Problem:
C: 同値命題

問題

$N$ 個の命題があり, それぞれ $1, 2, \cdots,N$ という名前がついている.

また, 命題に関する情報が $M$ 個与えられる. $i$ 番目の情報は「$a_i$ $b_i$」という形式で与えられ, これは $a_i$ ならば $b_i$ であることを表す.（「ならば」は論理包含であり、推移律が成り立つ）

各命題 $i$ に対して $i$ と同値な命題を全て昇順に出力せよ.

ただし命題 $i$ と命題 $i$ は常に同値である.

命題 $X$ と命題 $Y$ が同値とは,「$X$ ならば $Y$」かつ「$Y$ ならば $X$」のことである.

制約

入力値は全て整数である.

$ 2 \leq N \leq 300$

$ 1 \leq M \leq N(N - 1)$

$ a_i \neq b_i $

$1 \leq a_i, b_i \leq N $

入力形式

入力は以下の形式で与えられる.

$N\ M$

$a_1\ b_1$

$a_2\ b_2$

$\vdots$

$a_M\ b_M$

出力

$i$ 行目には命題 $i$ と同値である命題を昇順に空白区切りですべて出力せよ. また, 各行の末尾に改行を出力せよ.

サンプル

サンプル入力 1

5 2
1 2
2 1

サンプル出力 1

1 2
1 2
3
4
5

サンプル入力 2

3 3
1 2
2 3
3 1

サンプル出力 2

1 2 3
1 2 3
1 2 3

サンプル入力 3

6 7
1 2
1 3
2 6
3 4
4 5
5 3
6 2

サンプル出力 3

1
2 6
3 4 5
3 4 5
3 4 5
2 6

Solution in C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using static System.Console;
using static System.Convert;
using static System.Math;
//using static System.Globalization.CultureInfo;
using System.Text;
class Program
{
    public static bool chmin<T>(ref T num, T val) where T : IComparable<T>
    { if (num.CompareTo(val) == 1) { num = val; return true; } return false; }
    public static bool chmax<T>(ref T num, T val) where T : IComparable<T>
    { if (num.CompareTo(val) == -1) { num = val; return true; } return false; }
    public static void swap<T>(ref T v1, ref T v2)
    { var t = v2; v2 = v1; v1 = t; }
    static void Main(string[] args)
    {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
        new Program().Solve();
        Console.Out.Flush();
    }
    void Solve()
    {
        int num, m;
        Input.Make(out num, out m);
        var g = new DirectedGraph(num);
        for(var i = 0; i < m; i++)
        {
            int a, b;
            Input.Make(out a, out b);
            g.AddEdge(a - 1, b - 1);
        }
        int ct;
        var ar = g.StronglyConnectedComponents(out ct);
        var res = Input.edge<int>(num);
        for (var i = 0; i < num; i++)
            for (var j = 0; j < num; j++)
                if (ar[i] == ar[j])
                    res[i].Add(j+1);

        WriteLine(string.Join("\n", res.Select(a=>string.Join(" ",a))));
    }
}

public class DirectedGraph
{
    public List<int>[] adj, rev;
    private List<int> topoList;
    private Stack<int> st;
    private int[] scc;
    private bool[] th;
    public int Count { get; }
    public DirectedGraph(int num)
    {
        this.Count = num;
        adj = Enumerable.Repeat(0, Count).Select(_ => new List<int>()).ToArray();
        rev = Enumerable.Repeat(0, Count).Select(_ => new List<int>()).ToArray();
    }

    public void AddEdge(int u, int v, bool logRev = true)
    {
        adj[u].Add(v);
        if (logRev)
            rev[v].Add(u);
    }

    public bool IsDAG()
    {
        topoList = topoList ?? TopologicalSort();
        return topoList.Count == Count;
    }

    public List<int> TopologicalSort()
    {
        topoList = new List<int>(Count);
        var ct = new int[Count];
        st = new Stack<int>();
        for (var i = 0; i < Count; i++)
            if (rev[i].Count == 0)
                st.Push(i);
        while (st.Any())
        {
            var index = st.Pop();
            topoList.Add(index);
            foreach (var ad in adj[index])
            {
                ct[ad]++;
                if (ct[ad] == rev[ad].Count) st.Push(ad);
            }
        }
        return topoList;
    }

    public int[] StronglyConnectedComponents(out int ct)
    {
        th = new bool[Count];
        st = new Stack<int>();
        for (var i = 0; i < Count; i++)
            if (!th[i])
                SCCdfs(i);
        scc = Enumerable.Repeat(-1, Count).ToArray();
        ct = 0;
        while (st.Any())
        {
            SCCrdfs(st.Pop(), ct++);
            while (st.Any() && scc[st.Peek()] != -1)
                st.Pop();
        }
        return scc;
    }
    private void SCCdfs(int index)
    {
        th[index] = true;
        foreach (var ad in adj[index])
            if (!th[ad])
                SCCdfs(ad);
        st.Push(index);
    }
    private void SCCrdfs(int index, int ct)
    {
        scc[index] = ct;
        foreach (var ad in rev[index])
            if (scc[ad] == -1)
                SCCrdfs(ad, ct);
    }
}


public class Input
{
    public static string read => ReadLine().Trim();
    public static int[] ar => read.Split(' ').Select(int.Parse).ToArray();
    public static int num => ToInt32(read);
    public static long[] arL => read.Split(' ').Select(long.Parse).ToArray();
    public static long numL => ToInt64(read);
    public static T[] create<T>(int n, Func<int, T> f)
        => Enumerable.Repeat(0, n).Select(f).ToArray();
    public static char[][] grid(int h)
        => create(h, _ => read.ToCharArray());
    public static int[] ar1D(int n)
        => create(n, _ => num);
    public static long[] arL1D(int n)
        => create(n, _ => numL);
    public static string[] strs(int n)
        => create(n, _ => read);
    public static int[][] ar2D(int n)
        => create(n, _ => ar);
    public static long[][] arL2D(int n)
        => create(n, _ => arL);
    public static List<T>[] edge<T>(int n)
        => create(n, _ => new List<T>());
    public static T GetValue<T>(string g)
    {
        var t = typeof(T);
        if (t == typeof(int))
            return (T)(object)int.Parse(g);
        if (t == typeof(long))
            return (T)(object)long.Parse(g);
        if (t == typeof(string))
            return (T)(object)g;
        if (t == typeof(char))
            return (T)(object)char.Parse(g);
        if (t == typeof(double))
            return (T)(object)double.Parse(g);
        if (t == typeof(bool))
            return (T)(object)bool.Parse(g);
        return default(T);
    }
    public static void Make<T1, T2>(out T1 v1, out T2 v2)
    {
        v1 = Next<T1>();
        v2 = Next<T2>();
    }
    public static void Make<T1, T2, T3>(out T1 v1, out T2 v2, out T3 v3)
    {
        Make(out v1, out v2);
        v3 = Next<T3>();
    }
    public static void Make<T1, T2, T3, T4>(out T1 v1, out T2 v2, out T3 v3, out T4 v4)
    {
        Make(out v1, out v2, out v3);
        v4 = Next<T4>();
    }
    public static void Make<T1, T2, T3, T4, T5>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5)
    {
        Make(out v1, out v2, out v3, out v4);
        v5 = Next<T5>();
    }
    public static void Make<T1, T2, T3, T4, T5, T6>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5, out T6 v6)
    {
        Make(out v1, out v2, out v3, out v4, out v5);
        v6 = Next<T6>();
    }
    private static Queue<string> sc;
    public static T Next<T>() { sc = sc ?? new Queue<string>(); if (sc.Count == 0) foreach (var item in read.Split(' ')) sc.Enqueue(item); return GetValue<T>(sc.Dequeue()); }
    public static void Next<T>(ref T val) => val = Next<T>();
    public const long Inf = (long)1e18;
    public const double eps = 1e-6;
    public const string Alfa = "abcdefghijklmnopqrstuvwxyz";
    public const int MOD = 1000000007;
}

public class Pair<T1, T2> : IComparable<Pair<T1, T2>>
{
    public T1 v1 { get; set; }
    public T2 v2 { get; set; }
    public Pair() { v1 = Input.Next<T1>(); v2 = Input.Next<T2>(); }
    public Pair(T1 v1, T2 v2)
    { this.v1 = v1; this.v2 = v2; }

    public int CompareTo(Pair<T1, T2> p)
    {
        var c = Comparer<T1>.Default.Compare(v1, p.v1);
        if (c == 0)
            c = Comparer<T2>.Default.Compare(v2, p.v2);
        return c;
    }
    public override string ToString()
        => $"{v1.ToString()} {v2.ToString()}";
    public override bool Equals(object obj)
        => this == (Pair<T1, T2>)obj;
    public override int GetHashCode()
        => v1.GetHashCode() ^ v2.GetHashCode();
    public static bool operator ==(Pair<T1, T2> p1, Pair<T1, T2> p2)
        => p1.CompareTo(p2) == 0;
    public static bool operator !=(Pair<T1, T2> p1, Pair<T1, T2> p2)
        => p1.CompareTo(p2) != 0;
    public static bool operator >(Pair<T1, T2> p1, Pair<T1, T2> p2)
        => p1.CompareTo(p2) == 1;
    public static bool operator >=(Pair<T1, T2> p1, Pair<T1, T2> p2)
        => p1.CompareTo(p2) != -1;
    public static bool operator <(Pair<T1, T2> p1, Pair<T1, T2> p2)
        => p1.CompareTo(p2) == -1;
    public static bool operator <=(Pair<T1, T2> p1, Pair<T1, T2> p2)
        => p1.CompareTo(p2) != 1;
}

public class Pair<T1, T2, T3> : Pair<T1, T2>, IComparable<Pair<T1, T2, T3>>
{
    public T3 v3 { get; set; }
    public Pair() : base() { v3 = Input.Next<T3>(); }
    public Pair(T1 v1, T2 v2, T3 v3) : base(v1, v2)
    { this.v3 = v3; }

    public int CompareTo(Pair<T1, T2, T3> p)
    {
        var c = base.CompareTo(p);
        if (c == 0)
            c = Comparer<T3>.Default.Compare(v3, p.v3);
        return c;
    }
    public override string ToString()
        => $"{base.ToString()} {v3.ToString()}";
}