第5回PAST N 旅行会社

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("4 3");
            WillReturn.Add("3 6");
            WillReturn.Add("2 5");
            WillReturn.Add("1 2");
            WillReturn.Add("3 1");
            WillReturn.Add("2 2");
            WillReturn.Add("1 4");
            //3
            //3
            //2
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("6 3");
            WillReturn.Add("4 7");
            WillReturn.Add("3 8");
            WillReturn.Add("1 6");
            WillReturn.Add("5 9");
            WillReturn.Add("7 10");
            WillReturn.Add("5 1");
            WillReturn.Add("7 6");
            WillReturn.Add("4 6");
            //5
            //3
            //1
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    class EventInfoDef
    {
        // Type1 セグ木に0を設定
        // Type2 クエリに回答
        // Type3 セグ木に1を設定
        internal long Type;
        internal long City;   // Type1とType2とType3
        internal long Age;    // Type1とType2とType3
        internal long Time;   // Type2
        internal long Answer; // Type2
    }
    static List<EventInfoDef> mEventInfoList = new List<EventInfoDef>();

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

        long[] wkArr = { };
        Action<string> SplitAct = pStr =>
            wkArr = pStr.Split(' ').Select(pX => long.Parse(pX)).ToArray();

        SplitAct(InputList[0]);
        long N = wkArr[0];
        long SegUB = N;

        long CurrCity = 1;
        foreach (string EachStr in InputList.Skip(1).Take((int)N - 1)) {
            SplitAct(EachStr);

            var WillAdd1 = new EventInfoDef();
            WillAdd1.Type = 1;
            WillAdd1.City = CurrCity;
            WillAdd1.Age = wkArr[0];
            WillAdd1.Time = long.MinValue;
            WillAdd1.Answer = long.MinValue;
            mEventInfoList.Add(WillAdd1);

            var WillAdd3 = new EventInfoDef();
            WillAdd3.Type = 3;
            WillAdd3.City = CurrCity;
            WillAdd3.Age = wkArr[1];
            WillAdd3.Time = -1;
            WillAdd3.Answer = -1;
            mEventInfoList.Add(WillAdd3);

            CurrCity++;
        }

        long CurrTime = 1;
        foreach (string EachStr in InputList.Skip((int)N)) {
            SplitAct(EachStr);

            var WillAdd2 = new EventInfoDef();
            WillAdd2.Type = 2;
            WillAdd2.City = wkArr[1];
            WillAdd2.Age = wkArr[0];
            WillAdd2.Time = CurrTime++;
            WillAdd2.Answer = -1;
            mEventInfoList.Add(WillAdd2);
        }

        var InsSegmentTree = new SegmentTree(SegUB, 0);

        mEventInfoList = mEventInfoList.OrderBy(pX => pX.Age).ThenBy(pX => pX.Type).ToList();
        foreach (EventInfoDef EachEventInfo in mEventInfoList) {
            if (EachEventInfo.Type == 1) {
                long City = EachEventInfo.City;
                InsSegmentTree.Update(City, 1);
            }
            if (EachEventInfo.Type == 2) {
                // 左方向の0を調べる
                long RangeSta1 = 0;
                long RangeEnd1 = EachEventInfo.City - 1;

                long MinVal1;
                long MinValInd1;
                InsSegmentTree.GetMinInfo_Right(RangeSta1, RangeEnd1, out MinVal1, out MinValInd1);

                long LeftCnt = RangeEnd1 - MinValInd1;

                // 右方向の0を調べる
                long RangeSta2 = EachEventInfo.City;
                long RangeEnd2 = SegUB;

                long MinVal2;
                long MinValInd2;
                InsSegmentTree.GetMinInfo_Left(RangeSta2, RangeEnd2, out MinVal2, out MinValInd2);

                long RightCnt = MinValInd2 - RangeSta2;

                EachEventInfo.Answer = 1 + LeftCnt + RightCnt;
            }
            if (EachEventInfo.Type == 3) {
                long City = EachEventInfo.City;
                InsSegmentTree.Update(City, 0);
            }
        }

        foreach (EventInfoDef EachEventInfo in mEventInfoList.OrderBy(px => px.Time)) {
            if (EachEventInfo.Type == 2) {
                Console.WriteLine(EachEventInfo.Answer);
            }
        }
    }
}

#region SegmentTree
// SegmentTreeクラス (RMQ and 1点更新)
internal class SegmentTree
{
    private long[] mTreeNodeArr;
    private long UB; // 木のノードの配列のUB
    private long mLeafCnt; // 葉ノードの数
    private long mExternalArrUB;

    // 拡張機能 (最小値と、最小値を持つIndを返す)
    // 最小値が複数あったら、左側のIndを優先
    internal void GetMinInfo_Left(long pSearchStaInd, long pSearchEndInd,
        out long pMinVal, out long pMinValInd)
    {
        // 区間の最小値を求める
        pMinVal = Internal_Query(pSearchStaInd, pSearchEndInd);

        // 二分探索を行う
        long L = pSearchStaInd, R = pSearchEndInd;

        while (L + 1 < R) {
            long Mid = (L + R) / 2;
            long LeftMin = Internal_Query(L, Mid);

            if (LeftMin == pMinVal) R = Mid;
            else L = Mid;
        }
        pMinValInd = ((Internal_Query(L, L) == pMinVal) ? L : R);
    }

    // 拡張機能 (最小値と、最小値を持つIndを返す)
    // 最小値が複数あったら、右側のIndを優先
    internal void GetMinInfo_Right(long pSearchStaInd, long pSearchEndInd,
        out long pMinVal, out long pMinValInd)
    {
        // 区間の最小値を求める
        pMinVal = Internal_Query(pSearchStaInd, pSearchEndInd);

        // 二分探索を行う
        long L = pSearchStaInd, R = pSearchEndInd;

        while (L + 1 < R) {
            long Mid = (L + R) / 2;
            long RightMin = Internal_Query(Mid, R);

            if (RightMin == pMinVal) L = Mid;
            else R = Mid;
        }
        pMinValInd = ((Internal_Query(R, R) == pMinVal) ? R : L);
    }

    // ノードの添字を引数とし、範囲の開始添字と終了添字を持つ配列
    private struct RangeInfoDef
    {
        internal long StaInd;
        internal long EndInd;
    }
    private RangeInfoDef[] mRangeInfo;

    // ノードのIndexの列挙を返す
    internal IEnumerable<long> GetNodeIndEnum()
    {
        for (long I = 0; I <= mExternalArrUB; I++) {
            yield return I;
        }
    }

    // 木のノードのUBを返す
    internal long GetUB()
    {
        return mExternalArrUB;
    }

    // コンストラクタ
    internal SegmentTree(long pExternalArrUB, long pInitVal)
    {
        mExternalArrUB = pExternalArrUB;

        // 簡単のため、葉ノード数を2のべき乗に
        long ArrLength = 0;
        for (long I = 1; I < long.MaxValue; I *= 2) {
            ArrLength += I;
            mLeafCnt = I;

            if (pExternalArrUB + 1 < mLeafCnt) break;
        }

        // すべての値をpInitValに
        UB = ArrLength - 1;
        mTreeNodeArr = new long[UB + 1];
        for (long I = 0; I <= UB; I++) {
            mTreeNodeArr[I] = pInitVal;
        }

        // ノードの添字を引数とし、範囲の開始添字と終了添字を持つ配列の作成
        mRangeInfo = new RangeInfoDef[UB + 1];
        for (long I = 0; I <= UB; I++) {
            if (I == 0) {
                RangeInfoDef WillSet1;
                WillSet1.StaInd = 0;
                WillSet1.EndInd = mLeafCnt - 1;
                mRangeInfo[I] = WillSet1;
                continue;
            }
            long ParentNode = DeriveParentNode(I);
            RangeInfoDef ParentRangeInfo = mRangeInfo[ParentNode];

            RangeInfoDef WillSet2;
            long Mid = (ParentRangeInfo.StaInd + ParentRangeInfo.EndInd) / 2;

            if (I % 2 == 1) { // 奇数ノードの場合
                WillSet2.StaInd = ParentRangeInfo.StaInd;
                WillSet2.EndInd = Mid;
            }
            else { // 偶数ノードの場合
                WillSet2.StaInd = Mid + 1;
                WillSet2.EndInd = ParentRangeInfo.EndInd;
            }
            mRangeInfo[I] = WillSet2;
        }
    }

    // 親ノードの添字を取得
    private long DeriveParentNode(long pTarget)
    {
        return (pTarget - 1) / 2;
    }

    // 子ノードの添字(小さいほう)を取得
    private long DeriveChildNode(long pTarget)
    {
        return pTarget * 2 + 1;
    }

    // 葉ノードの配列の添字を木の添字に変換して返す
    private long DeriveTreeNode(long pLeafArrInd)
    {
        long BaseInd = UB - mLeafCnt + 1;
        return BaseInd + pLeafArrInd;
    }

    // 葉ノードの配列のK番目の値をNewValに変更
    internal void Update(long pK, long pNewVal)
    {
        long CurrNode = DeriveTreeNode(pK);
        mTreeNodeArr[CurrNode] = pNewVal;

        // 登りながら更新
        while (CurrNode > 0) {
            CurrNode = DeriveParentNode(CurrNode);
            long ChildNode1 = DeriveChildNode(CurrNode);
            long ChildNode2 = ChildNode1 + 1;
            mTreeNodeArr[CurrNode] =
                Math.Min(mTreeNodeArr[ChildNode1], mTreeNodeArr[ChildNode2]);
        }
    }

    // 開始添字と終了添字とカレントノードを引数として、最小値を返す
    internal long Internal_Query(long pSearchStaInd, long pSearchEndInd)
    {
        return Private_Query(pSearchStaInd, pSearchEndInd, 0);
    }
    private long Private_Query(long pSearchStaInd, long pSearchEndInd, long pCurrNode)
    {
        long CurrNodeStaInd = mRangeInfo[pCurrNode].StaInd;
        long CurrNodeEndInd = mRangeInfo[pCurrNode].EndInd;

        // OverLapしてなければ、long.MaxValue
        if (CurrNodeEndInd < pSearchStaInd || pSearchEndInd < CurrNodeStaInd)
            return long.MaxValue;

        // 完全に含んでいれば、このノードの値
        if (pSearchStaInd <= CurrNodeStaInd && CurrNodeEndInd <= pSearchEndInd)
            return mTreeNodeArr[pCurrNode];

        // そうでなければ、2つの子の最小値
        long ChildNode1 = DeriveChildNode(pCurrNode);
        long ChildNode2 = ChildNode1 + 1;

        long ChildVal1 = Private_Query(pSearchStaInd, pSearchEndInd, ChildNode1);
        long ChildVal2 = Private_Query(pSearchStaInd, pSearchEndInd, ChildNode2);
        return Math.Min(ChildVal1, ChildVal2);
    }

    internal void DebugPrint()
    {
        for (long I = 0; I <= UB; I++) {
            Console.WriteLine("mTreeNodeArr[{0}] = {1}", I, mTreeNodeArr[I]);
        }
    }
}
#endregion

解説

イベントソートと1点更新区間最小値取得なセグ木
を組み合わせてます。