Leetcode 310:minimum Height Trees

For a undirected graph with tree characteristics, we can choose any node as the root. The result graph is then a rooted tree. Among all possible rooted trees, those with minimum height is called minimum height trees (mhts). Given such a graph, write a function to find all the mhts and return a list of their root labels.

Format
The graph contains n nodes which is labeled from 0 to n - 1 . You'll be given the number and n a list of undirected edges (each edge is a pair of labels).

You can assume that no duplicate edges would appear in edges . Since all edges was undirected, is the same as and thus would not [0, 1] [1, 0] appear together in edges .

Example 1:

Given n = 4 ,edges = [[1, 0], [1, 2], [1, 3]]

        0        |        1       /       2   3

Return[1]

Example 2:

Given n = 6 ,edges = [[0, 3], [1, 3], [2, 3], [4, 3], [5, 4]]

     0  1  2      \ |/        3        |        4        |        5

Return[3, 4]

Note:

(1) According to the definition of the tree on Wikipedia: "A tree was an undirected graph in which any and vertices is connect Ed by exactly one path. In the other words, any connected graph without simple cycles is a tree. "

(2) The height of a rooted tree is the number of edges on the longest downward path between the root and a leaf.

Ideas:

(Initial idea: At any point as the root node, then breadth-first traversal graph, find the minimum depth, time complexity O (n (n+e)), the result timeout)

Post Reference http://www.cnblogs.com/grandyang/p/5000291.html

Starting from the leaf node, the first layer is deep into the center, and the last remaining nodes (less than two) are the result sets;

Note that there is only one point in the situation;

1 classSolution {2  Public:3vector<int> Findminheighttrees (intN, vector<pair<int,int>>&edges) {4vector<vector<int>> g (n,vector<int>());5vector<int> d (N,0);6         intLen =edges.size ();7          for(intI=0; i<len;i++)8         {9             intA =Edges[i].first;Ten             intb =Edges[i].second; One G[a].push_back (b); A G[b].push_back (a); -d[a]++; -d[b]++; the         } -queue<int>Q; -          for(intI=0; i<n;i++) -         { +             if(d[i]==1) - Q.push (i); +         } A          while(n>2) at         { -             intLen2 =q.size (); -              for(intI=0; i<len2;i++) -             { -n--; -                  intt =Q.front (); in Q.pop (); -                   for(intj=0; J<g[t].size (); j + +) to                  { +d[g[t][j]]--; -                      if(d[g[t][j]]==1) the Q.push (G[t][j]); *                  } $             }Panax Notoginseng         } -vector<int>ans; the          while(!q.empty ()) +         { A Ans.push_back (Q.front ()); the Q.pop (); +         } -         if(ans.size () = =0) $Ans.push_back (0); $         returnans; -     } -};

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Leetcode 310:minimum Height Trees