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Solution: Shortest Path Visiting All Nodes

Understand how to solve the shortest path problem for visiting all nodes in an undirected connected graph. Learn to use breadth-first search combined with bitmasking to track visited nodes and ensure finding the minimal path length. This lesson guides you through the state representation, algorithm steps, and the underlying complexity analysis.

Statement

You are given an undirected connected graph with n nodes numbered from 00 to n1n-1. The graph is provided as an adjacency list, graph, where graph[i] contains all nodes that share an edge with node i.

Your task is to find the length of the shortest path that visits every node. You may:

  • Start from any node.

  • End at any node.

  • Revisit nodes and reuse edges as many times as needed.

Constraints:

  • n ==== graph.length

  • 11 \leq n 12\leq 12 ...