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 are 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 are labeled from 0
to n - 1
. You will be given the number n
and a list of undirected edges
(each edge is a pair of labels).
You can assume that no duplicate edges will appear in edges
. Since all edges are undirected, [0, 1]
is the same as [1, 0]
and thus will not 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 tree on Wikipedia: “a tree is an undirected graph in which any two vertices are connected by exactlyone path. In 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.
关键是一层一层把叶子节点去掉直到剩下1/2个节点。
class Solution {
public:
struct Node
{
unordered_set<int> neighbor;
bool isLeaf()const{return neighbor.size()==1;}
};
vector<int> findMinHeightTrees(int n, vector<pair<int, int>>& edges) {
vector<int> buffer1;
vector<int> buffer2;
vector<int>* pB1 = &buffer1;
vector<int>* pB2 = &buffer2;
if(n==1)
{
buffer1.push_back(0);
return buffer1;
}
if(n==2)
{
buffer1.push_back(0);
buffer1.push_back(1);
return buffer1;
}
// build the graph
vector<Node> nodes(n);
for(auto p:edges)
{
nodes[p.first].neighbor.insert(p.second);
nodes[p.second].neighbor.insert(p.first);
}
// find all leaves
for(int i=0; i<n; ++i)
{
if(nodes[i].isLeaf()) pB1->push_back(i);
}
// remove leaves layer-by-layer
while(1)
{
for(int i : *pB1)
{
for(auto n: nodes[i].neighbor)
{
nodes[n].neighbor.erase(i);
if(nodes[n].isLeaf()) pB2->push_back(n);
}
}
if(pB2->empty())
{
return *pB1;
}
pB1->clear();
swap(pB1, pB2);
}
}
};