AOJ 0645 森林伐採

問題へのリンク(AOJ)
問題へのリンク(AtCoder)

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("2 3");
            WillReturn.Add("0 1 2");
            WillReturn.Add("3 4 5");
            //32
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("2 5");
            WillReturn.Add("0 5 0 0 0");
            WillReturn.Add("0 0 0 9 1");
            //13
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("2 5");
            WillReturn.Add("0 2 0 0 0");
            WillReturn.Add("0 0 0 9 1");
            //11
        }
        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);

        HashSet<long> GoalPosSet = DeriveGoalPosSet();

        var InsPQueue_Arr = new PQueue_Arr();
        PQueue_Arr.PQueueJyoutaiDef WillEnqueue;
        WillEnqueue.CurrX = 0;
        WillEnqueue.CurrY = 0;
        WillEnqueue.Kyori = 0;
        WillEnqueue.Cost = 0;
        InsPQueue_Arr.Enqueue(WillEnqueue);

        long Answer = long.MaxValue;

        var SegTreeDict = new Dictionary<long, SegmentTree>();
        for (long X = 0; X <= UB_X; X++) {
            for (long Y = 0; Y <= UB_Y; Y++) {
                SegTreeDict[GetHash(X, Y)] = new SegmentTree((UB_X + 1) * (UB_Y + 1), long.MaxValue);
            }
        }

        while (InsPQueue_Arr.Count() > 0) {
            PQueue_Arr.PQueueJyoutaiDef Deququed = InsPQueue_Arr.Dequeue();
            //Console.WriteLine("CurrX={0},CurrY={1},Kyori={2},Cost={3}",
            //    Deququed.CurrX, Deququed.CurrY, Deququed.Kyori, Deququed.Cost);

            long CurrPosHash = GetHash(Deququed.CurrX, Deququed.CurrY);

            if (Answer <= Deququed.Cost) {
                continue;
            }

            Action<long, long> EnqueueAct = (pNewX, pNewY) =>
            {
                if (pNewX < 0 || UB_X < pNewX) return;
                if (pNewY < 0 || UB_Y < pNewY) return;

                WillEnqueue.CurrX = pNewX;
                WillEnqueue.CurrY = pNewY;
                WillEnqueue.Kyori = Deququed.Kyori + 1;
                if (WillEnqueue.Kyori > (UB_X + 1) * (UB_Y + 1)) {
                    return;
                }

                long NewPosHash = GetHash(pNewX, pNewY);

                // クリア判定
                if (GoalPosSet.Contains(NewPosHash)) {
                    long AnswerKouho = Deququed.Cost + mBanArr[pNewX, pNewY];
                    AnswerKouho += (mBanArr[pNewX, pNewY] - 1) * Deququed.Kyori * 2; // 往復分
                    AnswerKouho += Deququed.Kyori; // 片道分
                    Answer = Math.Min(Answer, AnswerKouho);
                }
                else {
                    WillEnqueue.Cost = Deququed.Cost + mBanArr[pNewX, pNewY];
                    WillEnqueue.Cost += mBanArr[pNewX, pNewY] * Deququed.Kyori * 2 + 1;

                    // セグ木で枝切り
                    SegmentTree CurrSegTree = SegTreeDict[NewPosHash];
                    long RangeSta = 0;
                    long RangeEnd = WillEnqueue.Kyori;
                    long RangeMin = CurrSegTree.Internal_Query(RangeSta, RangeEnd);
                    if (RangeMin <= WillEnqueue.Cost) {
                        return;
                    }
                    CurrSegTree.Update(WillEnqueue.Kyori, WillEnqueue.Cost);
                    InsPQueue_Arr.Enqueue(WillEnqueue);
                }
            };

            EnqueueAct(Deququed.CurrX, Deququed.CurrY - 1);
            EnqueueAct(Deququed.CurrX, Deququed.CurrY + 1);
            EnqueueAct(Deququed.CurrX - 1, Deququed.CurrY);
            EnqueueAct(Deququed.CurrX + 1, Deququed.CurrY);
        }
        Console.WriteLine(Answer);
    }

    // ゴール座標のsetを返す
    static HashSet<long> DeriveGoalPosSet()
    {
        var GoalPosSet = new HashSet<long>();

        if (mBanArr[UB_X, UB_Y] != 0) {
            GoalPosSet.Add(GetHash(UB_X, UB_Y));
            return GoalPosSet;
        }

        var Stk = new Stack<JyoutaiDef>();
        JyoutaiDef WillPush;
        WillPush.CurrX = UB_X;
        WillPush.CurrY = UB_Y;
        Stk.Push(WillPush);

        var VisitedSet = new HashSet<long>();
        VisitedSet.Add(GetHash(UB_X, UB_Y));

        while (Stk.Count > 0) {
            JyoutaiDef Popped = Stk.Pop();

            Action<long, long> PushAct = (pNewX, pNewY) =>
            {
                if (pNewX < 0 || UB_X < pNewX) return;
                if (pNewY < 0 || UB_Y < pNewY) return;

                if (mBanArr[pNewX, pNewY] != 0) return;

                long CurrHash = GetHash(pNewX, pNewY);
                if (VisitedSet.Add(CurrHash)) {
                    WillPush.CurrX = pNewX;
                    WillPush.CurrY = pNewY;
                    Stk.Push(WillPush);
                }
            };

            PushAct(Popped.CurrX, Popped.CurrY - 1);
            PushAct(Popped.CurrX, Popped.CurrY + 1);
            PushAct(Popped.CurrX - 1, Popped.CurrY);
            PushAct(Popped.CurrX + 1, Popped.CurrY);
        }

        foreach (long EachPosHash in VisitedSet) {
            long CurrX = EachPosHash / 100;
            long CurrY = EachPosHash % 100;

            Action<long, long> AddAct = (pTargetX, pTargetY) =>
            {
                if (pTargetX < 0 || UB_X < pTargetX) return;
                if (pTargetY < 0 || UB_Y < pTargetY) return;

                if (mBanArr[pTargetX, pTargetY] == 0) return;

                long CurrHash = GetHash(pTargetX, pTargetY);
                GoalPosSet.Add(CurrHash);
            };
            AddAct(CurrX, CurrY - 1);
            AddAct(CurrX, CurrY + 1);
            AddAct(CurrX - 1, CurrY);
            AddAct(CurrX + 1, CurrY);
        }

        return GoalPosSet;
    }

    struct JyoutaiDef
    {
        internal long CurrX;
        internal long CurrY;
    }

    // 座標のハッシュ値を返す
    static long GetHash(long pX, long pY)
    {
        return pX * 100 + 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;
    }
}

#region PQueue_Arr
// 内部で配列使用の優先度付きキュー (根のValが最小)
internal class PQueue_Arr
{
    internal struct PQueueJyoutaiDef
    {
        internal long CurrX;
        internal long CurrY;
        internal long Kyori;
        internal long Cost;
    }

    private PQueueJyoutaiDef[] mHeapArr;
    private long mHeapArrCnt = 0;

    // コンストラクタ
    internal PQueue_Arr()
    {
        mHeapArr = new PQueueJyoutaiDef[65535];
    }

    internal bool IsEmpty()
    {
        return mHeapArrCnt == 0;
    }

    internal long Count()
    {
        return mHeapArrCnt;
    }

    internal long Peek()
    {
        return mHeapArr[1].Cost;
    }

    // エンキュー処理
    internal void Enqueue(PQueueJyoutaiDef pAddJyoutai)
    {
        long CurrNode = 1 + mHeapArrCnt;
        if (mHeapArr.GetUpperBound(0) < CurrNode) {
            ExtendArr();
        }

        mHeapArr[CurrNode] = pAddJyoutai;
        mHeapArrCnt++;

        while (1 < CurrNode && mHeapArr[CurrNode / 2].Cost > mHeapArr[CurrNode].Cost) {
            PQueueJyoutaiDef Swap = mHeapArr[CurrNode];
            mHeapArr[CurrNode] = mHeapArr[CurrNode / 2];
            mHeapArr[CurrNode / 2] = Swap;

            CurrNode /= 2;
        }
    }

    // 配列のExtend
    private void ExtendArr()
    {
        PQueueJyoutaiDef[] NewHeapArr = new PQueueJyoutaiDef[mHeapArrCnt * 2];
        mHeapArr.CopyTo(NewHeapArr, 0);
        mHeapArr = NewHeapArr;
    }

    // デキュー処理
    internal PQueueJyoutaiDef Dequeue()
    {
        PQueueJyoutaiDef TopNode = mHeapArr[1];
        long LastNode = mHeapArrCnt;
        mHeapArr[1] = mHeapArr[LastNode];
        mHeapArrCnt--;

        MinHeapify(1);
        return TopNode;
    }

    // 根ノードを指定し、根から葉へヒープ構築
    private void MinHeapify(long pRootNode)
    {
        if (mHeapArrCnt <= 1) {
            return;
        }

        long Left = pRootNode * 2;
        long Right = pRootNode * 2 + 1;

        // 左の子、自分、右の子で値が最小のノードを選ぶ
        long Smallest = mHeapArr[pRootNode].Cost;
        long SmallestNode = pRootNode;

        if (Left <= mHeapArrCnt && mHeapArr[Left].Cost < Smallest) {
            Smallest = mHeapArr[Left].Cost;
            SmallestNode = Left;
        }
        if (Right <= mHeapArrCnt && mHeapArr[Right].Cost < Smallest) {
            Smallest = mHeapArr[Right].Cost;
            SmallestNode = Right;
        }

        // 子ノードのほうが小さい場合
        if (SmallestNode != pRootNode) {
            PQueueJyoutaiDef Swap = mHeapArr[SmallestNode];
            mHeapArr[SmallestNode] = mHeapArr[pRootNode];
            mHeapArr[pRootNode] = Swap;

            // 再帰的に呼び出し
            MinHeapify(SmallestNode);
        }
    }
}
#endregion

#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;

    // 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

最初にゴールノードの候補をDFSで列挙してます。

それから、最良優先探索と
1点更新、区間最小値取得なセグ木での枝切りを組み合わせてます。