mirror of
https://github.com/TheAlgorithms/JavaScript.git
synced 2025-07-05 00:01:37 +08:00
Merge pull request #572 from algobytewise/add-BreadthFirstShortestPath
Add algorithm Breadth-first shortest path
This commit is contained in:
88
Graphs/BreadthFirstShortestPath.js
Normal file
88
Graphs/BreadthFirstShortestPath.js
Normal file
@ -0,0 +1,88 @@
|
|||||||
|
/*
|
||||||
|
Breadth-first approach can be applied to determine the shortest path between two nodes
|
||||||
|
in an equi-weighted graph. It searches the target node among all neighbors of the
|
||||||
|
starting node, then the process is repeated on the level of the neighbors of the
|
||||||
|
neighbors and so on.
|
||||||
|
(See also: https://en.wikipedia.org/wiki/Breadth-first_search )
|
||||||
|
(see also: https://www.koderdojo.com/blog/breadth-first-search-and-shortest-path-in-csharp-and-net-core )
|
||||||
|
*/
|
||||||
|
|
||||||
|
/*
|
||||||
|
Doctests
|
||||||
|
> breadthFirstShortestPath(graph, 'C', 'E')
|
||||||
|
[ 'C', 'D', 'A', 'B', 'E' ]
|
||||||
|
> breadthFirstShortestPath(graph, 'E', 'B')
|
||||||
|
[ 'E', 'D', 'A', 'B' ]
|
||||||
|
> breadthFirstShortestPath(graph, 'F', 'G')
|
||||||
|
[ 'F', 'G' ]
|
||||||
|
> breadthFirstShortestPath(graph, 'A', 'G')
|
||||||
|
[]
|
||||||
|
*/
|
||||||
|
|
||||||
|
function breadthFirstShortestPath (graph, startNode, targetNode) {
|
||||||
|
// check if startNode & targetNode are identical
|
||||||
|
if (startNode === targetNode) {
|
||||||
|
return [startNode]
|
||||||
|
}
|
||||||
|
|
||||||
|
// visited keeps track of all nodes visited
|
||||||
|
const visited = new Set()
|
||||||
|
|
||||||
|
// queue contains the paths to be explored in the future
|
||||||
|
const initialPath = [startNode]
|
||||||
|
const queue = [initialPath]
|
||||||
|
|
||||||
|
while (queue.length > 0) {
|
||||||
|
// start with the queue's first path
|
||||||
|
const path = queue.shift()
|
||||||
|
const node = path[path.length - 1]
|
||||||
|
|
||||||
|
// explore this node if it hasn't been visited yet
|
||||||
|
if (!visited.has(node)) {
|
||||||
|
// mark the node as visited
|
||||||
|
visited.add(node)
|
||||||
|
|
||||||
|
const neighbors = graph[node]
|
||||||
|
|
||||||
|
// create a new path in the queue for each neighbor
|
||||||
|
for (let i = 0; i < neighbors.length; i++) {
|
||||||
|
const newPath = path.concat([neighbors[i]])
|
||||||
|
|
||||||
|
// the first path to contain the target node is the shortest path
|
||||||
|
if (neighbors[i] === targetNode) {
|
||||||
|
return newPath
|
||||||
|
}
|
||||||
|
|
||||||
|
// queue the new path
|
||||||
|
queue.push(newPath)
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
// the target node was not reachable
|
||||||
|
return []
|
||||||
|
}
|
||||||
|
|
||||||
|
const graph = {
|
||||||
|
A: ['B', 'D'],
|
||||||
|
B: ['E'],
|
||||||
|
C: ['D'],
|
||||||
|
D: ['A'],
|
||||||
|
E: ['D'],
|
||||||
|
F: ['G'],
|
||||||
|
G: []
|
||||||
|
}
|
||||||
|
/*
|
||||||
|
A <-> B
|
||||||
|
ʌ |
|
||||||
|
| |
|
||||||
|
v v
|
||||||
|
C --> D <-- E
|
||||||
|
|
||||||
|
F --> G
|
||||||
|
*/
|
||||||
|
|
||||||
|
console.log(breadthFirstShortestPath(graph, 'C', 'E'))
|
||||||
|
console.log(breadthFirstShortestPath(graph, 'E', 'B'))
|
||||||
|
console.log(breadthFirstShortestPath(graph, 'F', 'G'))
|
||||||
|
console.log(breadthFirstShortestPath(graph, 'A', 'G'))
|
Reference in New Issue
Block a user