ABC005-D おいしいたこ焼きの焼き方

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");
            WillReturn.Add("3 2 1");
            WillReturn.Add("2 2 1");
            WillReturn.Add("1 1 1");
            WillReturn.Add("3");
            WillReturn.Add("1");
            WillReturn.Add("4");
            WillReturn.Add("9");
            //3
            //9
            //14
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("3");
            WillReturn.Add("1 1 1");
            WillReturn.Add("1 1 1");
            WillReturn.Add("9 9 9");
            WillReturn.Add("1");
            WillReturn.Add("4");
            //27
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static void Main()
    {
        List<string> InputList = GetInputList();
        long N = long.Parse(InputList[0]);

        long[,] BanArr = CreateBanArr(InputList.Skip(1).Take((int)N));
        long UB_X = BanArr.GetUpperBound(0);
        long UB_Y = BanArr.GetUpperBound(1);

        var QList = new List<long>();
        foreach (string EachStr in InputList.Skip(1 + (int)N + 1)) {
            QList.Add(long.Parse(EachStr));
        }

        // 2次元累積和を求める
        long[,] RunSumArr = (long[,])BanArr.Clone();

        // 累積和を設定する (横方向)
        for (long LoopX = 1; LoopX <= UB_X; LoopX++) {
            for (long LoopY = 0; LoopY <= UB_Y; LoopY++) {
                RunSumArr[LoopX, LoopY] += RunSumArr[LoopX - 1, LoopY];
            }
        }

        // 累積和を設定する (縦方向)
        for (long LoopX = 0; LoopX <= UB_X; LoopX++) {
            for (long LoopY = 1; LoopY <= UB_Y; LoopY++) {
                RunSumArr[LoopX, LoopY] += RunSumArr[LoopX, LoopY - 1];
            }
        }

        // RMaxQ and 1点更新なセグ木
        var InsSegmentTree = new SegmentTree(N * N + 1, long.MinValue);

        for (long StaX = 0; StaX <= UB_X; StaX++) {
            for (long EndX = StaX; EndX <= UB_X; EndX++) {
                for (long StaY = 0; StaY <= UB_Y; StaY++) {
                    for (long EndY = StaY; EndY <= UB_Y; EndY++) {
                        long CurrSum = DeriveSumRect(RunSumArr, EndX, EndY);
                        CurrSum -= DeriveSumRect(RunSumArr, StaX - 1, EndY);
                        CurrSum -= DeriveSumRect(RunSumArr, EndX, StaY - 1);
                        CurrSum += DeriveSumRect(RunSumArr, StaX - 1, StaY - 1);

                        // 長方形のマスの数
                        long MasuCnt = (EndX - StaX + 1) * (EndY - StaY + 1);

                        long SegVal = InsSegmentTree[MasuCnt];

                        if (SegVal < CurrSum) {
                            InsSegmentTree[MasuCnt] = CurrSum;
                        }
                    }
                }
            }
        }

        foreach (long EachQ in QList) {
            long SegVal = InsSegmentTree.Internal_Query(0, EachQ);
            Console.WriteLine(SegVal);
        }
    }

    // (0,0)と(pX,pY)からなる長方形の和を返す
    static long DeriveSumRect(long[,] pRunSumArr, long pX, long pY)
    {
        if (pX < 0) return 0;
        if (pY < 0) return 0;
        return pRunSumArr[pX, pY];
    }

    ////////////////////////////////////////////////////////////////
    // IEnumerable<string>をlongの2次元配列に設定
    ////////////////////////////////////////////////////////////////
    static long[,] CreateBanArr(IEnumerable<string> pStrEnum)
    {
        var StrList = new List<string>(pStrEnum);
        if (StrList.Count == 0) {
            return new long[0, 0];
        }

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

        SplitAct(StrList[0]);

        long UB_X = LongArr.GetUpperBound(0);
        long UB_Y = StrList.Count - 1;

        long[,] WillReturn = new long[UB_X + 1, UB_Y + 1];

        for (long Y = 0; Y <= UB_Y; Y++) {
            SplitAct(StrList[(int)Y]);
            for (long X = 0; X <= UB_X; X++) {
                WillReturn[X, Y] = LongArr[X];
            }
        }
        return WillReturn;
    }

    ////////////////////////////////////////////////////////////////
    // 2次元配列(int型)のデバッグ出力
    ////////////////////////////////////////////////////////////////
    static void PrintBan(int[,] pBanArr)
    {
        for (int Y = 0; Y <= pBanArr.GetUpperBound(1); Y++) {
            for (int X = 0; X <= pBanArr.GetUpperBound(0); X++) {
                Console.Write(pBanArr[X, Y]);
            }
            Console.WriteLine();
        }
    }
}

#region SegmentTree
// SegmentTreeクラス (RMaxQ 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;

    // 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;
    }

    // コンストラクタその1
    // 引数1 外部IndのUB
    // 引数2 単位元
    internal SegmentTree(long pExternalArrUB, long pInitVal)
    {
        mExternalArrUB = pExternalArrUB;

        ConstructorTreeInit();

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

    // コンストラクタその2
    // 引数1 初期化用の配列
    // 引数2 単位元
    internal SegmentTree(long[] pInitArr, long pInitVal)
    {
        mExternalArrUB = pInitArr.GetUpperBound(0);

        ConstructorTreeInit();

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

        for (long I = 0; I <= pInitArr.GetUpperBound(0); I++) {
            long TreeNode = DeriveTreeNode(I);
            mTreeNodeArr[TreeNode] = pInitArr[I];
        }

        // 木DPの要領で、葉から根に伝播
        ExecTreeDP();
    }

    // コンストラクタその3
    // 引数1 初期化用のList
    // 引数2 単位元
    internal SegmentTree(List<long> pInitList, long pInitVal)
    {
        mExternalArrUB = pInitList.Count - 1;

        ConstructorTreeInit();

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

        for (long I = 0; I <= pInitList.Count - 1; I++) {
            long TreeNode = DeriveTreeNode(I);
            mTreeNodeArr[TreeNode] = pInitList[(int)I];
        }

        // 木DPの要領で、葉から根に伝播
        ExecTreeDP();
    }

    // コンストラクタのヘルパメソッド(木の初期化)
    private void ConstructorTreeInit()
    {
        // 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 (mExternalArrUB + 1 < mLeafCnt) break;
        }

        UB = ArrLength - 1;
        mTreeNodeArr = new long[UB + 1];

        // 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;
        }
    }

    // 木DPの要領で、葉から根に伝播
    private void ExecTreeDP()
    {
        for (long I = UB; 0 < I; I--) {
            long SendNode = DeriveParentNode(I);
            mTreeNodeArr[SendNode] = Math.Max(mTreeNodeArr[SendNode], mTreeNodeArr[I]);
        }
    }

    // インデクサ
    internal long this[long pInd]
    {
        get
        {
            long CurrNode = DeriveTreeNode(pInd);
            return mTreeNodeArr[CurrNode];
        }
        set { Update(pInd, value); }
    }

    // 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.Max(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、最大値を返す
    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.MinValue
        if (CurrNodeEndInd < pSearchStaInd || pSearchEndInd < CurrNodeStaInd)
            return long.MinValue;

        // 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つの子の最大値
        long ChildNode1 = DeriveChildNode(pCurrNode);
        long ChildNode2 = ChildNode1 + 1;

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

解説

二次元累積和を使って、矩形の総和を求めつつ、
セグ木を使ってます。