Problem

题目大意：求顶点覆盖的最短路径。

https://leetcode.com/problems/shortest-path-visiting-all-nodes/description/

An undirected, connected graph of N nodes (labeled 0, 1, 2, ..., N-1) is given as graph.

graph.length = N, and j != i is in the list graph[i] exactly once, if and only if nodes i and j are connected.

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.

Example 1:

Input: [[1,2,3],[0],[0],[0]]
Output: 4
Explanation: One possible path is [1,0,2,0,3]

Example 2:

Input: [[1],[0,2,4],[1,3,4],[2],[1,2]]
Output: 4
Explanation: One possible path is [0,1,4,2,3]

Solution: BFS

Time complexity: O(n*2^n)

Space complexity: O(n*2^n)

C++

// Author: Huahua
// Running time: 34 ms
class Solution {
public:
  int shortestPathLength(vector<vector<int>>& graph) {
    const int kAns = (1 << (graph.size())) - 1;    
    queue<pair<int, int>> q;
    unordered_set<int> visited; // (cur_node << 16) | state
    for (int i = 0; i < graph.size(); ++i)
      q.push({i, 1 << i});
    int steps = 0;
    while (!q.empty()) {
      int s = q.size();      
      while (s--) {
        auto p = q.front(); 
        q.pop();
        int n = p.first;
        int state = p.second;
        if (state == kAns) return steps;
        int key = (n << 16) | state;
        if (visited.count(key)) continue;
        visited.insert(key);
        for (int next : graph[n])
          q.push({next, state | (1 << next)});
      }
      ++steps;
    }
    return -1;
  }
};

C++ / vector

// Author: Huahua
// Running time: 10 ms
class Solution {
public:
  int shortestPathLength(vector<vector<int>>& graph) {
    const int n = graph.size();
    const int kAns = (1 << n) - 1;
    queue<pair<int, int>> q;
    vector<vector<int>> visited(n, vector<int>(1 << n));
    for (int i = 0; i < n; ++i)
      q.push({i, 1 << i});
    int steps = 0;
    while (!q.empty()) {
      int s = q.size();
      while (s--) {
        auto p = q.front(); 
        q.pop();
        int node = p.first;
        int state = p.second;
        if (state == kAns) return steps;   
        if (visited[node][state]) continue;
        visited[node][state] = 1;
        for (int next : graph[node])
          q.push({next, state | (1 << next)});
      }
      ++steps;
    }
    return -1;
  }
};

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The post 花花酱 LeetCode 847. Shortest Path Visiting All Nodes appeared first on Huahua's Tech Road.