結果

問題 No.703 ゴミ拾い Easy
ユーザー EmKjp
提出日時 2020-02-20 22:42:41
言語 C#(csc)
(csc 3.9.0)
結果
AC  
実行時間 281 ms / 1,500 ms
コード長 7,961 bytes
コンパイル時間 1,859 ms
コンパイル使用メモリ 114,720 KB
実行使用メモリ 36,060 KB
最終ジャッジ日時 2025-01-02 14:26:36
合計ジャッジ時間 9,886 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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ファイルパターン 結果
sample AC * 4
other AC * 46
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 #
プレゼンテーションモードにする

using System;
using System.Collections;
using System.Collections.Generic;
using System.Globalization;
using System.IO;
using System.Linq;
using E = System.Linq.Enumerable;
using CHTType = System.Int64;
using System.Text;
internal partial class Solver {
    public void Run() {
        var n = ni();
        var a = ni(n);
        var x = ni(n);
        var y = ni(n);
        var dp = new long[n + 1];
        var inf = long.MaxValue >> 10;
        for (int i = 0; i <= n; i++) {
            dp[i] = inf;
        }
        dp[0] = 0;
        var cht = new ConvexHullTrick(true);
        for (int i = 0; i < n; i++) {
            //for (int j = 0; j <= i; j++) {
            //v = Math.Min(v, dp[j] + 1L * (x[j] - a[i]) * (x[j] - a[i]) + 1L * y[j] * y[j]);
            //}
            // min_j dp[j] + (x[j] - a[i]) ^ 2 + y[j] ^ 2
            // min_j dp[j] + x[j]^2 - 2 * a[i] * x[j] + a[i]^2 + y[j] ^ 2
            // min_j { dp[j] + x[j]^2 - 2 * a[i] * x[j] + y[j]^2 } + a[i]^2
            cht.Add(-2 * x[i], dp[i] + 1L * x[i] * x[i] + 1L * y[i] * y[i]);
            dp[i + 1] = cht.Get(a[i]) + 1L * a[i] * a[i];
        }
        cout.WriteLine(dp[n]);
    }
}
public class ConvexHullTrick {
    private class Line {
        public readonly CHTType Slope;
        public readonly CHTType Intercept;
        public Line(CHTType slope, CHTType intercept) {
            Slope = slope;
            Intercept = intercept;
        }
        public CHTType Evaluate(CHTType x) {
            return Slope * x + Intercept;
        }
    }
    private readonly List<Line> _envelope = new List<Line>();
    private readonly bool _isMin;
    public ConvexHullTrick(bool isMin = true) {
        _isMin = isMin;
    }
    // Add ax + b
    // <code>a</code> must be monotone decreasing
    public void Add(CHTType a, CHTType b) {
        if (!_isMin) {
            a = -a;
            b = -b;
        }
        var line = new Line(a, b);
        if (_envelope.Count > 0 && _envelope[_envelope.Count - 1].Slope < line.Slope) {
            throw new InvalidOperationException("Slope must be monotone " + (_isMin ? "decreasing" : "increasing"));
        }
        while (_envelope.Count >= 2 &&
            IsUnnecessary(_envelope[_envelope.Count - 2], _envelope[_envelope.Count - 1], line)) {
            _envelope.RemoveAt(_envelope.Count - 1);
        }
        _envelope.Add(line);
    }
    private static bool IsUnnecessary(Line l1, Line l2, Line l3) {
        return
            (l3.Intercept - l2.Intercept) * (l2.Slope - l1.Slope) >=
            (l2.Intercept - l1.Intercept) * (l3.Slope - l2.Slope);
    }
    public CHTType Get(CHTType x) {
        var best = CHTType.MaxValue;
        if (_envelope.Count == 1) {
            best = _envelope[0].Evaluate(x);
        } else {
            int lower = 0, upper = _envelope.Count - 2;
            while (lower <= upper) {
                var mid = (lower + upper) >> 1;
                var y0 = _envelope[mid].Evaluate(x);
                var y1 = _envelope[mid + 1].Evaluate(x);
                if (y0 > y1) {
                    best = y1;
                    lower = mid + 1;
                } else {
                    best = y0;
                    upper = mid - 1;
                }
            }
        }
        return _isMin ? best : -best;
    }
}
// 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 {
    public static T Dump<T>(this T obj) {
#if LOCAL
        return LINQPad.Extensions.Dump(obj);
#else
        return 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 InvalidOperationException();
            }
        }
        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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