[LeetCode］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 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]

BFS 从度数为1的叶节点开始BFS扩展，记录每层的点数，最后找到的点（2个或者1个和n的奇偶有关）就是最小树的高度点了。

自己定义了节点数据，注意图的构建。

class Solution {
struct  vertice{
int index;
unordered_set<int> adj;
};
public:
vector<int> findMinHeightTrees(int n, vector<pair<int, int>>& edges) {
vector<int> ret;
if(edges.size()==0){
ret.push_back(0);
return ret; //1个节点的特殊情况
}
vector<vertice> Vertices;
for(int i=0; i<n; ++i){
vertice a;
a.index = i;
Vertices.push_back(a);
}

for(auto i=edges.begin(); i!=edges.end(); ++i){
Vertices[i->first].adj.insert(i->second);
Vertices[i->second].adj.insert(i->first); //记录图的数据
}

vector<vertice> leavel;
for(int i=0; i<n; ++i){
if(Vertices[i].adj.size()==1)
leavel.push_back(Vertices[i]);//第一层节点
}

while(n>2){
n -= leavel.size();
vector<vertice> temp;
for(int i=0; i<leavel.size(); ++i){
int root = *(leavel[i].adj.begin()); //找到根节点
Vertices[root].adj.erase(leavel[i].index);//去除子节点
if(Vertices[root].adj.size()==1) //如果度数为1，记录新的一层
temp.push_back(Vertices[root]);
}
leavel = temp;
}

for(int i=0; i<leavel.size(); ++i ){
ret.push_back(leavel[i].index); //结果输出
}
return ret;
}
};