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 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 :
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:
According to the definition of tree on Wikipedia: “a tree is an undirected graph in which any two vertices are connected by exactly one path. In other words, any connected graph without simple cycles is a tree.”
The height of a rooted tree is the number of edges on the longest downward path between the root and a leaf.
class Solution {
// Basically, the idea is to eat up all the leaves at the same time,
// until one/two leaves are left.
public List<Integer> findMinHeightTrees(int n, int[][] edges) {
if (n == 1)
return Collections.singletonList(0);
// Adjacency List GRAPH
List<Set<Integer>> graph = new ArrayList<>(n);
for (int i = 0; i < n; ++i)
graph.add(new HashSet<>());
for (int[] edge : edges) {
graph.get(edge[0]).add(edge[1]);
graph.get(edge[1]).add(edge[0]);
}
// Creating a set of leaves(nodes with one 1 connection)
List<Integer> leaves = new ArrayList<>();
for (int i = 0; i < n; ++i)
if (graph.get(i).size() == 1)
leaves.add(i);
// While Number of remaining nodes > 2
while (n > 2) {
n -= leaves.size();
// Creating list for new leaves that will be created
// when we remove the old lists
List<Integer> newLeaves = new ArrayList<>();
for (int i : leaves) {
// Getting the only connection present in the set
int j = graph.get(i).iterator().next();
// Removing this connection from the inner node
graph.get(j).remove(i);
// Now if the inner node becomes a leaf
// then we will add it to the new leaves list
if (graph.get(j).size() == 1)
newLeaves.add(j);
}
leaves = newLeaves;
}
return leaves;
}
}
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