Merge pull request #572 from algobytewise/add-BreadthFirstShortestPath

Add algorithm Breadth-first shortest path

Graphs/BreadthFirstShortestPath.js

@@ -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'))