Minimum Height Trees
For an 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 containsn
nodes which are labeled from0
ton - 1
. You will be given the numbern
and a list of undirectededges
(each edge is a pair of labels).
You can assume that no duplicate edges will appear inedges
. Since all edges are undirected,[0, 1]
is the same as[1, 0]
and thus will not appear together inedges
.
Example
Example 1 :
Input:
n = 4, edges = [[1, 0], [1, 2], [1, 3]]
0
|
1
/ \
2 3
Output:
[1]
Example 2 :
Input:
n = 6, edges = [[0, 3], [1, 3], [2, 3], [4, 3], [5, 4]]
0 1 2
\ | /
3
|
4
|
5
Output:
[3, 4]
Note
使用类似拓扑排序的思路进行解题。
关键是要注意到这是一个无向图的问题,我们需要从外层向内部进行遍历,基于入度进行排序,一层一层把叶子删去,更新下一层的入度,进队列,最后剩下的节点就是答案
入度这里指的是联通性,最低是1,我们从1开始“删除”
Code
class Solution {
public List<Integer> findMinHeightTrees(int n, int[][] edges) {
List<Integer> res = new ArrayList<>();
if (n == 1) {
res.add(0);
return res;
}
Map<Integer, Set<Integer>> graph = new HashMap<>();
for (int i = 0; i < n; i++) {
graph.put(i, new HashSet<Integer>());
}
int[] indegree = new int[n];
for (int i = 0; i < edges.length; i++) {
int u = edges[i][0];
int v = edges[i][1];
graph.get(u).add(v);
graph.get(v).add(u);
indegree[u]++;
indegree[v]++;
}
Queue<Integer> q = new LinkedList<>();
for (int i = 0; i < n; i++) {
if (indegree[i] == 1) {
q.offer(i);
}
}
while (!q.isEmpty()) {
int size = q.size();
res = new ArrayList<Integer>();
for (int i = 0; i < size; i++) {
Integer leaf = q.poll();
res.add(leaf);
indegree[leaf]--;
for (Integer parent : graph.get(leaf)) {
indegree[parent]--;
if (indegree[parent] == 1) {
q.offer(parent);
}
}
}
}
return res;
}
}
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