The Algorithms logo
The Algorithms

Breadth First Shortest Path

import Queue from '../Data-Structures/Queue/Queue'
 * 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
 * @see
export 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 = new Queue()

  while (!queue.isEmpty()) {
    // start with the queue's first path
    const path = queue.dequeue()
    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

      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

  // the target node was not reachable
  return []