Minimum Height Trees(Medium)
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]
public List<Integer> findMinHeightTrees(int n, int[][] edges) {
List<Integer> result = new ArrayList<>();
if (n <= 0) {
return result;
}
// Corner case: there is a single node and no edge at all
if (n == 1 && edges.length == 0) {
result.add(0);
return result;
}
// Step 1: construct the graph
List<Set<Integer>> adjList = new ArrayList<>();
for (int i = 0; i < n; i++) {
adjList.add(new HashSet<>());
}
for (int[] edge : edges) {
int from = edge[0];
int to = edge[1];
adjList.get(from).add(to);
adjList.get(to).add(from);
}
// Remove leaf nodes
List<Integer> leaves = new ArrayList<>();
for (int i = 0; i < n; i++) {
if (adjList.get(i).size() == 1) {
leaves.add(i);
}
}
while (n > 2) {
// identify and remove all leaf nodes
n -= leaves.size();
List<Integer> newLeaves = new ArrayList<>();
for (int leaf : leaves) {
int neighbor = adjList.get(leaf).iterator().next();
adjList.get(neighbor).remove(leaf);
if (adjList.get(neighbor).size() == 1) {
newLeaves.add(neighbor);
}
}
leaves = newLeaves;
}
return leaves;
}