310 Minimum Height Trees¶
Problem:¶
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]
Hint:
How many MHTs can a graph have at most? Note:
(1) 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.”
(2) The height of a rooted tree is the number of edges on the longest downward path between the root and a leaf.
Solutions:¶
public class Solution {
public List<Integer> findMinHeightTrees(int n, int[][] edges) {
HashMap<Integer, LinkedList<Integer>> adj = new HashMap<Integer, LinkedList<Integer>>();
init(adj, n, edges);
List<Integer> leaves = new LinkedList<Integer>();
for (Integer i:adj.keySet()) {
if (adj.get(i).size() == 1) {
leaves.add(i);
}
}
if (leaves.size() == 0) {
leaves.add(0);
return leaves;
}
while (n > 2) {
n = n - leaves.size();
List<Integer> newLeaves = new LinkedList<Integer>();
for (Integer i:leaves) {
int nb = adj.get(i).get(0);
adj.get(nb).remove(i);
if (adj.get(nb).size() == 1) {
newLeaves.add(nb);
}
}
leaves = newLeaves;
}
return leaves;
}
private void init(HashMap<Integer, LinkedList<Integer>> adj, int n, int[][] edges) {
for (int i = 0; i < n; i ++) {
adj.put(i, new LinkedList<Integer>());
}
for (int i = 0; i < edges.length; i ++) {
adj.get(edges[i][0]).add(edges[i][1]);
adj.get(edges[i][1]).add(edges[i][0]);
}
}
}