80 lines
2.0 KiB
Java
80 lines
2.0 KiB
Java
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import java.util.*;
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import java.util.stream.Stream;
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public class TreeCenters {
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// returns 1 or 2 tree centers
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// http://en.wikipedia.org/wiki/Graph_center
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public static List<Integer> findTreeCenters(List<Integer>[] tree) {
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int n = tree.length;
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List<Integer> leaves = new ArrayList<>();
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int[] degree = new int[n];
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for (int i = 0; i < n; i++) {
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degree[i] = tree[i].size();
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if (degree[i] <= 1) {
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leaves.add(i);
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}
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}
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int removedLeaves = leaves.size();
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while (removedLeaves < n) {
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List<Integer> nleaves = new ArrayList<>();
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for (int u : leaves) {
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for (int v : tree[u]) {
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if (--degree[v] == 1) {
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nleaves.add(v);
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}
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}
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}
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leaves = nleaves;
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removedLeaves += leaves.size();
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}
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return leaves;
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}
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// returns vertex that has all its subtrees sizes <= n/2
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public static int findTreeCentroid(List<Integer>[] tree, int u, int p) {
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int n = tree.length;
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int cnt = 1;
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boolean goodCenter = true;
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for (int v : tree[u]) {
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if (v == p) continue;
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int res = findTreeCentroid(tree, v, u);
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if (res >= 0)
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return res;
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int size = -res;
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goodCenter &= size <= n / 2;
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cnt += size;
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}
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goodCenter &= n - cnt <= n / 2;
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return goodCenter ? u : -cnt;
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}
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public static int diameter(List<Integer>[] tree) {
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int furthestVertex = (int) dfs(tree, 0, -1, 0);
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return (int) (dfs(tree, furthestVertex, -1, 0) >>> 32);
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}
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static long dfs(List<Integer>[] tree, int u, int p, int depth) {
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long res = ((long) depth << 32) + u;
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for (int v : tree[u])
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if (v != p)
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res = Math.max(res, dfs(tree, v, u, depth + 1));
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return res;
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}
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// Usage example
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public static void main(String[] args) {
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int n = 4;
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List<Integer>[] tree = Stream.generate(ArrayList::new).limit(n).toArray(List[]::new);
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tree[3].add(0);
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tree[0].add(3);
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tree[3].add(1);
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tree[1].add(3);
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tree[3].add(2);
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tree[2].add(3);
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System.out.println(3 == findTreeCentroid(tree, 0, -1));
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System.out.println(3 == findTreeCenters(tree).get(0));
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System.out.println(2 == diameter(tree));
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}
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}
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