Protected_addTime Complexity: O(1) Space Complexity: O(1)
The function adds an edge to the graph by updating the adjacency list with the vertexMap of the edge.
The parameter "edge" is of type EO, which represents an edge in a graph.
a boolean value.
Time Complexity: O(n) Space Complexity: O(1)
The function is an implementation of the Symbol.iterator method that returns an iterable iterator.
Rest...args: any[]The args parameter in the code snippet represents a rest parameter. It
allows the function to accept any number of arguments as an array. In this case, the args
parameter is used to pass any additional arguments to the _getIterator method.
Time Complexity: O(V * E) - Quadratic time in the worst case (Bellman-Ford algorithm). Space Complexity: O(V + E) - Depends on the implementation (Bellman-Ford algorithm).
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 edgeMap for several rounds to gradually approximate the shortest paths. Due to its ability to handle negative-weight edgeMap, 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 vertexMap 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.
OptionalscanNegativeCycle: booleanA boolean flag indicating whether to scan for negative cycles in the graph.
OptionalgetMin: booleanThe getMin parameter is a boolean flag that determines whether the algorithm should
calculate the minimum distance from the source vertex to all other vertexMap in the graph. If getMin is set to
true, the algorithm will find the minimum distance and update the min variable with the minimum
OptionalgenPath: booleanA boolean flag indicating whether to generate paths for all vertexMap from the source vertex.
The function bellmanFord returns an object with the following properties:
The clone function creates a new UndirectedGraph object and copies the vertexMap and edgeMap from this graph to the new one. This is done by assigning each of these properties to their respective counterparts in the cloned graph. The clone function returns a reference to this newly created, cloned UndirectedGraph object.
A new instance of the undirectedgraph class
The function creates an undirected edge between two vertexMap with an optional weight and value.
The parameter v1 represents the first vertex of the edge.
The parameter v2 represents the second vertex of the edge.
Optionalweight: numberThe weight parameter is an optional number that represents the weight of the edge. If
no weight is provided, it defaults to 1.
Optionalvalue: EO["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.
a new instance of the UndirectedEdge class, which is casted as type EO.
The function creates a new vertex with an optional value and returns it.
The key parameter is the unique identifier for the vertex. It is used to distinguish one
vertex from another in the graph.
Optionalvalue: VO["value"]The value parameter is an optional value that can be assigned to the vertex. If a value is provided,
it will be used as the value of the vertex. If no value is provided, the key parameter will be used as the value of
the vertex.
The method is returning a new instance of the UndirectedVertex class, casted as type VO.
Time Complexity: O(1) Space Complexity: O(1)
The function degreeOf returns the degree of a vertex in a graph, which is the number of edgeMap connected to that
vertex.
The parameter vertexOrKey can be either a VertexKey or a VO.
The function degreeOf returns the degree of a vertex in a graph. The degree of a vertex is the number of
edgeMap connected to that vertex.
Time Complexity: O(E), where E is the number of edgeMap incident to the given vertex. Space Complexity: O(1)
The function deleteEdge deletes an edge between two endpoints in a graph.
The parameter edgeOrOneSideVertexKey can be
either an edge object or a vertex key.
OptionalotherSideVertexKey: VertexKeyThe parameter otherSideVertexKey is an optional
parameter that represents the key of the vertex on the other side of the edge. It is used when the
edgeOrOneSideVertexKey parameter is a vertex key, and it specifies the key of the vertex on the
other side of the
The deleteEdge function returns either the deleted edge object (EO) or undefined.
Time Complexity: O(|E|), where |E| is the number of edgeMap incident to the given vertex. Space Complexity: O(1)
The function removes an edge between two vertexMap in a graph and returns the removed edge.
the removed edge (EO) if it exists, or undefined if either of the endpoints (VO) does not exist.
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.
The parameter vertexOrKey can be either a vertex object (VO) or a vertex ID
(VertexKey).
The method is returning a boolean value.
Time Complexity: O((V + E) * log(V)) - Depends on the implementation (using a binary heap). Space Complexity: O(V + E) - Depends on the implementation (using a binary heap).
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.
Optionaldest: VertexKey | VO = undefinedThe 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 vertexMap from the source vertex.
OptionalgetMinDist: boolean = falseThe 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
OptionalgenPaths: boolean = falseThe 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 vertexMap in the graph. If genPaths @returns The function dijkstrareturns an object of typeDijkstraResult
Time Complexity: O(V^2 + E) - Quadratic time in the worst case (no heap optimization). Space Complexity: O(V + E) - Depends on the implementation (Dijkstra's algorithm).
The function dijkstraWithoutHeap implements Dijkstra's algorithm to find the shortest path between two vertexMap 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.
Optionaldest: VertexKey | VO = undefinedThe 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 undefined.
OptionalgetMinDist: boolean = falseThe 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
OptionalgenPaths: boolean = falseThe 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 vertexMap in the graph. If genPaths @returns The function dijkstraWithoutHeapreturns an object of typeDijkstraResult
Time Complexity: O(1) Space Complexity: O(1)
The function returns the edgeMap of a given vertex or vertex ID.
The parameter vertexOrKey can be either a VertexKey or a VO. A VertexKey is a
unique identifier for a vertex in a graph, while VO represents the type of the vertex.
an array of edgeMap.
Time Complexity: O(n) Space Complexity: O(1)
The every function checks if every element in a collection satisfies a given condition.
The predicate parameter is a callback function that takes three arguments:
value, key, and index. It should return a boolean value indicating whether the condition is
met for the current element in the iteration.
OptionalthisArg: anyThe thisArg parameter is an optional argument that specifies the value
to be used as this when executing the predicate function. If thisArg is provided, it will be
passed as the first argument to the predicate function. If thisArg is not provided
The every method is returning a boolean value. It returns true if every element in
the collection satisfies the provided predicate function, and false otherwise.
Time Complexity: O(n) Space Complexity: O(n)
The filter function iterates over key-value pairs in a data structure and returns an array of
pairs that satisfy a given predicate.
The predicate parameter is a callback function that takes four arguments:
value, key, index, and this. It is used to determine whether an element should be included
in the filtered array. The callback function should return true if the element should be
included, and @param {any} [thisArg] - ThethisArgparameter is an optional argument that allows you to specify the value ofthiswithin thepredicatefunction. It is used when you want to bind a specific object as the context for thepredicatefunction. IfthisArgis provided, it will be @returns Thefiltermethod returns an array of key-value pairs[VertexKey, V | undefined][]`
that satisfy the given predicate function.
OptionalthisArg: anyTime Complexity: O(n) Space Complexity: O(1)
The find function iterates over the entries of a collection and returns the first value for
which the callback function returns true.
The callback function that will be called for each entry in the collection. It takes three arguments: the value of the entry, the key of the entry, and the index of the entry in the collection. It should return a boolean value indicating whether the current entry matches the desired condition.
OptionalthisArg: anyThe thisArg parameter is an optional argument that specifies the value
to be used as this when executing the callbackfn function. If thisArg is provided, it will
be passed as the this value to the callbackfn function. If thisArg @returns The method findreturns the value of the first element in the iterable that satisfies the provided callback function. If no element satisfies the callback function,undefined` is
returned.
Time Complexity: O(V^3) - Cubic time (Floyd-Warshall algorithm). Space Complexity: O(V^2) - Quadratic space (Floyd-Warshall algorithm).
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 edgeMap, 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 vertexMap in a graph.
The function floydWarshall() returns an object with two properties: costs and predecessor. The costs
property is a 2D array of numbers representing the shortest path costs between vertexMap in a graph. The
predecessor property is a 2D array of vertexMap (or undefined) representing the predecessor vertexMap in the shortest
path between vertexMap in the
Time Complexity: O(n) Space Complexity: O(1)
The forEach function iterates over each key-value pair in a collection and executes a callback
function for each pair.
The callback function that will be called for each element in the collection. It takes four parameters: the value of the current element, the key of the current element, the index of the current element, and the collection itself.
OptionalthisArg: anyThe thisArg parameter is an optional argument that allows you to
specify the value of this within the callback function. If thisArg is provided, it will be
used as the this value when calling the callback function. If thisArg is not provided, `
Time Complexity: O(n) Space Complexity: O(1)
The get function retrieves the value associated with a given key from a collection.
K (the type of the key) - This parameter represents the key that is being searched for in the collection.
The get method returns the value associated with the specified key if it exists in the
collection, otherwise it returns undefined.
Time Complexity: O(P), where P is the number of paths found (in the worst case, exploring all paths). Space Complexity: O(P) - Linear space, where P is the number of paths found.
The function getAllPathsBetween finds all paths between two vertexMap in a graph using depth-first search.
The parameter v1 represents either a vertex object (VO) or a vertex ID (VertexKey).
It is the starting vertex for finding paths.
The parameter v2 represents either a vertex object (VO) or a vertex ID (VertexKey).
The count of limitation of result array.
The function getAllPathsBetween returns an array of arrays of vertexMap (VO[][]).
Time Complexity: O(|E|), where |E| is the number of edgeMap incident to the given vertex. Space Complexity: O(1)
The function getEdge returns the first edge that connects two endpoints, or undefined if no such edge exists.
The parameter v1 represents a vertex or vertex ID. It can be of type VO (vertex
object), undefined, or VertexKey (a string or number representing the ID of a vertex).
The parameter v2 represents a vertex or vertex ID. It can be of type VO (vertex
object), undefined, or VertexKey (vertex ID).
an edge (EO) or undefined.
Time Complexity: O(1) Space Complexity: O(1)
The function "getEndsOfEdge" returns the endpoints at the ends of an edge if the edge exists in the graph, otherwise it returns undefined.
The parameter "edge" is of type EO, which represents an edge in a graph.
The function getEndsOfEdge returns an array containing two endpoints [VO, VO] if the edge exists in the
graph. If the edge does not exist, it returns undefined.
Time Complexity: O(V + E) - Depends on the implementation (Dijkstra's algorithm). Space Complexity: O(V + E) - Depends on the implementation (Dijkstra's algorithm).
The function getMinCostBetween calculates the minimum cost between two vertexMap 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.
OptionalisWeight: booleanisWeight is an optional parameter that indicates whether the graph edgeMap 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 edgeMap. 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 vertexMap (v1
and v2). If the isWeight parameter is true, it calculates the minimum weight among all paths between the
vertexMap. If isWeight is false or not provided, it uses a breadth-first search (BFS) algorithm to calculate the
minimum number of
Time Complexity: O(V + E) - Depends on the implementation (Dijkstra's algorithm or DFS). Space Complexity: O(V + E) - Depends on the implementation (Dijkstra's algorithm or DFS).
The function getMinPathBetween returns the minimum path between two vertexMap 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 (VO) or a vertex ID (VertexKey).
VO | VertexKey - The second vertex or vertex ID between which we want to find the minimum path.
OptionalisWeight: booleanA boolean flag indicating whether to consider the weight of edgeMap 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.
If set to true, it enforces the use of getAllPathsBetween to first obtain all possible paths, followed by iterative computation of the shortest path. This approach may result in exponential time complexity, so the default method is to use the Dijkstra algorithm to obtain the shortest weighted path.
The function getMinPathBetween returns an array of vertexMap (VO[]) representing the minimum path between
two vertexMap (v1 and v2). If there is no path between the vertexMap, it returns undefined.
Time Complexity: O(|V| + |E|), where |V| is the number of vertexMap and |E| is the number of edgeMap. Space Complexity: O(|E|)
The function "getNeighbors" returns an array of neighboring endpoints for a given vertex or vertex ID.
The parameter vertexOrKey can be either a vertex object (VO) or a vertex ID
(VertexKey).
an array of vertexMap (VO[]).
Time Complexity: O(L), where L is the length of the path. Space Complexity: O(1) - Constant space.
The function calculates the sum of weights along a given path.
An array of vertexMap (VO) representing a path in a graph.
The function getPathSumWeight returns the sum of the weights of the edgeMap in the given path.
Time Complexity: O(1) - Constant time for Map lookup. Space Complexity: O(1) - Constant space, as it creates only a few variables.
The function "getVertex" returns the vertex with the specified ID or undefined if it doesn't exist.
The vertexKey parameter is the identifier of the vertex that you want to retrieve from
the _vertexMap map.
The method getVertex returns the vertex with the specified vertexKey if it exists in the _vertexMap
map. If the vertex does not exist, it returns undefined.
Time Complexity: O(n) Space Complexity: O(1)
The function checks if a given key exists in a collection.
The parameter "key" is of type K, which means it can be any type. It represents the key that we want to check for existence in the data structure.
a boolean value. It returns true if the key is found in the collection, and false otherwise.
Time Complexity: O(1) - Depends on the implementation in the concrete class. Space Complexity: O(1) - Depends on the implementation in the concrete class.
The function checks if there is an edge between two vertexMap and returns a boolean value indicating the result.
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 type of the vertex object itself.
The parameter v2 represents the second vertex in the edge. It can be either a
VertexKey or a VO type, which represents the type of the vertex.
A boolean value is being returned.
Time Complexity: O(n) Space Complexity: O(1)
The function checks if a given value exists in a collection.
The parameter "value" is the value that we want to check if it exists in the collection.
a boolean value, either true or false.
Time Complexity: O(1) - Constant time for Map lookup. Space Complexity: O(1) - Constant space, as it creates only a few variables.
The function checks if a vertex exists in a graph.
The parameter vertexOrKey can be either a vertex object (VO) or a vertex ID
(VertexKey).
a boolean value.
Time Complexity: O(n) Space Complexity: O(n)
The map function iterates over the elements of a collection and applies a callback function to
each element, returning an array of the results.
The callback parameter is a function that will be called for each element in the map. It takes four arguments:
OptionalthisArg: anyThe thisArg parameter is an optional argument that allows you to
specify the value of this within the callback function. If thisArg is provided, it will be
used as the this value when calling the callback function. If thisArg is not provided, @returns Themapfunction is returning an array of typeT[]`.
Time Complexity: O(n) Space Complexity: O(1)
The reduce function iterates over key-value pairs and applies a callback function to each pair,
accumulating a single value.
The callback function that will be called for each element in the collection. It takes four arguments: the current accumulator value, the current value of the element, the key of the element, and the index of the element in the collection. It should return the updated accumulator value.
The initialValue parameter is the initial value of the accumulator. It
is the value that will be used as the first argument to the callbackfn function when reducing
the elements of the collection.
The reduce method is returning the final value of the accumulator after iterating over
all the elements in the collection.
Time Complexity: O(K), where K is the number of vertexMap to be removed. Space Complexity: O(1) - Constant space, as it creates only a few variables.
The function removes all vertexMap from a graph and returns a boolean indicating if any vertexMap were removed.
The vertexMap parameter can be either an array of vertexMap (VO[]) or an array
of vertex IDs (VertexKey[]).
a boolean value. It returns true if at least one vertex was successfully removed, and false if no vertexMap were removed.
Time Complexity: O(1) - Constant time for Map and Edge operations. Space Complexity: O(1) - Constant space, as it creates only a few variables.
The function sets the weight of an edge between two vertexMap in a graph.
The srcOrKey parameter can be either a VertexKey or a VO object. It represents
the source vertex of the edge.
The destOrKey parameter represents the destination vertex of the edge. It can be
either a VertexKey or a vertex object VO.
The weight parameter represents the weight of the edge between the source vertex (srcOrKey) and the destination vertex (destOrKey).
a boolean value. If the edge exists between the source and destination vertexMap, the function will update the weight of the edge and return true. If the edge does not exist, the function will return false.
Time Complexity: O(n) Space Complexity: O(1)
The "some" function iterates over a collection and returns true if at least one element satisfies a given predicate.
The predicate parameter is a callback function that takes three arguments:
value, key, and index. It should return a boolean value indicating whether the condition is
met for the current element in the iteration.
OptionalthisArg: anyThe thisArg parameter is an optional argument that specifies the value
to be used as the this value when executing the predicate function. If thisArg is provided,
it will be passed as the first argument to the predicate function. If thisArg is
a boolean value. It returns true if the predicate function returns true for any pair in the collection, and false otherwise.
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.
The function tarjan implements the Tarjan's algorithm to find bridges and cut vertices in a
graph.
The function tarjan() returns an object with the following properties:
The constructor initializes a new Map object to store edgeMap.