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| 1 | +/* |
| 2 | +Breadth-first approach can be applied to determine the shortest path between two nodes in a 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. |
| 3 | +(See also: https://en.wikipedia.org/wiki/Breadth-first_search ) |
| 4 | +(see also: https://www.koderdojo.com/blog/breadth-first-search-and-shortest-path-in-csharp-and-net-core ) |
| 5 | +*/ |
| 6 | + |
| 7 | +/* |
| 8 | +Doctests |
| 9 | +> breadthFirstShortestPath(graph, 'C', 'E') |
| 10 | +[ 'C', 'D', 'A', 'B', 'E' ] |
| 11 | +> breadthFirstShortestPath(graph, 'E', 'B') |
| 12 | +[ 'E', 'D', 'A', 'B' ] |
| 13 | +> breadthFirstShortestPath(graph, 'F', 'G') |
| 14 | +[ 'F', 'G' ] |
| 15 | +> breadthFirstShortestPath(graph, 'A', 'G') |
| 16 | +[] |
| 17 | +*/ |
| 18 | + |
| 19 | +function breadthFirstShortestPath (graph, startNode, targetNode) { |
| 20 | + // check if startNode & targetNode are identical |
| 21 | + if (startNode === targetNode) { |
| 22 | + return [startNode] |
| 23 | + } |
| 24 | + |
| 25 | + // visited keeps track of all nodes visited |
| 26 | + const visited = [] |
| 27 | + |
| 28 | + // queue contains the paths to be explored in the future |
| 29 | + const initialPath = [startNode] |
| 30 | + const queue = [initialPath] |
| 31 | + |
| 32 | + while (queue.length > 0) { |
| 33 | + // start with the queue's first path |
| 34 | + const path = queue.shift() |
| 35 | + const node = path[path.length - 1] |
| 36 | + |
| 37 | + // explore this node if it hasn't been visited yet |
| 38 | + if (!visited.includes(node)) { |
| 39 | + // mark the node as visited |
| 40 | + visited.push(node) |
| 41 | + |
| 42 | + const neighbors = graph[node] |
| 43 | + |
| 44 | + // create a new path in the queue for each neighbor |
| 45 | + for (let i = 0; i < neighbors.length; i++) { |
| 46 | + const newPath = path.concat([neighbors[i]]) |
| 47 | + |
| 48 | + // the first path to contain the target node is the shortest path |
| 49 | + if (neighbors[i] === targetNode) { |
| 50 | + return newPath |
| 51 | + } |
| 52 | + |
| 53 | + // queue the new path |
| 54 | + queue.push(newPath) |
| 55 | + } |
| 56 | + } |
| 57 | + } |
| 58 | + |
| 59 | + // the target node was not reachable |
| 60 | + return [] |
| 61 | +} |
| 62 | + |
| 63 | +const graph = { |
| 64 | + A: ['B', 'D'], |
| 65 | + B: ['E'], |
| 66 | + C: ['D'], |
| 67 | + D: ['A'], |
| 68 | + E: ['D'], |
| 69 | + F: ['G'], |
| 70 | + G: [] |
| 71 | +} |
| 72 | +/* |
| 73 | + A <-> B |
| 74 | + ʌ | |
| 75 | + | | |
| 76 | + v v |
| 77 | +C --> D <-- E |
| 78 | + |
| 79 | +F --> G |
| 80 | +*/ |
| 81 | + |
| 82 | +console.log(breadthFirstShortestPath(graph, 'C', 'E')) |
| 83 | +console.log(breadthFirstShortestPath(graph, 'E', 'B')) |
| 84 | +console.log(breadthFirstShortestPath(graph, 'F', 'G')) |
| 85 | +console.log(breadthFirstShortestPath(graph, 'A', 'G')) |
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