310 Minimum Height Trees

1. Question

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 containsnnodes which are labeled from0ton - 1. You will be given the numbernand 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 1:
Givenn = 4,edges = [[1, 0], [1, 2], [1, 3]]
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0
2
|
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1
4
/ \
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2 3
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return[1]
Example 2:
Givenn = 6,edges = [[0, 3], [1, 3], [2, 3], [4, 3], [5, 4]]
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0 1 2
2
\ | /
3
3
4
|
5
4
6
|
7
5
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return[3, 4]
Note:
(1) According to the definition of tree on Wikipedia: “a tree is an undirected graph in which any two vertices are connected byexactlyone 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.

2. Implementation

(1) BFS
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class Solution {
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public List<Integer> findMinHeightTrees(int n, int[][] edges) {
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List<Integer> res = new ArrayList<>();
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if (n == 1) {
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res.add(0);
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return res;
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}
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List<Set<Integer>> adjList = new ArrayList<>();
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for (int i = 0; i < n; i++) {
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adjList.add(new HashSet<>());
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}
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for (int[] edge : edges) {
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adjList.get(edge[0]).add(edge[1]);
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adjList.get(edge[1]).add(edge[0]);
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}
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List<Integer> leaves = new ArrayList<>();
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List<Integer> newLeaves = null;
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for (int i = 0; i < n; i++) {
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if (adjList.get(i).size() == 1) {
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leaves.add(i);
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}
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}
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while (n > 2) {
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n -= leaves.size();
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newLeaves = new ArrayList<>();
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for (int node : leaves) {
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for (int parent : adjList.get(node)) {
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adjList.get(parent).remove(node);
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if (adjList.get(parent).size() == 1) {
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newLeaves.add(parent);
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}
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}
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}
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leaves = newLeaves;
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}
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return leaves;
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}
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}
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3. Time & Space Complexity

BFS: 时间复杂度O(n), 空间复杂度O(n)