ABC343-F Second Largest Query

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("5 4");
            WillReturn.Add("3 3 1 4 5");
            WillReturn.Add("2 1 3");
            WillReturn.Add("2 5 5");
            WillReturn.Add("1 3 3");
            WillReturn.Add("2 2 4");
            //1
            //0
            //2
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("1 1");
            WillReturn.Add("1000000000");
            WillReturn.Add("2 1 1");
            //0
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("8 9");
            WillReturn.Add("2 4 4 3 9 1 1 2");
            WillReturn.Add("1 5 4");
            WillReturn.Add("2 7 7");
            WillReturn.Add("2 2 6");
            WillReturn.Add("1 4 4");
            WillReturn.Add("2 2 5");
            WillReturn.Add("2 2 7");
            WillReturn.Add("1 1 1");
            WillReturn.Add("1 8 1");
            WillReturn.Add("2 1 8");
            //0
            //1
            //0
            //2
            //4
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static void Main()
    {
        List<string> InputList = GetInputList();
        int[] AArr = InputList[1].Split(' ').Select(pX => int.Parse(pX)).ToArray();
        int UB = AArr.GetUpperBound(0);

        var InsSegmentTree = new SegmentTree(UB);
        for (int I = 0; I <= UB; I++) {
            InsSegmentTree.Update(I, AArr[I]);
        }

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

        var sb = new System.Text.StringBuilder();
        foreach (string EachStr in InputList.Skip(2)) {
            SplitAct(EachStr);
            int Type = wkArr[0];
            if (Type == 1) {
                int Ind = wkArr[1] - 1;
                int NewVal = wkArr[2];

                InsSegmentTree.Update(Ind, NewVal);
            }

            if (Type == 2) {
                int Sta = wkArr[1] - 1;
                int End = wkArr[2] - 1;

                SegmentTree.MaxInfo Result = InsSegmentTree.Internal_Query(Sta, End);
                if (Result.SecondMax == 0) {
                    sb.AppendLine("0");
                }
                else {
                    sb.Append(Result.SecondCnt);
                    sb.AppendLine();
                }
            }
        }
        Console.Write(sb.ToString());
    }
}

#region SegmentTree
// SegmentTreeクラス (区間の最大値情報 and 1点更新)
internal class SegmentTree
{
    private MaxInfo[] 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;

    internal struct MaxInfo
    {
        internal long FirstMax;
        internal long FirstCnt;
        internal long SecondMax;
        internal long SecondCnt;
    }

    // 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)
    {
        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;
        }

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

        // 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] = new MaxInfo();
        mTreeNodeArr[CurrNode].FirstMax = pNewVal;
        mTreeNodeArr[CurrNode].FirstCnt = 1;

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

    static MaxInfo ExecMerge(MaxInfo pInfo1, MaxInfo pInfo2)
    {
        MaxInfo WillReturn = pInfo1;
        Action<long, long> UpdateAct = (pVal, pCnt) =>
        {
            if (WillReturn.FirstMax < pVal) {
                WillReturn.SecondMax = WillReturn.FirstMax;
                WillReturn.SecondCnt = WillReturn.FirstCnt;

                WillReturn.FirstMax = pVal;
                WillReturn.FirstCnt = pCnt;
                return;
            }
            if (WillReturn.FirstMax == pVal) {
                WillReturn.FirstCnt += pCnt;
                return;
            }
            if (WillReturn.SecondMax < pVal) {
                WillReturn.SecondMax = pVal;
                WillReturn.SecondCnt = pCnt;
                return;
            }
            if (WillReturn.SecondMax == pVal) {
                WillReturn.SecondCnt += pCnt;
                return;
            }
        };
        UpdateAct(pInfo2.FirstMax, pInfo2.FirstCnt);
        UpdateAct(pInfo2.SecondMax, pInfo2.SecondCnt);

        return WillReturn;
    }

    // 開始添字と終了添字とカレントノードを引数として、MaxInfoを返す
    internal MaxInfo Internal_Query(long pSearchStaInd, long pSearchEndInd)
    {
        return Private_Query(pSearchStaInd, pSearchEndInd, 0);
    }
    private MaxInfo 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、空情報
        if (CurrNodeEndInd < pSearchStaInd || pSearchEndInd < CurrNodeStaInd)
            return new MaxInfo();

        // 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Merge結果
        long ChildNode1 = DeriveChildNode(pCurrNode);
        long ChildNode2 = ChildNode1 + 1;

        MaxInfo ChildVal1 = Private_Query(pSearchStaInd, pSearchEndInd, ChildNode1);
        MaxInfo ChildVal2 = Private_Query(pSearchStaInd, pSearchEndInd, ChildNode2);
        return ExecMerge(ChildVal1, ChildVal2);
    }
}
#endregion

解説

セグ木に区間の最大値情報として、
{最大値,最大値の個数,SecondMax,SecondMaxの個数}
を乗せてます。

ExecMergeメソッドでDictionary<int,int>()
を使って楽な実装をしたらTLEしたので、
構造体を場合分けで更新するようしました。