Problem:
Score : 300 points

Problem Statement

There are N cities numbered 1 through N, and M bidirectional roads numbered 1 through M.
Road i connects City A_i and City B_i.

Snuke can perform the following operation zero or more times:

Choose two distinct cities that are not directly connected by a road, and build a new road between the two cities.

After he finishes the operations, it must be possible to travel from any city to any other cities by following roads (possibly multiple times).

What is the minimum number of roads he must build to achieve the goal?

Constraints

2 \leq N \leq 100,000

1 \leq M \leq 100,000

1 \leq A_i < B_i \leq N

No two roads connect the same pair of cities.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
:
A_M B_M

Output

Print the answer.

Sample Input 1

3 1
1 2

Sample Output 1

1

Initially, there are three cities, and there is a road between City 1 and City 2.

Snuke can achieve the goal by building one new road, for example, between City 1 and City 3.
After that,

We can travel between 1 and 2 directly.

We can travel between 1 and 3 directly.

We can travel between 2 and 3 by following both roads (2 - 1 - 3).

Solution in Java (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;
import java.io.*;
 
public class Main {
    public static void main(String[] args) throws Exception {
        FastScanner sc = new FastScanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        StringBuilder sb = new StringBuilder();
        int N = sc.nextInt();
        int M = sc.nextInt();
        SCC scc = new SCC(N);
        for(int i = 0; i < M; i++){
            int f = sc.nextInt()-1;
            int t = sc.nextInt()-1;
            scc.addEdge(f,t);
            scc.addEdge(t,f);
        }
        int[][] map = scc.build();
        int sCnt = map.length;
        pw.println(sCnt-1);
        pw.flush();
    }
}

/**
 * @verified https://atcoder.jp/contests/practice2/tasks/practice2_g
 */
class SCC {
 
    static class Edge {
        int from, to;
        public Edge(int from, int to) {
            this.from = from; this.to = to;
        }
    }
 
    final int n;
    int m;
    final java.util.ArrayList<Edge> unorderedEdges;
    final int[] start;
    final int[] ids;
    boolean hasBuilt = false;
 
    public SCC(int n) {
        this.n = n;
        this.unorderedEdges = new java.util.ArrayList<>();
        this.start = new int[n + 1];
        this.ids = new int[n];
    }
 
    public void addEdge(int from, int to) {
        unorderedEdges.add(new Edge(from, to));
        start[from + 1]++;
        this.m++;
    }
 
    public int id(int i) {
        if (!hasBuilt) {
            throw new UnsupportedOperationException(
                "Graph hasn't been built."
            );
        }
        return ids[i];
    }
    
    public int[][] build() {
        for (int i = 1; i <= n; i++) {
            start[i] += start[i - 1];
        }
        Edge[] orderedEdges = new Edge[m];
        int[] count = new int[n + 1];
        System.arraycopy(start, 0, count, 0, n + 1);
        for (Edge e : unorderedEdges) {
            orderedEdges[count[e.from]++] = e;
        }
        int nowOrd = 0;
        int groupNum = 0;
        int k = 0;
        // parent
        int[] par = new int[n];
        int[] vis = new int[n];
        int[] low = new int[n];
        int[] ord = new int[n];
        java.util.Arrays.fill(ord, -1);
        // u = lower32(stack[i]) : visiting vertex
        // j = upper32(stack[i]) : jth child
        long[] stack = new long[n];
        // size of stack
        int ptr = 0;
        // non-recursional DFS
        for (int i = 0; i < n; i++) {
            if (ord[i] >= 0) continue;
            par[i] = -1;
            // vertex i, 0th child.
            stack[ptr++] = 0l << 32 | i;
            // stack is not empty
            while (ptr > 0) {
                // last element
                long p = stack[--ptr];
                // vertex
                int u = (int) (p & 0xffff_ffffl);
                // jth child
                int j = (int) (p >>> 32);
                if (j == 0) { // first visit
                    low[u] = ord[u] = nowOrd++;
                    vis[k++] = u;
                }
                if (start[u] + j < count[u]) { // there are more children
                    // jth child
                    int to = orderedEdges[start[u] + j].to;
                    // incr children counter
                    stack[ptr++] += 1l << 32;
                    if (ord[to] == -1) { // new vertex
                        stack[ptr++] = 0l << 32 | to;
                        par[to] = u;
                    } else { // backward edge
                        low[u] = Math.min(low[u], ord[to]);
                    }
                } else { // no more children (leaving)
                    while (j --> 0) {
                        int to = orderedEdges[start[u] + j].to;
                        // update lowlink
                        if (par[to] == u) low[u] = Math.min(low[u], low[to]);
                    }
                    if (low[u] == ord[u]) { // root of a component
                        while (true) { // gathering verticies
                            int v = vis[--k];
                            ord[v] = n;
                            ids[v] = groupNum;
                            if (v == u) break;
                        }
                        groupNum++; // incr the number of components
                    }
                }
            }
        }
        for (int i = 0; i < n; i++) {
            ids[i] = groupNum - 1 - ids[i];
        }
        
        int[] counts = new int[groupNum];
        for (int x : ids) counts[x]++;
        int[][] groups = new int[groupNum][];
        for (int i = 0; i < groupNum; i++) {
            groups[i] = new int[counts[i]];
        }
        for (int i = 0; i < n; i++) {
            int cmp = ids[i];
            groups[cmp][--counts[cmp]] = i;
        }
        hasBuilt = true;
        return groups;
    }
}

class FastScanner {
    private BufferedReader reader = null;
    private StringTokenizer tokenizer = null;
    public FastScanner(InputStream in) {
        reader = new BufferedReader(new InputStreamReader(in));
        tokenizer = null;
    }

    public String next() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public String nextLine() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken("\n");
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public double nextDouble() {
         return Double.parseDouble(next());
    }
    
    public String[] nextArray(int n) {
        String[] a = new String[n];
        for (int i = 0; i < n; i++)
            a[i] = next();
        return a;
    }

    public int[] nextIntArray(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = nextInt();
        return a;
    }

    public long[] nextLongArray(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = nextLong();
        return a;
    } 
}