programming-examples/java/Data_Structures/TreeCenters.java

import java.util.*;
import java.util.stream.Stream;

public class TreeCenters {

	// returns 1 or 2 tree centers
	// http://en.wikipedia.org/wiki/Graph_center
	public static List<Integer> findTreeCenters(List<Integer>[] tree) {
		int n = tree.length;
		List<Integer> leaves = new ArrayList<>();
		int[] degree = new int[n];
		for (int i = 0; i < n; i++) {
			degree[i] = tree[i].size();
			if (degree[i] <= 1) {
				leaves.add(i);
			}
		}
		int removedLeaves = leaves.size();
		while (removedLeaves < n) {
			List<Integer> nleaves = new ArrayList<>();
			for (int u : leaves) {
				for (int v : tree[u]) {
					if (--degree[v] == 1) {
						nleaves.add(v);
					}
				}
			}
			leaves = nleaves;
			removedLeaves += leaves.size();
		}
		return leaves;
	}

	// returns vertex that has all its subtrees sizes <= n/2
	public static int findTreeCentroid(List<Integer>[] tree, int u, int p) {
		int n = tree.length;
		int cnt = 1;
		boolean goodCenter = true;
		for (int v : tree[u]) {
			if (v == p) continue;
			int res = findTreeCentroid(tree, v, u);
			if (res >= 0)
				return res;
			int size = -res;
			goodCenter &= size <= n / 2;
			cnt += size;
		}
		goodCenter &= n - cnt <= n / 2;
		return goodCenter ? u : -cnt;
	}

	public static int diameter(List<Integer>[] tree) {
		int furthestVertex = (int) dfs(tree, 0, -1, 0);
		return (int) (dfs(tree, furthestVertex, -1, 0) >>> 32);
	}

	static long dfs(List<Integer>[] tree, int u, int p, int depth) {
		long res = ((long) depth << 32) + u;
		for (int v : tree[u])
			if (v != p)
				res = Math.max(res, dfs(tree, v, u, depth + 1));
		return res;
	}

	// Usage example
	public static void main(String[] args) {
		int n = 4;
		List<Integer>[] tree = Stream.generate(ArrayList::new).limit(n).toArray(List[]::new);
		tree[3].add(0);
		tree[0].add(3);
		tree[3].add(1);
		tree[1].add(3);
		tree[3].add(2);
		tree[2].add(3);
		System.out.println(3 == findTreeCentroid(tree, 0, -1));
		System.out.println(3 == findTreeCenters(tree).get(0));
		System.out.println(2 == diameter(tree));
	}
}