given nodes in topological order.\n     */\n    #toOrderedIterable(ids: Iterable<T>): Iterable<T> {\n        const queue = new PriorityQueue<T>();\n\n        for (const id of ids) {\n            queue.enqueue(id, this.#nodes.get(id)!.order);\n        }\n\n        return queue;\n    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