第7回PAST N モノクロデザイン

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("2");
            WillReturn.Add("0 0 2 2");
            WillReturn.Add("1 1 3 3");
            //6
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("1");
            WillReturn.Add("-1000000000 -1000000000 1000000000 1000000000");
            //4000000000000000000
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static void Main()
    {
        List<string> InputList = GetInputList();
        long Result = Solve(InputList);
        Console.WriteLine(Result);
    }

    static long Solve(List<string> pInputList)
    {
        long[] wkArr = { };
        Action<string> SplitAct = pStr =>
            wkArr = pStr.Split(' ').Select(pX => long.Parse(pX)).ToArray();

        foreach (string EachStr in pInputList.Skip(1)) {
            SplitAct(EachStr);

            EventInfoDef WillAdd1;
            WillAdd1.IsAdd = true;
            WillAdd1.X = wkArr[0];
            WillAdd1.StaY = wkArr[1];
            WillAdd1.EndY = wkArr[3];
            mEventInfoList.Add(WillAdd1);

            EventInfoDef WillAdd2;
            WillAdd2.IsAdd = false;
            WillAdd2.X = wkArr[2];
            WillAdd2.StaY = wkArr[1];
            WillAdd2.EndY = wkArr[3];
            mEventInfoList.Add(WillAdd2);
        }

        // 登場する座標の先読み
        var PosSet = new HashSet<long>();
        mEventInfoList.ForEach(pX => PosSet.Add(pX.StaY));
        mEventInfoList.ForEach(pX => PosSet.Add(pX.EndY));

        Dictionary<long, long> ZaatuDict = DeriveZaatuDict(PosSet);
        var NodeDefList = new List<LazySegmentTree.NodeDef>();

        long[] KeysArr = ZaatuDict.Keys.ToArray();
        Array.Sort(KeysArr);
        long KeysArr_UB = KeysArr.GetUpperBound(0);
        for (long I = 0; I <= KeysArr_UB - 1; I++) {
            long CurrKey = KeysArr[I];
            long NextKey = KeysArr[I + 1];

            LazySegmentTree.NodeDef WillAdd;
            WillAdd.StaY = CurrKey;
            WillAdd.EndY = NextKey;
            WillAdd.BlackArea = 0;
            NodeDefList.Add(WillAdd);
        }

        mInsLazySegmentTree = new LazySegmentTree(NodeDefList.ToArray());

        long Answer = 0;

        long SegUB = ZaatuDict.Values.Max();

        mEventInfoList = mEventInfoList.OrderBy(pX => pX.X).ToList();
        int mEventInfoList_UB = mEventInfoList.Count - 1;
        for (int I = 0; I <= mEventInfoList_UB; I++) {
            EventInfoDef CurrEvent = mEventInfoList[I];
            long StaY = ZaatuDict[CurrEvent.StaY];
            long EndY = ZaatuDict[CurrEvent.EndY] - 1;
            mInsLazySegmentTree.Internal_RangeUpdate(StaY, EndY);

            // 次のクエリとX座標が違うなら集計
            if (I < mEventInfoList_UB) {
                long CurrX = CurrEvent.X;
                long NextX = mEventInfoList[I + 1].X;
                long XDiff = Math.Abs(CurrX - NextX);
                if (CurrX < NextX) {
                    long BlackArea = mInsLazySegmentTree.Internal_Query(0, SegUB).BlackArea;
                    long CurrAnswer = XDiff * BlackArea;
                    Answer += CurrAnswer;
                }
            }
        }
        return Answer;
    }

    struct EventInfoDef
    {
        internal bool IsAdd;
        internal long X;
        internal long StaY;
        internal long EndY;
    }
    static List<EventInfoDef> mEventInfoList = new List<EventInfoDef>();

    static LazySegmentTree mInsLazySegmentTree;

    //////////////////////////////////////////////////////////////////////////
    // 列挙を引数として、座標圧縮し、座圧後の値[座圧前の値]なDictを返す
    //////////////////////////////////////////////////////////////////////////
    static Dictionary<long, long> DeriveZaatuDict(IEnumerable<long> pEnum)
    {
        var ZaatuDict = new Dictionary<long, long>();
        var ValSet = new HashSet<long>(pEnum);
        long No = 0;
        foreach (long EachVal in ValSet.OrderBy(pX => pX)) {
            ZaatuDict[EachVal] = No;
            No++;
        }
        return ZaatuDict;
    }
}

#region LazySegmentTree
// LazySegmentTreeクラス (RSQ and RUQ)
internal class LazySegmentTree
{
    private NodeDef[] 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;

    private bool[] mLazyArr; // 遅延配列

    // ノードの情報
    internal struct NodeDef
    {
        internal long? StaY; // 開始Y座標
        internal long? EndY; // 終了Y座標
        internal long BlackArea; // 黒色の面積
    }

    // ノードの合併
    private NodeDef MergeNode(NodeDef pNode1, NodeDef pNode2)
    {
        NodeDef WillReturn;
        WillReturn.BlackArea = pNode1.BlackArea + pNode2.BlackArea;
        if (pNode1.StaY.HasValue && pNode2.EndY.HasValue) {
            WillReturn.StaY = pNode1.StaY;
            WillReturn.EndY = pNode2.EndY;
        }
        else if (pNode1.StaY.HasValue && pNode2.EndY.HasValue == false) {
            WillReturn.StaY = pNode1.StaY;
            WillReturn.EndY = pNode1.EndY;
        }
        else if (pNode1.StaY.HasValue == false && pNode2.EndY.HasValue) {
            WillReturn.StaY = pNode2.StaY;
            WillReturn.EndY = pNode2.EndY;
        }
        else {
            WillReturn.StaY = null;
            WillReturn.EndY = null;
        }
        return WillReturn;
    }

    // ノードの反転
    private NodeDef RevNode(NodeDef pNode)
    {
        NodeDef WillReturn;
        WillReturn.StaY = pNode.StaY;
        WillReturn.EndY = pNode.EndY;

        if (pNode.StaY.HasValue && pNode.EndY.HasValue) {
            WillReturn.BlackArea = (pNode.EndY.Value - pNode.StaY.Value) - pNode.BlackArea;
        }
        else {
            WillReturn.BlackArea = 0;
        }
        return WillReturn;
    }

    // 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 LazySegmentTree(NodeDef[] pNodeDefArr)
    {
        mExternalArrUB = pNodeDefArr.GetUpperBound(0);

        // 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 (pNodeDefArr.GetUpperBound(0) + 1 < mLeafCnt) break;
        }

        UB = ArrLength - 1;

        // 遅延配列を初期化
        mLazyArr = new bool[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;
        }

        // 葉ノードのIndのList
        var AllLeafIndList = new List<long>();
        var UseLeafIndList = new List<long>();
        for (long I = 0; I <= UB; I++) {
            if (mRangeInfo[I].StaInd == mRangeInfo[I].EndInd) {
                AllLeafIndList.Add(I);
            }
        }
        long UseCnt = mExternalArrUB + 1;
        UseLeafIndList = AllLeafIndList.Take((int)UseCnt).ToList();

        // ノードの値の初期設定
        var UseLeafSet = new HashSet<long>(UseLeafIndList);

        mTreeNodeArr = new NodeDef[UB + 1];
        long CurrInd = pNodeDefArr.GetUpperBound(0);
        long MinLeaf = UseLeafSet.Min();
        for (long I = UB; 0 <= I; I--) {
            if (UseLeafSet.Contains(I)) {
                mTreeNodeArr[I] = pNodeDefArr[CurrInd];
                CurrInd--;
            }
            else {
                if (MinLeaf > I) {
                    long ChildNode1 = DeriveChildNode(I);
                    long ChildNode2 = ChildNode1 + 1;
                    mTreeNodeArr[I] = MergeNode(mTreeNodeArr[ChildNode1], mTreeNodeArr[ChildNode2]);
                }
            }
        }
    }

    // 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;
    }

    // カレントノードを引数として、遅延評価を行う
    private void LazyEval(long pCurrNode)
    {
        // 遅延配列が空なら何もしない
        if (mLazyArr[pCurrNode] == false) return;

        // 白黒反転を行う
        mTreeNodeArr[pCurrNode] = RevNode(mTreeNodeArr[pCurrNode]);

        long ChildNode1 = DeriveChildNode(pCurrNode);
        long ChildNode2 = ChildNode1 + 1;

        if (ChildNode1 <= UB) mLazyArr[ChildNode1] = (mLazyArr[ChildNode1] == false);
        if (ChildNode2 <= UB) mLazyArr[ChildNode2] = (mLazyArr[ChildNode2] == false);

        // 伝播が終わったので、自ノードの遅延配列をfalseにする
        mLazyArr[pCurrNode] = false;
    }

    // 開始添字と終了添字とカレントノードを引数として、区間反転を行う
    internal void Internal_RangeUpdate(long pSearchStaInd, long pSearchEndInd)
    {
        Private_RangeUpdate(pSearchStaInd, pSearchEndInd, 0);
    }
    private void Private_RangeUpdate(long pSearchStaInd, long pSearchEndInd, long pCurrNode)
    {
        // カレントノードの遅延評価を行う
        LazyEval(pCurrNode);

        long CurrNodeStaInd = mRangeInfo[pCurrNode].StaInd;
        long CurrNodeEndInd = mRangeInfo[pCurrNode].EndInd;

        // OverLapしてなければ、何もしない
        if (CurrNodeEndInd < pSearchStaInd || pSearchEndInd < CurrNodeStaInd) {
            return;
        }

        // 完全に含んでいれば、遅延配列に値を入れた後に評価
        if (pSearchStaInd <= CurrNodeStaInd && CurrNodeEndInd <= pSearchEndInd) {
            mLazyArr[pCurrNode] = (mLazyArr[pCurrNode] == false);
            LazyEval(pCurrNode);
            return;
        }

        // そうでなければ、2つの区間に再帰呼出し
        long ChildNode1 = DeriveChildNode(pCurrNode);
        long ChildNode2 = ChildNode1 + 1;

        Private_RangeUpdate(pSearchStaInd, pSearchEndInd, ChildNode1);
        Private_RangeUpdate(pSearchStaInd, pSearchEndInd, ChildNode2);
        mTreeNodeArr[pCurrNode] = MergeNode(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、NodeDefを返す
    internal NodeDef Internal_Query(long pSearchStaInd, long pSearchEndInd)
    {
        return Private_Query(pSearchStaInd, pSearchEndInd, 0);
    }
    internal NodeDef Private_Query(long pSearchStaInd, long pSearchEndInd, long pCurrNode)
    {
        // 該当ノードを遅延評価する
        LazyEval(pCurrNode);

        long CurrNodeStaInd = mRangeInfo[pCurrNode].StaInd;
        long CurrNodeEndInd = mRangeInfo[pCurrNode].EndInd;

        // OverLapしてなければ、単位元
        if (CurrNodeEndInd < pSearchStaInd || pSearchEndInd < CurrNodeStaInd) {
            NodeDef WillReturn;
            WillReturn.StaY = null;
            WillReturn.EndY = null;
            WillReturn.BlackArea = 0;
            return WillReturn;
        }

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

        NodeDef ChildVal1 = Private_Query(pSearchStaInd, pSearchEndInd, ChildNode1);
        NodeDef ChildVal2 = Private_Query(pSearchStaInd, pSearchEndInd, ChildNode2);
        return MergeNode(ChildVal1, ChildVal2);
    }

}
#endregion

解説

遅延セグ木を拡張して区間反転できるようにしてから、
平面走査とイベントソートで解いてます。