847. Shortest Path Visiting All Nodes 

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class Solution {
    private static class State {
        private final int node;
        private int visitedMask;
        private int pathLength;

        public State(int node, int visitedMask, int pathLength) {
            this.node = node;
            this.visitedMask = visitedMask;
            this.pathLength = pathLength;
        }
    }

    public int shortestPathLength(int[][] graph) {
        int n = graph.length;

        boolean[][] nodeVisitedMap = new boolean[n][1 << n]; // 表示访问 i 且状态为 j 时是否被访问过，如果访问过，说明之前的路径更短，此次扫描没有必要
        Queue<State> queue = new LinkedList<>();
        for (int i = 0; i < n; i++) {
            // 从每个节点出发
            queue.offer(new State(i, 1 << i, 0));
            nodeVisitedMap[i][1 << i] = true;
        }

        while (!queue.isEmpty()) {
            State state = queue.poll();
            if (state.visitedMask == (1 << n) - 1) {
                return state.pathLength;
            }

            for (int nextNode : graph[state.node]) {
                int mask = state.visitedMask | (1 << nextNode);
                if (!nodeVisitedMap[nextNode][mask]) {
                    queue.offer(new State(nextNode, mask, state.pathLength + 1));
                    nodeVisitedMap[nextNode][mask] = true;
                }
            }
        }

        return -1;
    }
}

References

847. Shortest Path Visiting All Nodes