310. Minimum Height Trees

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本文介绍了一种算法，用于找出特定图中的最小高度树，并通过实例展示了如何实现这一过程。该算法通过逐步移除外围节点直至剩余一或两个节点来确定根节点。

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]]

return [1]

Example 2:

Given n = 6, edges = [[0, 3], [1, 3], [2, 3], [4, 3], [5, 4]]

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;
        
    }
}