#847 - Shortest Path Visiting All Nodes

Hard • View on LeetCode • View on GitHub

Dynamic Programming Breadth-First Search Bit Manipulation Graph Bitmask

Problem Description

You have an undirected, connected graph of n nodes labeled from 0 to n - 1. You are given an array graph where graph[i] is a list of all the nodes connected with node i by an edge.

Return the length of the shortest path that visits every node. You may start and stop at any node, you may revisit nodes multiple times, and you may reuse edges.

Solution

/**
 * @param {number[][]} graph
 * @return {number}
 */
var shortestPathLength = function(graph) {
  const n = graph.length;

  if (n === 1) return 0;

  const allVisited = (1 << n) - 1;
  const queue = [];
  const visited = new Set();

  for (let i = 0; i < n; i++) {
    const initialState = (1 << i);
    queue.push([i, initialState, 0]);
    visited.add(`${i},${initialState}`);
  }

  while (queue.length > 0) {
    const [node, state, distance] = queue.shift();
    if (state === allVisited) {
      return distance;
    }
    for (const neighbor of graph[node]) {
      const newState = state | (1 << neighbor);
      const key = `${neighbor},${newState}`;
      if (!visited.has(key)) {
        visited.add(key);
        queue.push([neighbor, newState, distance + 1]);
      }
    }
  }

  return -1;
};