結果

問題 No.187 中華風 (Hard)
ユーザー EmKjpEmKjp
提出日時 2020-06-25 09:11:24
言語 C#(csc)
(csc 3.9.0)
結果
AC  
実行時間 224 ms / 3,000 ms
コード長 8,257 bytes
コンパイル時間 2,954 ms
コンパイル使用メモリ 119,348 KB
実行使用メモリ 26,680 KB
最終ジャッジ日時 2024-07-03 20:41:56
合計ジャッジ時間 5,352 ms
ジャッジサーバーID
（参考情報） 		judge5 / 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 24 ms
22,456 KB
testcase_01 AC 26 ms
26,392 KB
testcase_02 AC 176 ms
24,408 KB
testcase_03 AC 174 ms
22,580 KB
testcase_04 AC 220 ms
24,540 KB
testcase_05 AC 221 ms
24,412 KB
testcase_06 AC 222 ms
24,540 KB
testcase_07 AC 224 ms
24,432 KB
testcase_08 AC 162 ms
26,332 KB
testcase_09 AC 162 ms
26,336 KB
testcase_10 AC 165 ms
24,672 KB
testcase_11 AC 224 ms
24,176 KB
testcase_12 AC 222 ms
24,420 KB
testcase_13 AC 77 ms
24,428 KB
testcase_14 AC 77 ms
24,296 KB
testcase_15 AC 162 ms
22,200 KB
testcase_16 AC 165 ms
22,332 KB
testcase_17 AC 26 ms
24,552 KB
testcase_18 AC 25 ms
24,324 KB
testcase_19 AC 26 ms
24,492 KB
testcase_20 AC 174 ms
24,288 KB
testcase_21 AC 26 ms
24,388 KB
testcase_22 AC 221 ms
24,180 KB
testcase_23 AC 26 ms
24,684 KB
testcase_24 AC 26 ms
26,680 KB
権限があれば一括ダウンロードができます
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 static long Gcd(long s, long t) {
        var r = s % t;
        while (r > 0) {
            s = t;
            t = r;
            r = s % t;
        }
        return t;
    }
    private static long ExtendedGcd(long a, long b, out long x, out long y) {
        long s = a, sx = 1, sy = 0;
        long t = b, tx = 0, ty = 1;
        while (s % t != 0) {
            var d = s / t;
            var u = s - t * d;
            var ux = sx - tx * d;
            var uy = sy - ty * d;
            s = t; sx = tx; sy = ty;
            t = u; tx = ux; ty = uy;
        }
        x = tx; y = ty;
        return t;
    }

    private static long Inverse(long a, long mod) {
        long x = 0, y = 0;
        if (ExtendedGcd(a, mod, out x, out y) == 1) {
            return (x + mod) % mod;
        } else {
            throw new Exception("Invalid inverse " + a + " " + mod);
        }
    }

    /// <summary>
    /// m 同士がすべて互いに素になるように変換する
    /// </summary>
    public static bool PreGarner(long[] b, long[] m) {
        for (int i = 0; i < b.Length; i++) {
            for (int j = 0; j < i; j++) {
                var gcd = Gcd(m[i], m[j]);
                if (b[i] % gcd != b[j] % gcd) return false;
                var gi = m[i] / gcd;
                var lcm = gi * m[j];
                while (true) {
                    var g = Gcd(gi * gi, gcd);
                    if (g == 1) break;
                    gi *= g;
                    gcd /= g;
                };
                m[i] = gi;
                m[j] = lcm / gi;
            }
        }
        for (int i = 0; i < b.Length; i++) {
            b[i] %= m[i];
        }
        return true;
    }

    /// <summary>
    /// X = b[i] (mod m[i]) for all i
    /// を満たす最小の X % mod を返す
    /// m はすべて互いに素でなければならない
    /// </summary>
    public static long Garner(long[] b, long[] m, long mod) {
        // x = c1 + c2 m1 + c3 m1 m2 + c4 m1 m2 m3 ...
        var c = new long[m.Length];
        long sum = 0;
        for (int i = 0; i <= m.Length; i++) {
            long coef = 1; // m1*m2*m3* ...
            var modInternal = i == m.Length ? mod : m[i];
            sum = 0;
            for (int j = 0; j < i; j++) {
                sum += coef * c[j]; sum %= modInternal;
                coef *= m[j]; coef %= modInternal;
            }
            if (i == m.Length) break;
            c[i] = (b[i] - sum) * Inverse(coef, modInternal) % modInternal;
            if (c[i] < 0) c[i] += modInternal;
        }
        return sum;
    }

    public void Run() {
        var n = ni();
        var x = new long[n];
        var y = new long[n];
        var mod = 1000000007;
        for (int i = 0; i < n; i++) {
            x[i] = nl();
            y[i] = nl();
        }

        if (!PreGarner(x, y)) {
            cout.WriteLine(-1);
        } else if (x.All(a => a == 0)) {
            var ans = y.Aggregate((a, b) => a * b % mod);
            cout.WriteLine(ans);
        } else {
            var g = Garner(x, y, mod);
            cout.WriteLine(g);
        }
    }
}

// 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
}

internal static class LinqPadExtension {
    [Conditional("DEBUG")]
    public static void Dump<T>(this T obj) {
#if DEBUG
        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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