310. Minimum Height Trees
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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.
Solution:
Keep removing the most outside node util there is only one node left or two nodes left, what left is the answer.
Code:
public class Solution { public List<Integer> findMinHeightTrees(int n, int[][] edges) { int[] indegree = new int[n]; HashMap<Integer,HashSet<Integer>> hm = new HashMap(); for(int[] e : edges){ indegree[e[0]] += 1; indegree[e[1]] += 1; hm.computeIfAbsent(e[0], k -> new HashSet<Integer>()).add(e[1]); hm.computeIfAbsent(e[1], k -> new HashSet<Integer>()).add(e[0]); } ArrayList<Integer> next = new ArrayList<Integer>(); int total = n; for(int i = 0; i < n; i++){ if(indegree[i] <= 1){ // use <= here because of the special case [1] next.add(i); } } while(total > 2){ ArrayList<Integer> temp = new ArrayList<>(); for(int i : next){ total -= 1; for(int j : hm.get(i)){ indegree[j] -= 1; if(indegree[j] == 1){ temp.add(j); } } } next = temp; } return next; }}
- 310. Minimum Height Trees
- 310. Minimum Height Trees
- 310. Minimum Height Trees
- 310. Minimum Height Trees
- 310. Minimum Height Trees
- 310. Minimum Height Trees
- 310. Minimum Height Trees
- 310. Minimum Height Trees
- 310. Minimum Height Trees
- 310. Minimum Height Trees
- 310. Minimum Height Trees
- 310. Minimum Height Trees
- 310. Minimum Height Trees
- 310. Minimum Height Trees
- 310. Minimum Height Trees
- 310. Minimum Height Trees
- 310. Minimum Height Trees
- 310. Minimum Height Trees
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