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();
        int N = int.Parse(InputList[0]);

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

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

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

        // 累積和を設定する (横方向)
        for (int LoopX = 1; LoopX <= UB_X; LoopX++) {
            for (int 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 (int LoopX = 0; LoopX <= UB_X; LoopX++) {
            for (int 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);

        for (int StaX = 0; StaX <= UB_X; StaX++) {
            for (int EndX = StaX; EndX <= UB_X; EndX++) {
                for (int StaY = 0; StaY <= UB_Y; StaY++) {
                    for (int EndY = StaY; EndY <= UB_Y; EndY++) {
                        int 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
                        int MasuCnt = (EndX - StaX + 1) * (EndY - StaY + 1);

                        int SegVal = InsSegmentTree.Query(MasuCnt, MasuCnt, 0);

                        if (SegVal < CurrSum) {
                            InsSegmentTree.Update(MasuCnt, CurrSum);
                        }
                    }
                }
            }
        }

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

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

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

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

        SplitAct(StrList[0]);

        int UB_X = IntArr.GetUpperBound(0);
        int UB_Y = StrList.Count - 1;

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

        for (int Y = 0; Y <= UB_Y; Y++) {
            SplitAct(StrList[Y]);
            for (int X = 0; X <= UB_X; X++) {
                WillReturn[X, Y] = IntArr[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 int[] mTreeNodeArr;
    private int UB; // 木のノードの配列のUB
    private int mLeafCnt; // 葉ノードの数

    // 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 int StaInd;
        internal int EndInd;
    }
    private RangeInfoDef[] mRangeInfo;

    // コンストラクタ
    internal SegmentTree(int pLeafCnt)
    {
        // 簡単のため、葉ノード数を2のべき乗に
        int ArrLength = 0;
        for (int I = 1; I < int.MaxValue; I *= 2) {
            ArrLength += I;
            mLeafCnt = I;

            if (pLeafCnt < mLeafCnt) break;
        }

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

        // 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 (int I = 0; I <= UB; I++) {
            if (I == 0) {
                RangeInfoDef WillSet1;
                WillSet1.StaInd = 0;
                WillSet1.EndInd = mLeafCnt - 1;
                mRangeInfo[I] = WillSet1;
                continue;
            }
            int ParentNode = DeriveParentNode(I);
            RangeInfoDef ParentRangeInfo = mRangeInfo[ParentNode];

            RangeInfoDef WillSet2;
            int 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 int DeriveParentNode(int pTarget)
    {
        return (pTarget - 1) / 2;
    }

    // 子ノードの添字(小さいほう)を取得
    private int DeriveChildNode(int 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 int DeriveTreeNode(int pLeafArrInd)
    {
        int 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(int pK, int pNewVal)
    {
        int CurrNode = DeriveTreeNode(pK);
        mTreeNodeArr[CurrNode] = pNewVal;

        // 登りながら更新
        while (CurrNode > 0) {
            CurrNode = DeriveParentNode(CurrNode);
            int ChildNode1 = DeriveChildNode(CurrNode);
            int 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 int Query(int pSearchStaInd, int pSearchEndInd, int pCurrNode)
    {
        int CurrNodeStaInd = mRangeInfo[pCurrNode].StaInd;
        int CurrNodeEndInd = mRangeInfo[pCurrNode].EndInd;

        // OverLapしてなければ、int.MinValue
        if (CurrNodeEndInd < pSearchStaInd || pSearchEndInd < CurrNodeStaInd)
            return int.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
        int ChildNode1 = DeriveChildNode(pCurrNode);
        int ChildNode2 = ChildNode1 + 1;

        int ChildVal1 = Query(pSearchStaInd, pSearchEndInd, ChildNode1);
        int ChildVal2 = 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。