Problem:
Score : 400 points

Problem Statement

There are N persons called Person 1 through Person N.

You are given M facts that "Person A_i and Person B_i are friends." The same fact may be given multiple times.

If X and Y are friends, and Y and Z are friends, then X and Z are also friends. There is no friendship that cannot be derived from the M given facts.

Takahashi the evil wants to divide the N persons into some number of groups so that every person has no friend in his/her group.

At least how many groups does he need to make?

Constraints

2 \leq N \leq 2\times 10^5

0 \leq M \leq 2\times 10^5

1\leq A_i,B_i\leq N

A_i \neq B_i

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
\vdots
A_M B_M

Output

Print the answer.

Sample Input 1

5 3
1 2
3 4
5 1

Sample Output 1

3

Dividing them into three groups such as \{1,3\}, \{2,4\}, and \{5\} achieves the goal.

Sample Input 2

4 10
1 2
2 1
1 2
2 1
1 2
1 3
1 4
2 3
2 4
3 4

Sample Output 2

4

Sample Input 3

10 4
3 1
4 1
5 9
2 6

Sample Output 3

3

Solution in Java (OpenJDK 11.0.6) (judge verdict: Accepted)


/**
 * Date: 25 Aug, 2020
 * Link: 
 * 
 * @author: Prasad Chaudhari
 * @linkedIn: https://www.linkedin.com/in/prasad-chaudhari-841655a6/
 * @git: https://github.com/Prasad-Chaudhari
 */
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileOutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.LinkedList;

class Main {

    public static void main(String[] args) throws IOException {
        FastIO in = new FastIO(args);
        int n = in.ni();
        int m = in.ni();
        UnionFind uf = new UnionFind(n);
        for (int i = 0; i < m; i++) {
            uf.union(in.ni(), in.ni());
        }
        int max = 0;
        for (int i = 1; i <= n; i++) {
            max = Math.max(max, uf.members.get(i).size());
        }
        System.out.println(max);
        in.bw.flush();
    }

    static class UnionFind {

        private int noOfComponents, n;
        private int component[], size[];
        private ArrayList<LinkedList<Integer>> members;

        public UnionFind(int p) {
            n = p;
            noOfComponents = n;
            component = new int[n + 1];
            size = new int[n + 1];
            members = new ArrayList<>();
            for (int i = 0; i <= n; i++) {
                component[i] = i;
                size[i] = 1;
                members.add(new LinkedList<Integer>());
                members.get(i).add(i);
            }
        }

        public int find(int k) {
            return component[k];
        }

        public void union(int a, int b) {
            a = find(a);
            b = find(b);
            if (a == b) {
                return;
            }
            if (size[a] > size[b]) {
                a = a ^ b;
                b = a ^ b;
                a = a ^ b;
            }
            LinkedList<Integer> membersofa = members.get(a);
            LinkedList<Integer> membersofb = members.get(b);
            for (int i = 0; i < size[a]; i++) {
                int member = membersofa.removeFirst();
                component[member] = component[b];
                membersofb.add(member);
            }
            size[b] = size[b] + size[a];
            noOfComponents--;
        }

        public int noOfComponents() {
            return noOfComponents;
        }
    }

    static class Data implements Comparable<Data> {

        int a, b;

        public Data(int a, int b) {
            this.a = a;
            this.b = b;
        }

        @Override
        public int compareTo(Data o) {
            if (a == o.a) {
                return Integer.compare(b, o.b);
            }
            return Integer.compare(a, o.a);
        }

        public static void sort(int a[]) {
            Data d[] = new Data[a.length];
            for (int i = 0; i < a.length; i++) {
                d[i] = new Data(a[i], 0);
            }
            Arrays.sort(d);
            for (int i = 0; i < a.length; i++) {
                a[i] = d[i].a;
            }
        }
    }

    static class FastIO {

        private final BufferedReader br;
        private final BufferedWriter bw;
        private String s[];
        private int index;

        public FastIO(String[] args) throws IOException {
            if (args.length > 1) {
                br = new BufferedReader(new InputStreamReader(new FileInputStream(new File(args[0]))));
                bw = new BufferedWriter(new OutputStreamWriter(new FileOutputStream(new File(args[1]))));
            } else {
                br = new BufferedReader(new InputStreamReader(System.in));
                bw = new BufferedWriter(new OutputStreamWriter(System.out, "UTF-8"));
            }
            s = br.readLine().split(" ");
            index = 0;
        }

        public int ni() throws IOException {
            return Integer.parseInt(nextToken());
        }

        public double nd() throws IOException {
            return Double.parseDouble(nextToken());
        }

        public long nl() throws IOException {
            return Long.parseLong(nextToken());
        }

        public String next() throws IOException {
            return nextToken();
        }

        public String nli() throws IOException {
            try {
                return br.readLine();
            } catch (IOException ex) {

            }
            return null;
        }

        public int[] gia(int n) throws IOException {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }

        public int[] gia(int n, int start, int end) throws IOException {
            validate(n, start, end);
            int a[] = new int[n];
            for (int i = start; i < end; i++) {
                a[i] = ni();
            }
            return a;
        }

        public double[] gda(int n) throws IOException {
            double a[] = new double[n];
            for (int i = 0; i < n; i++) {
                a[i] = nd();
            }
            return a;
        }

        public double[] gda(int n, int start, int end) throws IOException {
            validate(n, start, end);
            double a[] = new double[n];
            for (int i = start; i < end; i++) {
                a[i] = nd();
            }
            return a;
        }

        public long[] gla(int n) throws IOException {
            long a[] = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nl();
            }
            return a;
        }

        public long[] gla(int n, int start, int end) throws IOException {
            validate(n, start, end);
            long a[] = new long[n];
            for (int i = start; i < end; i++) {
                a[i] = nl();
            }
            return a;
        }

        public int[][][] gwtree(int n) throws IOException {
            int m = n - 1;
            int adja[][] = new int[n + 1][];
            int weight[][] = new int[n + 1][];
            int from[] = new int[m];
            int to[] = new int[m];
            int count[] = new int[n + 1];
            int cost[] = new int[n + 1];
            for (int i = 0; i < m; i++) {
                from[i] = i + 1;
                to[i] = ni();
                cost[i] = ni();
                count[from[i]]++;
                count[to[i]]++;
            }
            for (int i = 0; i <= n; i++) {
                adja[i] = new int[count[i]];
                weight[i] = new int[count[i]];
            }
            for (int i = 0; i < m; i++) {
                adja[from[i]][count[from[i]] - 1] = to[i];
                adja[to[i]][count[to[i]] - 1] = from[i];
                weight[from[i]][count[from[i]] - 1] = cost[i];
                weight[to[i]][count[to[i]] - 1] = cost[i];
                count[from[i]]--;
                count[to[i]]--;
            }
            return new int[][][] { adja, weight };
        }

        public int[][][] gwg(int n, int m) throws IOException {
            int adja[][] = new int[n + 1][];
            int weight[][] = new int[n + 1][];
            int from[] = new int[m];
            int to[] = new int[m];
            int count[] = new int[n + 1];
            int cost[] = new int[n + 1];
            for (int i = 0; i < m; i++) {
                from[i] = ni();
                to[i] = ni();
                cost[i] = ni();
                count[from[i]]++;
                count[to[i]]++;
            }
            for (int i = 0; i <= n; i++) {
                adja[i] = new int[count[i]];
                weight[i] = new int[count[i]];
            }
            for (int i = 0; i < m; i++) {
                adja[from[i]][count[from[i]] - 1] = to[i];
                adja[to[i]][count[to[i]] - 1] = from[i];
                weight[from[i]][count[from[i]] - 1] = cost[i];
                weight[to[i]][count[to[i]] - 1] = cost[i];
                count[from[i]]--;
                count[to[i]]--;
            }
            return new int[][][] { adja, weight };
        }

        public int[][] gtree(int n) throws IOException {
            int adja[][] = new int[n + 1][];
            int from[] = new int[n - 1];
            int to[] = new int[n - 1];
            int count[] = new int[n + 1];
            for (int i = 0; i < n - 1; i++) {
                from[i] = i + 1;
                to[i] = ni();
                count[from[i]]++;
                count[to[i]]++;
            }
            for (int i = 0; i <= n; i++) {
                adja[i] = new int[count[i]];
            }
            for (int i = 0; i < n - 1; i++) {
                adja[from[i]][--count[from[i]]] = to[i];
                adja[to[i]][--count[to[i]]] = from[i];
            }
            return adja;
        }

        public int[][] gg(int n, int m) throws IOException {
            int adja[][] = new int[n + 1][];
            int from[] = new int[m];
            int to[] = new int[m];
            int count[] = new int[n + 1];
            for (int i = 0; i < m; i++) {
                from[i] = ni();
                to[i] = ni();
                count[from[i]]++;
                count[to[i]]++;
            }
            for (int i = 0; i <= n; i++) {
                adja[i] = new int[count[i]];
            }
            for (int i = 0; i < m; i++) {
                adja[from[i]][--count[from[i]]] = to[i];
                adja[to[i]][--count[to[i]]] = from[i];
            }
            return adja;
        }

        public void print(String s) throws IOException {
            bw.write(s);
        }

        public void println(String s) throws IOException {
            bw.write(s);
            bw.newLine();
        }

        public void print(int s) throws IOException {
            bw.write(s + "");
        }

        public void println(int s) throws IOException {
            bw.write(s + "");
            bw.newLine();
        }

        public void print(long s) throws IOException {
            bw.write(s + "");
        }

        public void println(long s) throws IOException {
            bw.write(s + "");
            bw.newLine();
        }

        public void print(double s) throws IOException {
            bw.write(s + "");
        }

        public void println(double s) throws IOException {
            bw.write(s + "");
            bw.newLine();
        }

        private String nextToken() throws IndexOutOfBoundsException, IOException {
            if (index == s.length) {
                s = br.readLine().split(" ");
                index = 0;
            }
            return s[index++];
        }

        private void validate(int n, int start, int end) {
            if (start < 0 || end >= n) {
                throw new IllegalArgumentException();
            }
        }
    }
}