第12回PAST K 連結チェック

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("5 3");
            WillReturn.Add("1 3");
            WillReturn.Add("2 3");
            WillReturn.Add("4 5");
            WillReturn.Add("4");
            WillReturn.Add("1 1 4");
            WillReturn.Add("3 1 5");
            WillReturn.Add("2 2 3");
            WillReturn.Add("3 1 5");
            //Yes
            //Yes
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("5 2");
            WillReturn.Add("1 3");
            WillReturn.Add("2 4");
            WillReturn.Add("2");
            WillReturn.Add("2 2 4");
            WillReturn.Add("2 1 3");
            //
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static long mN;
    static long mM;

    static HashSet<long> mEdgeHashSet = new HashSet<long>();

    class QueryInfoDef
    {
        internal long Type;
        internal long FromNode;
        internal long ToNode;
        internal string Answer;
    }
    static List<QueryInfoDef> mQueryInfoList = new List<QueryInfoDef>();

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

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

        SplitAct(InputList[0]);
        mN = wkArr[0];
        mM = wkArr[1];

        foreach (string EachStr in InputList.Skip(1).Take((int)mM)) {
            SplitAct(EachStr);
            long FromNode = wkArr[0];
            long ToNode = wkArr[1];
            long Hash = GetEdgeHash(FromNode, ToNode);
            mEdgeHashSet.Add(Hash);
        }

        foreach (string EachStr in InputList.Skip(1 + (int)mM + 1)) {
            SplitAct(EachStr);
            var WillAdd = new QueryInfoDef();
            WillAdd.Type = wkArr[0];
            WillAdd.FromNode = wkArr[1];
            WillAdd.ToNode = wkArr[2];
            mQueryInfoList.Add(WillAdd);
        }

        foreach (QueryInfoDef EachQueryInfo in mQueryInfoList) {
            long FromNode = EachQueryInfo.FromNode;
            long ToNode = EachQueryInfo.ToNode;
            long Hash = GetEdgeHash(FromNode, ToNode);
            if (EachQueryInfo.Type == 1) {
                mEdgeHashSet.Add(Hash);
            }
            if (EachQueryInfo.Type == 2) {
                mEdgeHashSet.Remove(Hash);
            }
        }

        UnionFind InsUnionFind = InitUnionFind();

        int UB = mQueryInfoList.Count - 1;
        for (int I = UB; 0 <= I; I--) {
            long Type = mQueryInfoList[I].Type;
            long FromNode = mQueryInfoList[I].FromNode;
            long ToNode = mQueryInfoList[I].ToNode;
            long Hash = GetEdgeHash(FromNode, ToNode);

            // 辺の追加のキャンセル
            if (Type == 1) {
                mEdgeHashSet.Remove(Hash);
                InsUnionFind = InitUnionFind();
            }

            // 辺の削除のキャンセル
            if (Type == 2) {
                mEdgeHashSet.Add(Hash);
                InsUnionFind.Unite(FromNode, ToNode);
            }

            if (Type == 3) {
                long Root1 = InsUnionFind.FindSet(FromNode);
                long Root2 = InsUnionFind.FindSet(ToNode);

                if (Root1 == Root2) {
                    mQueryInfoList[I].Answer = "Yes";
                }
                else {
                    mQueryInfoList[I].Answer = "No";
                }
            }
        }

        foreach (QueryInfoDef EachQueryInfo in mQueryInfoList) {
            if (EachQueryInfo.Type == 3) {
                Console.WriteLine(EachQueryInfo.Answer);
            }
        }
    }

    // UnionFindクラスを初期構築して返す
    static UnionFind InitUnionFind()
    {
        var InsUnionFind = new UnionFind();
        for (long I = 1; I <= mN; I++) {
            InsUnionFind.MakeSet(I);
        }

        foreach (long EachHash in mEdgeHashSet) {
            long FromNode = EachHash / Geta;
            long ToNode = EachHash % Geta;
            InsUnionFind.Unite(FromNode, ToNode);
        }
        return InsUnionFind;
    }

    const long Geta = 1000000;

    static long GetEdgeHash(long pFromNode, long pToNode)
    {
        long MinNode = Math.Min(pFromNode, pToNode);
        long MaxNode = Math.Max(pFromNode, pToNode);

        return MinNode * Geta + MaxNode;
    }
}

#region UnionFind
// UnionFindクラス
internal class UnionFind
{
    private class NodeInfoDef
    {
        internal long ParentNode;
        internal long Rank;
    }
    private Dictionary<long, NodeInfoDef> mNodeInfoDict =
        new Dictionary<long, NodeInfoDef>();

    // 要素が1つである木を森に追加
    internal void MakeSet(long pNode)
    {
        NodeInfoDef WillAdd = new NodeInfoDef();
        WillAdd.ParentNode = pNode;
        WillAdd.Rank = 0;
        mNodeInfoDict[pNode] = WillAdd;
    }

    // 合併処理
    internal void Unite(long pX, long pY)
    {
        long XNode = FindSet(pX);
        long YNode = FindSet(pY);
        long XRank = mNodeInfoDict[XNode].Rank;
        long YRank = mNodeInfoDict[YNode].Rank;

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

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

解説

UnionFindでは、
連結は高速ですが、
切断は時間がかかるので、
クエリを逆から処理し、切断の回数を減らしてます。

切断時のUnionFindの再構築に備えて、
現在の枝をHashSetで管理してます。