ARC126-B Cross-free Matching

問題へのリンク

C#のソース

using System;
using System.Collections.Generic;
using System.Linq;

class Program
{
    static string InputPattern = "InputX";

    static List<string> GetInputList()
    {
        var WillReturn = new List<string>();

        if (InputPattern == "Input1") {
            WillReturn.Add("3 3");
            WillReturn.Add("1 2");
            WillReturn.Add("2 3");
            WillReturn.Add("3 1");
            //2
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("3 5");
            WillReturn.Add("1 1");
            WillReturn.Add("2 1");
            WillReturn.Add("2 2");
            WillReturn.Add("3 2");
            WillReturn.Add("3 3");
            //3
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("7 5");
            WillReturn.Add("1 7");
            WillReturn.Add("7 1");
            WillReturn.Add("3 4");
            WillReturn.Add("2 6");
            WillReturn.Add("5 2");
            //1
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static long[] GetSplitArr(string pStr)
    {
        return (pStr == "" ? new string[0] : pStr.Split(' ')).Select(pX => long.Parse(pX)).ToArray();
    }

    struct ItemInfoDef
    {
        internal long StaX;
        internal long EndX;
    }
    static List<ItemInfoDef> mItemInfoList = new List<ItemInfoDef>();

    static void Main()
    {
        List<string> InputList = GetInputList();

        long[] wkArr = { };
        Action<string> SplitAct = (pStr) => wkArr = GetSplitArr(pStr);

        foreach (string EachStr in InputList.Skip(1)) {
            SplitAct(EachStr);
            ItemInfoDef WillAdd;
            WillAdd.StaX = wkArr[0];
            WillAdd.EndX = wkArr[1];
            mItemInfoList.Add(WillAdd);
        }

        var ValList = new List<long>();
        foreach (var Item in mItemInfoList.OrderBy(pX => pX.StaX).ThenByDescending(pX => pX.EndX)) {
            ValList.Add(Item.EndX);
        }

        long Answer = ClassDeriveStrictLISLength.DeriveLength(ValList);
        Console.WriteLine(Answer);
    }
}

#region ClassDeriveStrictLISLength
// LIS(狭義単調増加)の長さを返す
internal class ClassDeriveStrictLISLength
{
    // 引数 long型の列挙
    // 戻り値 LISの長さ
    internal static long DeriveLength(IEnumerable<long> pEnum)
    {
        // LISの最終値の最小値[LISの長さ] なDP表
        var DPSortedList = new SortedList<long, long>();

        foreach (long EachVal in pEnum) {
            if (DPSortedList.Count == 0) {
                DPSortedList[1] = EachVal;
                continue;
            }
            long UpsertKeyInd = ExecNibunhou(DPSortedList, EachVal);

            long CurrUB = DPSortedList.Count - 1;
            var Keys = DPSortedList.Keys;

            // 更新する位置によって分岐
            if (UpsertKeyInd <= CurrUB) {
                DPSortedList[Keys[(int)UpsertKeyInd]] = EachVal;
            }
            else {
                long PrevKey = Keys[(int)CurrUB];
                DPSortedList[PrevKey + 1] = EachVal;
            }
        }

        if (DPSortedList.Count == 0) {
            return 0;
        }
        int UB = DPSortedList.Count - 1;
        return DPSortedList.Keys[UB];
    }

    // 二分法で、引数の値を設定する、キーの配列の添字を返す
    private static long ExecNibunhou(SortedList<long, long> pDPSortedList, long pTargetVal)
    {
        int UB = pDPSortedList.Count - 1;
        var Keys = pDPSortedList.Keys;

        // 最小値以下の場合
        if (pTargetVal <= pDPSortedList[Keys[0]]) {
            return 0;
        }

        // 最大値より大きい場合
        if (pTargetVal > pDPSortedList[Keys[UB]]) {
            return UB + 1;
        }

        int L = 0;
        int R = UB;

        while (L + 1 < R) {
            int Mid = (L + R) / 2;
            if (pDPSortedList[Keys[Mid]] < pTargetVal) {
                L = Mid;
            }
            else {
                R = Mid;
            }
        }
        return R;
    }
}
#endregion

解説

考察すると、
StaXの昇順でのEndXのLISを求めれば、分かります。
(StaXが同じ場合は、EndXが降順になるようにする必要があります)

類題

ABC439-E Kite