#414411 (C#(csc)) No.947 ABC包囲網

• 問題: No.947 ABC包囲網
• ユーザー: EmKjp
• 提出日時: 2020-01-05 10:57:02
• 言語: C#(csc) (csc 3.9.0)
• 結果: AC
• 実行時間: 39 ms / 2,000 ms
• コード長: 7,492 bytes
• コンパイル時間: 1,082 ms
• コンパイル使用メモリ: 111,232 KB
• 実行使用メモリ: 19,144 KB
• 最終ジャッジ日時: 2024-11-22 21:56:46
• 合計ジャッジ時間: 4,458 ms
• ジャッジサーバーID （参考情報）: judge1 / judge4

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	29 ms; 18,176 KB
testcase_01	AC	28 ms; 18,048 KB
testcase_02	AC	29 ms; 18,176 KB
testcase_03	AC	29 ms; 18,048 KB
testcase_04	AC	29 ms; 18,048 KB
testcase_05	AC	29 ms; 18,176 KB
testcase_06	AC	28 ms; 18,176 KB
testcase_07	AC	29 ms; 18,176 KB
testcase_08	AC	29 ms; 18,048 KB
testcase_09	AC	29 ms; 18,048 KB
testcase_10	AC	29 ms; 18,304 KB
testcase_11	AC	28 ms; 17,920 KB
testcase_12	AC	29 ms; 18,176 KB
testcase_13	AC	29 ms; 18,176 KB
testcase_14	AC	29 ms; 18,048 KB
testcase_15	AC	31 ms; 18,432 KB
testcase_16	AC	30 ms; 18,048 KB
testcase_17	AC	30 ms; 17,920 KB
testcase_18	AC	31 ms; 18,432 KB
testcase_19	AC	30 ms; 18,176 KB
testcase_20	AC	30 ms; 18,304 KB
testcase_21	AC	32 ms; 18,176 KB
testcase_22	AC	31 ms; 18,176 KB
testcase_23	AC	30 ms; 18,048 KB
testcase_24	AC	30 ms; 18,176 KB
testcase_25	AC	30 ms; 18,048 KB
testcase_26	AC	29 ms; 18,304 KB
testcase_27	AC	30 ms; 17,920 KB
testcase_28	AC	38 ms; 18,816 KB
testcase_29	AC	37 ms; 19,072 KB
testcase_30	AC	37 ms; 19,140 KB
testcase_31	AC	38 ms; 18,816 KB
testcase_32	AC	38 ms; 19,144 KB
testcase_33	AC	38 ms; 19,144 KB
testcase_34	AC	38 ms; 19,072 KB
testcase_35	AC	38 ms; 19,072 KB
testcase_36	AC	39 ms; 18,944 KB
testcase_37	AC	38 ms; 19,072 KB
testcase_38	AC	38 ms; 19,072 KB
testcase_39	AC	38 ms; 18,944 KB
testcase_40	AC	36 ms; 18,816 KB
testcase_41	AC	36 ms; 18,816 KB
testcase_42	AC	36 ms; 18,688 KB
testcase_43	AC	36 ms; 18,816 KB
testcase_44	AC	38 ms; 18,816 KB
testcase_45	AC	36 ms; 19,072 KB
testcase_46	AC	36 ms; 18,816 KB
testcase_47	AC	36 ms; 18,816 KB
testcase_48	AC	36 ms; 18,816 KB
testcase_49	AC	37 ms; 19,140 KB
testcase_50	AC	35 ms; 18,944 KB
testcase_51	AC	30 ms; 18,176 KB
testcase_52	AC	30 ms; 18,048 KB
testcase_53	AC	30 ms; 18,176 KB
testcase_54	AC	29 ms; 18,048 KB
testcase_55	AC	30 ms; 18,176 KB
testcase_56	AC	29 ms; 17,920 KB
testcase_57	AC	32 ms; 18,176 KB
testcase_58	AC	30 ms; 18,176 KB
testcase_59	AC	31 ms; 18,176 KB

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

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 x = new int[n];
        var y = new int[n];
        for (int i = 0; i < n; i++) {
            x[i] = ni();
            y[i] = ni();
        }

        long ans = CountTriangleNumContainsOrigin(n, x, y);
        cout.WriteLine(ans);
    }

    public struct Angle : IComparable<Angle> {
        public long X { get; private set; }
        public long Y { get; private set; }

        private readonly long _a;
        private readonly long _b;
        public int Quadrant { get; private set; }

        public static long Gcd(long s, long t) {
            return t != 0 ? Gcd(t, s % t) : s;
        }

        public Angle(long x, long y) {
            if (x == 0 && y == 0) throw new ArgumentException();
            var g = Gcd(Math.Abs(x), Math.Abs(y));
            _a = X = x / g;
            _b = Y = y / g;
            Quadrant = 0;
            while (!(_a > 0 && _b >= 0)) {
                var t = _a; _a = _b; _b = -t;
                Quadrant++;
            }
        }

        public int CompareTo(Angle other) {
            var cmp = Quadrant.CompareTo(other.Quadrant);
            if (cmp != 0) return cmp;
            return (_b * other._a).CompareTo(other._b * _a);
        }
    }

    private long CountTriangleNumContainsOrigin(int n, int[] x, int[] y, bool strict = true) {
        var angles = new List<Angle>();
        for (int j = 0; j < n; j++) {
            var dx = x[j];
            var dy = y[j];
            angles.Add(new Angle(dx, dy));
        }
        angles.Sort();
        angles.AddRange(angles);

        int atMostFlat = 0;
        int lessThenFlat = 0;
        int zeroIndex = 0;
        long ans = 1L * n * (n - 1) * (n - 2) / 6;
        for (int i = 0; i < n; i++) {
            var angle1 = angles[i];
            while (zeroIndex + 1 < i + n && (angle1.CompareTo(angles[zeroIndex + 1]) == 0)) {
                zeroIndex++;
            }
            if (lessThenFlat < zeroIndex) lessThenFlat = zeroIndex;
            while (lessThenFlat + 1 < i + n && angle1.X * angles[lessThenFlat + 1].Y - angle1.Y * angles[lessThenFlat + 1].X > 0) {
                lessThenFlat++;
            }
            if (atMostFlat < lessThenFlat) atMostFlat = lessThenFlat;
            while (atMostFlat + 1 < i + n && angle1.X * angles[atMostFlat + 1].Y - angle1.Y * angles[atMostFlat + 1].X >= 0) {
                atMostFlat++;
            }

            long half = atMostFlat - lessThenFlat;
            long middle = lessThenFlat - zeroIndex;
            long zero = zeroIndex - i + 1;

            ans -= zero * (zero - 1) * (zero - 2) / 6;
            ans -= middle * (middle - 1) / 2 * zero;
            ans -= middle * zero * (zero - 1) / 2;

            // LINE
            if (strict) {
                ans -= half * zero * (zero - 1) / 2;
                ans -= half * middle * zero;
            }

            i = zeroIndex;
        }

        return ans;
    }

    public static Tuple<long, long> Normalize(long x, long y) {
        var g = Gcd(Math.Abs(x), Math.Abs(y));
        x /= g;
        y /= g;
        return Tuple.Create(x, y);
    }

    public static long Gcd(long s, long t) {
        return t != 0 ? Gcd(t, s % t) : s;
    }
}

// PREWRITEN CODE BEGINS FROM HERE
internal partial class Solver : Scanner {
    public static void Main(string[] args) {
#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;
#pragma warning restore IDE0052

    public Solver(TextReader reader, TextWriter writer)
        : base(reader) {
        cin = reader;
        cout = writer;
    }
    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 Queue<string> TokenQueue = new Queue<string>();
    private readonly CultureInfo ci = CultureInfo.InvariantCulture;

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

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

    public int NextInt() { return int.Parse(Next(), ci); }
    public long NextLong() { return long.Parse(Next(), ci); }
    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 (TokenQueue.Count == 0) {
            if (!StockTokens()) {
                throw new InvalidOperationException();
            }
        }
        return TokenQueue.Dequeue();
    }

    public bool HasNext() {
        if (TokenQueue.Count > 0) {
            return true;
        }

        return StockTokens();
    }

    private static readonly char[] _separator = new[] { ' ', '\t' };
    private bool StockTokens() {
        while (true) {
            string line = Reader.ReadLine();
            if (line == null) {
                return false;
            }

            string[] tokens = line.Split(_separator, StringSplitOptions.RemoveEmptyEntries);
            if (tokens.Length == 0) {
                continue;
            }

            foreach (string token in tokens) {
                TokenQueue.Enqueue(token);
            }

            return true;
        }
    }
}