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AOJ 0749 塗りつぶし (Painting)


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 4");
            WillReturn.Add("1 2 3 1");
            WillReturn.Add("2 2 3 1");
            WillReturn.Add("1 2 3 1");
            WillReturn.Add("3 3 2 2");
            //9
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("2 10");
            WillReturn.Add("1 2 2 1 3 3 3 3 1 1");
            WillReturn.Add("1 1 1 1 1 1 1 3 3 3");
            //18
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("5 5");
            WillReturn.Add("1 1 1 1 1");
            WillReturn.Add("1 1 1 1 1");
            WillReturn.Add("1 1 1 1 1");
            WillReturn.Add("1 1 1 1 1");
            WillReturn.Add("1 1 1 1 1");
            //25
        }
        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();
    }

    static long[,] mBanArr;
    static long UB_X;
    static long UB_Y;

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

        mBanArr = CreateBanArr(InputList.Skip(1));
        UB_X = mBanArr.GetUpperBound(0);
        UB_Y = mBanArr.GetUpperBound(1);

        var InsUnionFindWithAnyInfo = new UnionFindWithAnyInfo();

        // UnionFindのノードを作成
        for (long Y = 0; Y <= UB_Y; Y++) {
            for (long X = 0; X <= UB_X; X++) {
                long CurrHash = GetHash(X, Y);
                InsUnionFindWithAnyInfo.MakeSet(CurrHash, mBanArr[X, Y]);
            }
        }

        // 4近傍と接続
        for (long Y = 0; Y <= UB_Y; Y++) {
            for (long X = 0; X <= UB_X; X++) {
                Action<long, long> ConnAct = (pTargetX, pTargetY) =>
                {
                    if (pTargetX < 0 || UB_X < pTargetX) return;
                    if (pTargetY < 0 || UB_Y < pTargetY) return;

                    long BaseColor = mBanArr[X, Y];
                    if (mBanArr[pTargetX, pTargetY] != BaseColor) return;

                    long BaseHash = GetHash(X, Y);
                    long TargetHash = GetHash(pTargetX, pTargetY);
                    InsUnionFindWithAnyInfo.Unite(BaseHash, TargetHash);
                };

                ConnAct(X, Y - 1);
                ConnAct(X, Y + 1);
                ConnAct(X - 1, Y);
                ConnAct(X + 1, Y);
            }
        }

        var RootNodeSet = new HashSet<long>();
        for (long Y = 0; Y <= UB_Y; Y++) {
            for (long X = 0; X <= UB_X; X++) {
                long BaseHash = GetHash(X, Y);
                long RootNode = InsUnionFindWithAnyInfo.FindSet(BaseHash);
                RootNodeSet.Add(RootNode);
            }
        }

        // 解候補を列挙
        var AnswerList = new List<long>();
        foreach (long EachRootNode in RootNodeSet) {
            HashSet<long> ShimaNodeSet = InsUnionFindWithAnyInfo.GetNodeSet(EachRootNode);

            // 隣接ノードの代表ノードのSet
            HashSet<long> RinsetuRootNodeSet = new HashSet<long>();
            Action<long, long> AddAct = (pTargetX, pTargetY) =>
            {
                if (pTargetX < 0 || UB_X < pTargetX) return;
                if (pTargetY < 0 || UB_Y < pTargetY) return;

                long BaseCoor = InsUnionFindWithAnyInfo.GetColor(EachRootNode);
                if (mBanArr[pTargetX, pTargetY] == BaseCoor) return;

                long CurrHash = GetHash(pTargetX, pTargetY);
                long CurrRoot = InsUnionFindWithAnyInfo.FindSet(CurrHash);
                RinsetuRootNodeSet.Add(CurrRoot);
            };

            foreach (long EachShimaNode in ShimaNodeSet) {
                long CurrX = EachShimaNode / 1000;
                long CurrY = EachShimaNode % 1000;
                AddAct(CurrX, CurrY - 1);
                AddAct(CurrX, CurrY + 1);
                AddAct(CurrX - 1, CurrY);
                AddAct(CurrX + 1, CurrY);
            }

            // マス合計[色]なDict
            var CntDict = new Dictionary<long, long>();

            foreach (long EachRinsetuRootNode in RinsetuRootNodeSet) {
                long CurrColor = InsUnionFindWithAnyInfo.GetColor(EachRinsetuRootNode);
                HashSet<long> CurrNodeSet = InsUnionFindWithAnyInfo.GetNodeSet(EachRinsetuRootNode);

                if (CntDict.ContainsKey(CurrColor) == false) {
                    CntDict[CurrColor] = 0;
                }
                CntDict[CurrColor] += CurrNodeSet.Count;
            }

            AnswerList.Add(ShimaNodeSet.Count);
            foreach (var EachPair in CntDict) {
                AnswerList.Add(ShimaNodeSet.Count + EachPair.Value);
            }
        }
        Console.WriteLine(AnswerList.Max());
    }

    static long GetHash(long pX, long pY)
    {
        return pX * 1000 + 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;
    }
}

// UnionFindWithAnyInfoクラス
internal class UnionFindWithAnyInfo
{
    private class NodeInfoDef
    {
        internal long ParentNode;
        internal long Rank;
        internal long Size;    // 木のノード数
        internal long EdgeCnt; // 木の枝の数
        internal long Color;   // 色
        internal HashSet<long> NodeSet;
    }
    private Dictionary<long, NodeInfoDef> mNodeInfoDict =
        new Dictionary<long, NodeInfoDef>();

    // 森にある木の数
    private long mTreeCnt = 0;

    // 森にある木の数を返す
    internal long TreeCnt
    {
        get { return mTreeCnt; }
    }

    // 要素が1つである木を森に追加
    internal void MakeSet(long pNode, long pColor)
    {
        mTreeCnt++;
        NodeInfoDef WillAdd = new NodeInfoDef();
        WillAdd.ParentNode = pNode;
        WillAdd.Rank = 0;
        WillAdd.Size = 1;
        WillAdd.EdgeCnt = 0;
        WillAdd.Color = pColor;
        WillAdd.NodeSet = new HashSet<long>() { pNode };
        mNodeInfoDict[pNode] = WillAdd;
    }

    // 合併処理
    internal void Unite(long pX, long pY)
    {
        long XNode = FindSet(pX);
        long YNode = FindSet(pY);

        // 既に同じ木の場合
        if (XNode == YNode) {
            mNodeInfoDict[XNode].EdgeCnt++;
            return;
        }
        mTreeCnt--;

        long XRank = mNodeInfoDict[XNode].Rank;
        long YRank = mNodeInfoDict[YNode].Rank;

        if (XRank > YRank) {
            mNodeInfoDict[YNode].ParentNode = XNode;
            mNodeInfoDict[XNode].Size += mNodeInfoDict[YNode].Size;

            mNodeInfoDict[XNode].EdgeCnt++;
            mNodeInfoDict[XNode].EdgeCnt += mNodeInfoDict[YNode].EdgeCnt;

            mNodeInfoDict[XNode].NodeSet.UnionWith(mNodeInfoDict[YNode].NodeSet);
        }
        else {
            mNodeInfoDict[XNode].ParentNode = YNode;
            mNodeInfoDict[YNode].Size += mNodeInfoDict[XNode].Size;

            mNodeInfoDict[YNode].EdgeCnt++;
            mNodeInfoDict[YNode].EdgeCnt += mNodeInfoDict[XNode].EdgeCnt;
            mNodeInfoDict[YNode].NodeSet.UnionWith(mNodeInfoDict[XNode].NodeSet);

            if (XRank == YRank) {
                mNodeInfoDict[YNode].Rank++;
            }
        }
    }

    // ノードを引数として、木の根を取得
    internal long FindSet(long pTargetNode)
    {
        // 根までの経路上のノードのList
        var PathNodeList = new List<long>();

        long CurrNode = pTargetNode;
        while (CurrNode != mNodeInfoDict[CurrNode].ParentNode) {
            PathNodeList.Add(CurrNode);
            CurrNode = mNodeInfoDict[CurrNode].ParentNode;
        }

        // 経路圧縮 (親ポインタの付け替え)
        foreach (long EachPathNode in PathNodeList) {
            mNodeInfoDict[EachPathNode].ParentNode = CurrNode;
        }
        return CurrNode;
    }

    // ノードを引数として、木のサイズを取得
    internal long GetSize(long pNode)
    {
        long RootNode = FindSet(pNode);
        return mNodeInfoDict[RootNode].Size;
    }

    // ノードを引数として、木の枝数を取得
    internal long GetEdgeCnt(long pNode)
    {
        long RootNode = FindSet(pNode);
        return mNodeInfoDict[RootNode].EdgeCnt;
    }

    // ノードを引数として、色を取得
    internal long GetColor(long pNode)
    {
        long RootNode = FindSet(pNode);
        return mNodeInfoDict[RootNode].Color;
    }

    // ノードを引数として、NodeSetを取得
    internal HashSet<long> GetNodeSet(long pNode)
    {
        long RootNode = FindSet(pNode);
        return mNodeInfoDict[RootNode].NodeSet;
    }

    internal void DebugPrint()
    {
        foreach (var EachPair in mNodeInfoDict.OrderBy(pX => pX.Key)) {
            Console.WriteLine("mNodeInfoDict[{0}].ParentNode={1}",
                EachPair.Key, EachPair.Value.ParentNode);
        }
    }
}


解説

UnionFindの代表ノードに座標のHashSetとColorを持てるようにし、
UnionFindで4近傍と接続した木で考えてます。