結果

問題 No.1078 I love Matrix Construction
ユーザー EmKjpEmKjp
提出日時 2020-07-20 00:58:37
言語 C#(csc)
(csc 3.9.0)
結果
AC  
実行時間 1,144 ms / 2,000 ms
コード長 11,585 bytes
コンパイル時間 1,505 ms
コンパイル使用メモリ 117,544 KB
実行使用メモリ 163,732 KB
最終ジャッジ日時 2024-05-10 01:29:59
合計ジャッジ時間 13,904 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 33 ms
18,944 KB
testcase_01 AC 33 ms
18,944 KB
testcase_02 AC 147 ms
45,096 KB
testcase_03 AC 425 ms
79,720 KB
testcase_04 AC 555 ms
101,500 KB
testcase_05 AC 508 ms
88,556 KB
testcase_06 AC 137 ms
45,972 KB
testcase_07 AC 68 ms
29,056 KB
testcase_08 AC 473 ms
87,432 KB
testcase_09 AC 43 ms
21,888 KB
testcase_10 AC 1,144 ms
163,732 KB
testcase_11 AC 594 ms
101,532 KB
testcase_12 AC 962 ms
138,452 KB
testcase_13 AC 1,069 ms
154,620 KB
testcase_14 AC 727 ms
119,232 KB
testcase_15 AC 1,013 ms
145,660 KB
testcase_16 AC 66 ms
32,716 KB
testcase_17 AC 34 ms
19,072 KB
testcase_18 AC 112 ms
39,152 KB
testcase_19 AC 246 ms
57,724 KB
testcase_20 AC 247 ms
57,348 KB
testcase_21 AC 36 ms
20,156 KB
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コンパイルメッセージ
Microsoft (R) Visual C# Compiler version 3.9.0-6.21124.20 (db94f4cc)
Copyright (C) Microsoft Corporation. All rights reserved.

ソースコード

diff # 

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.Globalization;
using System.IO;
using System.Text;
using System.Linq;

using E = System.Linq.Enumerable;

internal partial class Solver {
    public void Run() {
        var n = ni();
        var s = ni(n);
        var t = ni(n);
        var u = ni(n);
        var twoSat = new TwoSat(n * n);
        for (int i = 0; i < n; i++) {
            int sv = s[i] - 1;
            int tv = t[i] - 1;
            for (int j = 0; j < n; j++) {
                var asj = sv * n + j;
                var ajt = j * n + tv;
                for (int p = 0; p < 2; p++) {
                    for (int q = 0; q < 2; q++) {
                        if (p + q * 2 == u[i]) {
                            twoSat.AddImplication(asj, p == 1, ajt, !(q == 1));
                            twoSat.AddImplication(ajt, q == 1, asj, !(p == 1));
                        }
                    }
                }
            }
        }
        if (twoSat.Solve(out var result)) {
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    if (j > 0) cout.Write(" ");
                    if (result[i * n + j]) {
                        cout.Write(1);
                    } else {
                        cout.Write(0);
                    }
                }
                cout.WriteLine();
            }
        } else {
            cout.WriteLine(-1);
        }
    }
}

public class TwoSat {
    private struct TwoSatVariable {
        public int Index;
        public bool TrueOfFalse;
    }

    private class TwoSatImplication {
        public TwoSatVariable Variable1;
        public TwoSatVariable Variable2;
    }

    private readonly int _n;
    private readonly List<TwoSatImplication> _implications = new List<TwoSatImplication>();

    public TwoSat(int n) { _n = n; }

    /// <summary>
    /// P OR Q
    /// </summary>
    public void AddOrClause(int variable1, bool trueOrFalse1, int variable2, bool trueOrFalse2) {
        // P or Q === (~P => Q) and (~Q =>P)
        AddImplication(variable1, !trueOrFalse1, variable2, trueOrFalse2);
        AddImplication(variable2, !trueOrFalse2, variable1, trueOrFalse1);
    }

    /// <summary>
    /// ~(P AND Q) (=== ~P OR ~Q)
    /// </summary>
    public void AddNandClause(int variable1, bool trueOrFalse1, int variable2, bool trueOrFalse2) {
        AddOrClause(variable1, !trueOrFalse1, variable2, !trueOrFalse2);
    }

    /// <summary>
    /// P (=== P OR P)
    /// </summary>
    public void AddIsTrueClause(int variable, bool trueOrFalse) {
        AddImplication(variable, !trueOrFalse, variable, trueOrFalse);
    }

    /// <summary>
    /// (P XOR Q) (=== (P OR Q) AND (~P OR ~Q))
    /// </summary>
    public void AddXorClause(int variable1, bool trueOrFalse1, int variable2, bool trueOrFalse2) {
        AddOrClause(variable1, trueOrFalse1, variable2, trueOrFalse2);
        AddOrClause(variable1, !trueOrFalse1, variable2, !trueOrFalse2);
    }

    /// <summary>
    /// P -> Q
    /// </summary>
    public void AddImplication(int variable1, bool trueOrFalse1, int variable2, bool trueOrFalse2) {
        _implications.Add(new TwoSatImplication {
            Variable1 = new TwoSatVariable { Index = variable1, TrueOfFalse = trueOrFalse1 },
            Variable2 = new TwoSatVariable { Index = variable2, TrueOfFalse = trueOrFalse2 },
        });
    }

    private int ToIndex(TwoSatVariable v) {
        return v.TrueOfFalse ? v.Index : v.Index + _n;
    }

    public bool Solve(out bool[] value) {
        value = null;
        var adj = Enumerable.Range(0, _n * 2).Select(_ => new List<int>()).ToArray();
        foreach (var c in _implications) {
            adj[ToIndex(c.Variable1)].Add(ToIndex(c.Variable2));
        }
        var scc = new StronglyConnectedComponent(adj);
        int[] groupIndex = scc.GetGroupArray();

        for (int i = 0; i < _n; i++) {
            if (groupIndex[i] == groupIndex[i + _n]) {
                return false;
            }
        }

        value = new bool[_n];
        for (int i = 0; i < _n; i++) {
            if (groupIndex[i] > groupIndex[i + _n]) {
                value[i] = true;
            }
        }

        return true;
    }
}

public class StronglyConnectedComponent {
    private readonly int _n;
    private readonly bool[] _isVisited;
    private readonly List<int>[] _adjacent;
    private readonly List<int>[] _inverseAdjacent;
    private readonly Stack<int> _stack = new Stack<int>();

    public StronglyConnectedComponent(List<int>[] adj) {
        _adjacent = adj;
        _n = adj.Length;
        _isVisited = new bool[_n];
        _inverseAdjacent = new List<int>[_n];
        for (var i = 0; i < _n; i++) {
            _inverseAdjacent[i] = new List<int>();
        }

        for (var i = 0; i < _n; i++) {
            foreach (var x in adj[i]) {
                _inverseAdjacent[x].Add(i);
            }
        }
    }

    private void Traverse(int k, List<int>[] adjacent, List<int> label) {
        if (_isVisited[k]) {
            return;
        }
        _stack.Push(k);
        while (_stack.Count > 0) {
            int top = _stack.Pop();
            if (top < 0) {
                label.Add(-top - 1);
                continue;
            }
            if (_isVisited[top]) {
                continue;
            }
            _isVisited[top] = true;
            _stack.Push(-(top + 1));
            foreach (int x in adjacent[top]) {
                if (!_isVisited[x]) {
                    _stack.Push(x);
                }
            }
        }
    }

    public List<List<int>> Run() {
        var label = new List<int>();
        for (var i = 0; i < _n; i++) {
            Traverse(i, _adjacent, label);
        }

        label.Reverse();
        Array.Clear(_isVisited, 0, _isVisited.Length);
        var components = new List<List<int>>();
        foreach (var x in label) {
            if (!_isVisited[x]) {
                var group = new List<int>();
                Traverse(x, _inverseAdjacent, group);
                components.Add(group);
            }
        }
        return components;
    }

    public int[] GetGroupArray() {
        var component = Run();
        var group = new int[_n];
        for (var i = 0; i < component.Count; i++) {
            foreach (var x in component[i]) {
                group[x] = i;
            }
        }
        return group; // group index is topological order
    }
}
// PREWRITEN CODE BEGINS FROM HERE

static public class StringExtensions {
    static public string JoinToString<T>(this IEnumerable<T> source, string separator = " ") {
        return string.Join(separator, source);
    }
}

internal partial class Solver : Scanner {
    public static void Main() {
#if LOCAL
        byte[] inputBuffer = new byte[1000000];
        var inputStream = Console.OpenStandardInput(inputBuffer.Length);
        using (var reader = new StreamReader(inputStream, Console.InputEncoding, false, inputBuffer.Length)) {
            Console.SetIn(reader);
            new Solver(Console.In, Console.Out).Run();
        }
#else
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        new Solver(Console.In, Console.Out).Run();
        Console.Out.Flush();
#endif
    }

#pragma warning disable IDE0052
    private readonly TextReader cin;
    private readonly TextWriter cout;
    private readonly TextWriter cerr;
#pragma warning restore IDE0052

    public Solver(TextReader reader, TextWriter writer)
        : base(reader) {
        cin = reader;
        cout = writer;
        cerr = Console.Error;
    }

    public Solver(string input, TextWriter writer)
        : this(new StringReader(input), writer) {
    }

#pragma warning disable IDE1006
#pragma warning disable IDE0051
    private int ni() { return NextInt(); }
    private int[] ni(int n) { return NextIntArray(n); }
    private long nl() { return NextLong(); }
    private long[] nl(int n) { return NextLongArray(n); }
    private double nd() { return NextDouble(); }
    private double[] nd(int n) { return NextDoubleArray(n); }
    private string ns() { return Next(); }
    private string[] ns(int n) { return NextArray(n); }
#pragma warning restore IDE1006
#pragma warning restore IDE0051
}

#if DEBUG
internal static class LinqPadExtension {
    public static string TextDump<T>(this T obj) {
        if (obj is IEnumerable) return (obj as IEnumerable).Cast<object>().JoinToString().Dump();
        else return obj.ToString().Dump();
    }
    public static T Dump<T>(this T obj) {
        return LINQPad.Extensions.Dump(obj);
    }
}
#endif

public class Scanner {
    private readonly TextReader Reader;
    private readonly CultureInfo ci = CultureInfo.InvariantCulture;

    private readonly char[] buffer = new char[2 * 1024];
    private int cursor = 0, length = 0;
    private string Token;
    private readonly StringBuilder sb = new StringBuilder(1024);

    public Scanner()
        : this(Console.In) {
    }

    public Scanner(TextReader reader) {
        Reader = reader;
    }

    public int NextInt() { return checked((int)NextLong()); }
    public long NextLong() {
        var s = Next();
        long r = 0;
        int i = 0;
        bool negative = false;
        if (s[i] == '-') {
            negative = true;
            i++;
        }
        for (; i < s.Length; i++) {
            r = r * 10 + (s[i] - '0');
#if DEBUG
            if (!char.IsDigit(s[i])) throw new FormatException();
#endif
        }
        return negative ? -r : r;
    }
    public double NextDouble() { return double.Parse(Next(), ci); }
    public string[] NextArray(int size) {
        string[] array = new string[size];
        for (int i = 0; i < size; i++) {
            array[i] = Next();
        }

        return array;
    }
    public int[] NextIntArray(int size) {
        int[] array = new int[size];
        for (int i = 0; i < size; i++) {
            array[i] = NextInt();
        }

        return array;
    }

    public long[] NextLongArray(int size) {
        long[] array = new long[size];
        for (int i = 0; i < size; i++) {
            array[i] = NextLong();
        }

        return array;
    }

    public double[] NextDoubleArray(int size) {
        double[] array = new double[size];
        for (int i = 0; i < size; i++) {
            array[i] = NextDouble();
        }

        return array;
    }

    public string Next() {
        if (Token == null) {
            if (!StockToken()) {
                throw new Exception();
            }
        }
        var token = Token;
        Token = null;
        return token;
    }

    public bool HasNext() {
        if (Token != null) {
            return true;
        }

        return StockToken();
    }

    private bool StockToken() {
        while (true) {
            sb.Clear();
            while (true) {
                if (cursor >= length) {
                    cursor = 0;
                    if ((length = Reader.Read(buffer, 0, buffer.Length)) <= 0) {
                        break;
                    }
                }
                var c = buffer[cursor++];
                if (33 <= c && c <= 126) {
                    sb.Append(c);
                } else {
                    if (sb.Length > 0) break;
                }
            }

            if (sb.Length > 0) {
                Token = sb.ToString();
                return true;
            }

            return false;
        }
    }
}
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