Private _inPrivate _outProtected _addThe function _addEdgeOnly adds an edge to a graph if the source and destination vertices exist.
The parameter edge is of type E, which represents an edge in a graph. It is the edge that
needs to be added to the graph.
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 _addProtected _getProtected _getProtected _setProtected _setProtected _setOptional val: V["val"]BellmanFord time:O(VE) space:O(V) one to rest pairs /
/**
BellmanFord time:O(VE) space:O(V)
one to rest pairs
The Bellman-Ford algorithm is also used to find the shortest paths from a source node to all other nodes in a graph. Unlike Dijkstra's algorithm, it can handle edge weights that are negative. Its basic idea involves iterative relaxation of all edges for several rounds to gradually approximate the shortest paths. Due to its ability to handle negative-weight edges, the Bellman-Ford algorithm is more flexible in some scenarios.
The bellmanFord function implements the Bellman-Ford algorithm to find the shortest path from a source vertex to
all other vertices in a graph, and optionally detects negative cycles and generates the minimum path.
The src parameter is the source vertex from which the Bellman-Ford algorithm will
start calculating the shortest paths. It can be either a vertex object or a vertex ID.
Optional scanNegativeCycle: booleanA boolean flag indicating whether to scan for negative cycles in the graph.
Optional getMin: booleanThe getMin parameter is a boolean flag that determines whether the algorithm should
calculate the minimum distance from the source vertex to all other vertices in the graph. If getMin is set to
true, the algorithm will find the minimum distance and update the min variable with the minimum
Optional genPath: booleanA boolean flag indicating whether to generate paths for all vertices from the source vertex.
The function bellmanFord returns an object with the following properties:
The function creates a directed edge between two vertices with an optional weight and value.
The source vertex ID of the edge. It represents the starting point of the edge.
The dest parameter is the identifier of the destination vertex for the edge.
Optional weight: numberThe weight parameter is an optional number that represents the weight of the edge. If no weight is provided, it defaults to 1.
Optional val: E["val"]The 'val' 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.
a new instance of a DirectedEdge object, casted as type E.
The function creates a new vertex with an optional value and returns it.
The id parameter is the unique identifier for the vertex. It is of type VertexId, which
could be a number or a string depending on how you want to identify your vertices.
Optional val: V["val"]The 'val' parameter is an optional value that can be assigned to the vertex. If a value is provided, it will be assigned to the 'val' property of the vertex. If no value is provided, the 'val' property will be assigned the same value as the 'id' parameter
a new instance of a DirectedVertex object, casted as type V.
The function "degreeOf" returns the total degree of a vertex, which is the sum of its out-degree and in-degree.
The parameter vertexOrId can be either a VertexId or a V.
The sum of the out-degree and in-degree of the specified vertex or vertex ID.
Dijkstra algorithm time: O(logVE) space: O(V + E)
Dijkstra's algorithm only solves the single-source shortest path problem, while the Bellman-Ford algorithm and Floyd-Warshall algorithm can address shortest paths between all pairs of nodes. Dijkstra's algorithm is suitable for graphs with non-negative edge weights, whereas the Bellman-Ford algorithm and Floyd-Warshall algorithm can handle negative-weight edges. The time complexity of Dijkstra's algorithm and the Bellman-Ford algorithm depends on the size of the graph, while the time complexity of the Floyd-Warshall algorithm is O(V^3), where V is the number of nodes. For dense graphs, Floyd-Warshall might become slower.
/
/**
Dijkstra's algorithm is used to find the shortest paths from a source node to all other nodes in a graph. Its basic idea is to repeatedly choose the node closest to the source node and update the distances of other nodes using this node as an intermediary. Dijkstra's algorithm requires that the edge weights in the graph are non-negative.
The dijkstra function implements Dijkstra's algorithm to find the shortest path between a source vertex and an
optional destination vertex, and optionally returns the minimum distance, the paths, and other information.
The src parameter represents the source vertex from which the Dijkstra algorithm will
start. It can be either a vertex object or a vertex ID.
Optional dest: null | VertexId | VThe dest parameter is the destination vertex or vertex ID. It specifies the
vertex to which the shortest path is calculated from the source vertex. If no destination is provided, the algorithm
will calculate the shortest paths to all other vertices from the source vertex.
Optional getMinDist: booleanThe getMinDist parameter is a boolean flag that determines whether the minimum
distance from the source vertex to the destination vertex should be calculated and returned in the result. If
getMinDist is set to true, the minDist property in the result will contain the minimum distance
Optional genPaths: booleanThe genPaths parameter is a boolean flag that determines whether or not to generate
paths in the Dijkstra algorithm. If genPaths is set to true, the algorithm will calculate and return the
shortest paths from the source vertex to all other vertices in the graph. If genPaths @returns The function dijkstrareturns an object of typeDijkstraResult
Dijkstra algorithm time: O(VE) space: O(V + E) /
/**
Dijkstra algorithm time: O(VE) space: O(V + E)
The function dijkstraWithoutHeap implements Dijkstra's algorithm to find the shortest path between two vertices in
a graph without using a heap data structure.
The source vertex from which to start the Dijkstra's algorithm. It can be either a vertex object or a vertex ID.
Optional dest: null | VertexId | VThe dest parameter in the dijkstraWithoutHeap function is an optional
parameter that specifies the destination vertex for the Dijkstra algorithm. It can be either a vertex object or its
identifier. If no destination is provided, the value is set to null.
Optional getMinDist: booleanThe getMinDist parameter is a boolean flag that determines whether the minimum
distance from the source vertex to the destination vertex should be calculated and returned in the result. If
getMinDist is set to true, the minDist property in the result will contain the minimum distance
Optional genPaths: booleanThe genPaths parameter is a boolean flag that determines whether or not to generate
paths in the Dijkstra algorithm. If genPaths is set to true, the algorithm will calculate and return the
shortest paths from the source vertex to all other vertices in the graph. If genPaths @returns The function dijkstraWithoutHeapreturns an object of typeDijkstraResult
The function "edgesOf" returns an array of both outgoing and incoming edges of a given vertex or vertex ID.
The parameter vertexOrId can be either a VertexId or a V.
The function edgesOf returns an array of edges.
Floyd algorithm time: O(V^3) space: O(V^2), not support graph with negative weight cycle all pairs /
/** Floyd algorithm time: O(V^3) space: O(V^2), not support graph with negative weight cycle all pairs The Floyd-Warshall algorithm is used to find the shortest paths between all pairs of nodes in a graph. It employs dynamic programming to compute the shortest paths from any node to any other node. The Floyd-Warshall algorithm's advantage lies in its ability to handle graphs with negative-weight edges, and it can simultaneously compute shortest paths between any two nodes. The function implements the Floyd-Warshall algorithm to find the shortest path between all pairs of vertices in a graph.
The function floyd() returns an object with two properties: costs and predecessor. The costs
property is a 2D array of numbers representing the shortest path costs between vertices in a graph. The
predecessor property is a 2D array of vertices (or null) representing the predecessor vertices in the shortest
path between vertices in the
The function getDestinations returns an array of destination vertices connected to a given vertex.
The vertex parameter represents the starting vertex from which we want to
find the destinations. It can be either a V object, a VertexId value, or null.
an array of vertices (V[]).
The getEdge function retrieves an edge between two vertices based on their source and destination IDs.
The source vertex or its ID. It can be either a vertex object or a vertex ID.
The destOrId parameter in the getEdge function represents the
destination vertex of the edge. It can be either a vertex object (V), a vertex ID (VertexId), or null if the
destination is not specified.
the first edge found between the source and destination vertices, or null if no such edge is found.
The function "getEndsOfEdge" returns the source and destination vertices of an edge if it exists in the graph, otherwise it returns null.
The parameter edge is of type E, which represents an edge in a graph.
The function getEndsOfEdge returns an array containing two vertices [V, V] if the edge exists in the
graph. If the edge does not exist, it returns null.
The function getMinCostBetween calculates the minimum cost between two vertices in a graph, either based on edge
weights or using a breadth-first search algorithm.
The parameter v1 represents the starting vertex or its ID.
The parameter v2 represents the destination vertex or its ID. It is the vertex to which
you want to find the minimum cost or weight from the source vertex v1.
Optional isWeight: booleanisWeight is an optional parameter that indicates whether the graph edges have weights. If isWeight is set to true, the function will calculate the minimum cost between v1 and v2 based on the weights of the edges. If isWeight is set to false or not provided, the function will calculate the
The function getMinCostBetween returns a number representing the minimum cost between two vertices (v1
and v2). If the isWeight parameter is true, it calculates the minimum weight among all paths between the
vertices. If isWeight is false or not provided, it uses a breadth-first search (BFS) algorithm to calculate the
minimum number of
The function getMinPathBetween returns the minimum path between two vertices in a graph, either based on weight or
using a breadth-first search algorithm.
The parameter v1 represents the starting vertex of the path. It can be either a vertex
object (V) or a vertex ID (VertexId).
V | VertexId - The second vertex or vertex ID between which we want to find the minimum path.
Optional isWeight: booleanA boolean flag indicating whether to consider the weight of edges in finding the minimum path. If set to true, the function will use Dijkstra's algorithm to find the minimum weighted path. If set to false, the function will use breadth-first search (BFS) to find the minimum path.
The function getMinPathBetween returns an array of vertices (V[]) representing the minimum path between
two vertices (v1 and v2). If there is no path between the vertices, it returns null.
The function getNeighbors returns an array of neighboring vertices of a given vertex or vertex ID in a graph.
The parameter vertexOrId can be either a vertex object (V) or a vertex ID
(VertexId).
an array of vertices (V[]).
The function "getVertex" returns the vertex with the specified ID or null if it doesn't exist.
The vertexId parameter is the identifier of the vertex that you want to retrieve from
the _vertices map.
The method getVertex returns the vertex with the specified vertexId if it exists in the _vertices
map. If the vertex does not exist, it returns null.
The function checks if there is an edge between two vertices and returns a boolean value indicating the result.
The parameter v1 can be either a VertexId or a V. A VertexId represents the unique identifier of a vertex in a graph, while V represents the type of the vertex object itself.
The parameter v2 represents the second vertex in the edge. It can be either a
VertexId or a V type, which represents the type of the vertex.
A boolean value is being returned.
The function checks if a vertex exists in a graph.
The parameter vertexOrId can be either a vertex object (V) or a vertex ID
(VertexId).
a boolean value.
The function "inDegreeOf" returns the number of incoming edges for a given vertex.
The parameter vertexOrId can be either a VertexId or a V.
The number of incoming edges of the specified vertex or vertex ID.
The function incomingEdgesOf returns an array of incoming edges for a given vertex or vertex ID.
The parameter vertexOrId can be either a vertex object (V) or a vertex ID
(VertexId).
The method incomingEdgesOf returns an array of edges (E[]).
The function outDegreeOf returns the number of outgoing edges from a given vertex.
The parameter vertexOrId can be either a VertexId or a V.
The number of outgoing edges from the specified vertex or vertex ID.
The function outgoingEdgesOf returns an array of outgoing edges from a given vertex or vertex ID.
The parameter vertexOrId can accept either a vertex object (V) or a vertex ID
(VertexId).
The method outgoingEdgesOf returns an array of edges (E[]).
The function removes all vertices from a graph and returns a boolean indicating if any vertices were removed.
The vertices parameter can be either an array of vertices (V[]) or an array
of vertex IDs (VertexId[]).
a boolean value. It returns true if at least one vertex was successfully removed, and false if no vertices were removed.
The function removes an edge from a graph and returns the removed edge, or null if the edge was not found.
The edge parameter is an object that represents an edge in a graph. It has two properties: src
and dest, which represent the source and destination vertices of the edge, respectively.
The method removeEdge returns the removed edge (E) if it exists, or null if the edge does not exist.
The function removes edges between two vertices and returns the removed edges.
The parameter v1 can be either a VertexId or a V. A VertexId represents the
unique identifier of a vertex in a graph, while V represents the actual vertex object.
The parameter v2 represents either a VertexId or a V object. It is used to specify
the second vertex in the edge that needs to be removed.
an array of removed edges (E[]).
The removeVertex function removes a vertex from a graph by its ID or by the vertex object itself.
The parameter vertexOrId can be either a vertex object (V) or a vertex ID
(VertexId).
The method is returning a boolean value.
The function sets the weight of an edge between two vertices in a graph.
The srcOrId parameter can be either a VertexId or a V object. It represents
the source vertex of the edge.
The destOrId parameter represents the destination vertex of the edge. It can be
either a VertexId or a vertex object V.
The weight parameter represents the weight of the edge between the source vertex (srcOrId) and the destination vertex (destOrId).
a boolean value. If the edge exists between the source and destination vertices, the function will update the weight of the edge and return true. If the edge does not exist, the function will return false.
Tarjan is an algorithm based on DFS,which is used to solve the connectivity problem of graphs. Tarjan can find cycles in directed or undirected graph Tarjan can find the articulation points and bridges(critical edges) of undirected graphs in linear time, Tarjan solve the bi-connected components of undirected graphs; Tarjan can find the SSC(strongly connected components), articulation points, and bridges of directed graphs. /
/**
Tarjan is an algorithm based on DFS,which is used to solve the connectivity problem of graphs.
Tarjan can find cycles in directed or undirected graph
Tarjan can find the articulation points and bridges(critical edges) of undirected graphs in linear time,
Tarjan solve the bi-connected components of undirected graphs;
Tarjan can find the SSC(strongly connected components), articulation points, and bridges of directed graphs.
The tarjan function is used to perform various graph analysis tasks such as finding articulation points, bridges,
strongly connected components (SCCs), and cycles in a graph.
Optional needArticulationPoints: booleanA boolean value indicating whether or not to calculate and return the articulation points in the graph. Articulation points are the vertices in a graph whose removal would increase the number of connected components in the graph.
Optional needBridges: booleanA boolean flag indicating whether the algorithm should find and return the bridges (edges whose removal would increase the number of connected components in the graph).
Optional needSCCs: booleanA boolean value indicating whether the Strongly Connected Components (SCCs) of the graph are needed. If set to true, the function will calculate and return the SCCs of the graph. If set to false, the SCCs will not be calculated or returned.
Optional needCycles: booleanA boolean flag indicating whether the algorithm should find cycles in the graph. If set to true, the algorithm will return a map of cycles, where the keys are the low values of the SCCs and the values are arrays of vertices that form cycles within the SCCs.
The function tarjan returns an object with the following properties:
The topologicalSort function performs a topological sort on a graph and returns an array of vertices or vertex IDs
in the sorted order, or null if the graph contains a cycle.
Optional propertyName: "id" | "vertex"The propertyName parameter is an optional parameter that specifies the
property to use for sorting the vertices. It can have two possible values: 'vertex' or 'id'. If 'vertex' is
specified, the vertices themselves will be used for sorting. If 'id' is specified, the ids of
an array of vertices or vertex IDs in topological order. If there is a cycle in the graph, it returns null.
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The constructor function initializes an instance of a class.