ABC394-E Palindromic Shortest Path

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");
            WillReturn.Add("ab--");
            WillReturn.Add("--b-");
            WillReturn.Add("---a");
            WillReturn.Add("c---");
            //0 1 2 4
            //-1 0 1 -1
            //3 -1 0 1
            //1 -1 -1 0
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("5");
            WillReturn.Add("us---");
            WillReturn.Add("-st--");
            WillReturn.Add("--s--");
            WillReturn.Add("u--s-");
            WillReturn.Add("---ts");
            //0 1 3 -1 -1
            //-1 0 1 -1 -1
            //-1 -1 0 -1 -1
            //1 3 -1 0 -1
            //-1 -1 5 1 0
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    struct EdgeInfoDef
    {
        internal int ToNode;
        internal char Moji;
    }
    static Dictionary<int, List<EdgeInfoDef>> mSeiEdgeInfoListDict =
        new Dictionary<int, List<EdgeInfoDef>>();

    static Dictionary<int, HashSet<int>> mNodeSetDict = new Dictionary<int, HashSet<int>>();

    static Dictionary<char, Dictionary<int, List<int>>> mRevListDictDict =
        new Dictionary<char, Dictionary<int, List<int>>>();

    static void Main()
    {
        List<string> InputList = GetInputList();
        int NodeCnt = int.Parse(InputList[0]);
        int UB = NodeCnt - 1;
        char[,] BanArr = CreateBanArr(InputList.Skip(1));

        for (int Y = 0; Y <= UB; Y++) {
            for (int X = 0; X <= UB; X++) {
                if (BanArr[X, Y] == '-') continue;

                int FromNode = Y;
                int ToNode = X;

                if (mSeiEdgeInfoListDict.ContainsKey(FromNode) == false) {
                    mSeiEdgeInfoListDict[FromNode] = new List<EdgeInfoDef>();
                }
                EdgeInfoDef WillAdd1;
                WillAdd1.ToNode = ToNode;
                WillAdd1.Moji = BanArr[X, Y];
                mSeiEdgeInfoListDict[FromNode].Add(WillAdd1);

                if (mNodeSetDict.ContainsKey(FromNode) == false) {
                    mNodeSetDict[FromNode] = new HashSet<int>();
                }
                mNodeSetDict[FromNode].Add(ToNode);

                // 逆辺も作る
                char CurrMoji = BanArr[X, Y];
                if (mRevListDictDict.ContainsKey(CurrMoji) == false) {
                    mRevListDictDict[CurrMoji] = new Dictionary<int, List<int>>();
                }
                if (mRevListDictDict[CurrMoji].ContainsKey(ToNode) == false) {
                    mRevListDictDict[CurrMoji][ToNode] = new List<int>();
                }
                mRevListDictDict[CurrMoji][ToNode].Add(FromNode);
            }
        }

        var sb = new System.Text.StringBuilder();
        for (int Y = 0; Y <= UB; Y++) {
            var AnswerList = new List<int>();
            for (int X = 0; X <= UB; X++) {
                int CurrAnswer = DeriveAnswer(Y, X);
                AnswerList.Add(CurrAnswer);
            }
            sb.AppendLine(IntEnumJoin(" ", AnswerList));
        }
        Console.Write(sb.ToString());
    }

    // セパレータとLong型の列挙を引数として、結合したstringを返す
    static string IntEnumJoin(string pSeparater, IEnumerable<int> pEnum)
    {
        string[] StrArr = Array.ConvertAll(pEnum.ToArray(), pX => pX.ToString());
        return string.Join(pSeparater, StrArr);
    }

    // FromNodeとToNodeを引数として、解を返す
    static Dictionary<int, int> mMemo = new Dictionary<int, int>();
    static int DeriveAnswer(int pFromNode, int pToNode)
    {
        int CallHash = GetHash(pFromNode, pToNode);
        if (pFromNode == pToNode) {
            return 0;
        }

        var Que = new Queue<JyoutaiDef>();
        JyoutaiDef WillEnq;
        WillEnq.Node1 = pFromNode;
        WillEnq.Node2 = pToNode;
        WillEnq.Level = 0;

        Que.Enqueue(WillEnq);

        bool HasAnswer = false;
        int Answer = int.MaxValue;

        var VisitedSet = new HashSet<int>();

        while (Que.Count > 0) {
            JyoutaiDef Deq = Que.Dequeue();

            if (Answer <= Deq.Level) continue;

            if (Deq.Node1 == Deq.Node2) {
                HasAnswer = true;
                Answer = Math.Min(Answer, Deq.Level);
                continue;
            }

            if (mNodeSetDict.ContainsKey(Deq.Node1)) {
                if (mNodeSetDict[Deq.Node1].Contains(Deq.Node2)) {
                    HasAnswer = true;
                    Answer = Math.Min(Answer, Deq.Level + 1);
                    continue;
                }
            }

            // メモを使って定数倍改善
            int CurrHash = GetHash(Deq.Node1, Deq.Node2);
            if (mMemo.ContainsKey(CurrHash)) {
                if (mMemo[CurrHash] == -1) {
                    continue;
                }
                HasAnswer = true;
                Answer = Math.Min(Answer, Deq.Level + mMemo[CurrHash]);
                continue;
            }

            if (mSeiEdgeInfoListDict.ContainsKey(Deq.Node1)) {
                foreach (EdgeInfoDef EachEdge1 in mSeiEdgeInfoListDict[Deq.Node1]) {
                    if (mRevListDictDict.ContainsKey(EachEdge1.Moji)) {
                        if (mRevListDictDict[EachEdge1.Moji].ContainsKey(Deq.Node2)) {
                            foreach (int EachNode2 in mRevListDictDict[EachEdge1.Moji][Deq.Node2]) {
                                int NewNode1 = EachEdge1.ToNode;
                                int NewNode2 = EachNode2;
                                int Hash = GetHash(NewNode1, NewNode2);

                                if (VisitedSet.Add(Hash)) {
                                    WillEnq.Node1 = NewNode1;
                                    WillEnq.Node2 = NewNode2;
                                    WillEnq.Level = Deq.Level + 2;
                                    Que.Enqueue(WillEnq);
                                }
                            }
                        }
                    }
                }
            }
        }

        if (HasAnswer == false) {
            return mMemo[CallHash] = -1;
        }
        else {
            return mMemo[CallHash] = Answer;
        }
    }

    static int GetHash(int pNode1, int pNode2)
    {
        int Hash = pNode1 * 1000 + pNode2;
        return Hash;
    }

    struct JyoutaiDef
    {
        internal int Node1;
        internal int Node2;
        internal int Level;
    }

    ////////////////////////////////////////////////////////////////
    // IEnumerable<string>をcharの2次元配列に設定
    ////////////////////////////////////////////////////////////////
    static char[,] CreateBanArr(IEnumerable<string> pStrEnum)
    {
        var StrList = pStrEnum.ToList();
        if (StrList.Count == 0) {
            return new char[0, 0];
        }
        int UB_X = StrList[0].Length - 1;
        int UB_Y = StrList.Count - 1;

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

        for (int Y = 0; Y <= UB_Y; Y++) {
            for (int X = 0; X <= UB_X; X++) {
                WillReturn[X, Y] = StrList[Y][X];
            }
        }
        return WillReturn;
    }
}

解説

回文なので双方向探索なBFSを繰り返してます。
BFSの結果は、メモして再利用できるタイミングで再利用してます。