ABC233-F Swap and Sort

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("6");
            WillReturn.Add("5 3 2 4 6 1");
            WillReturn.Add("4");
            WillReturn.Add("1 5");
            WillReturn.Add("5 6");
            WillReturn.Add("1 2");
            WillReturn.Add("2 3");
            //3
            //4 2 1
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("5");
            WillReturn.Add("3 4 1 2 5");
            WillReturn.Add("2");
            WillReturn.Add("1 3");
            WillReturn.Add("2 5");
            //-1
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("4");
            WillReturn.Add("1 2 3 4");
            WillReturn.Add("6");
            WillReturn.Add("1 2");
            WillReturn.Add("1 3");
            WillReturn.Add("1 4");
            WillReturn.Add("2 3");
            WillReturn.Add("2 4");
            WillReturn.Add("3 4");
            //0
            //
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static int mN;

    struct EdgeInfoDef
    {
        internal int EdgeID; // 答えで、枝番号を出力する必要あり
        internal int ToNode;
    }

    // 隣接リスト
    static Dictionary<int, List<EdgeInfoDef>> mToNodeListDict = new Dictionary<int, List<EdgeInfoDef>>();

    static int[] mPArr;

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

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

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

        var InsUnionFind = new UnionFind();
        for (int I = 0; I <= mN - 1; I++) {
            InsUnionFind.MakeSet(I);
        }

        mPArr = InputList[1].Split(' ').Select(pX => int.Parse(pX)).ToArray();
        for (int I = 0; I <= mPArr.GetUpperBound(0); I++) {
            mPArr[I]--;
        }

        int CurrEdgeID = 0;
        foreach (string EachStr in InputList.Skip(3)) {
            CurrEdgeID++;
            SplitAct(EachStr);
            int CurrFromNode = wkArr[0] - 1;
            int CurrToNode = wkArr[1] - 1;

            // サイクルになる枝は、接続しない
            int Root1 = InsUnionFind.FindSet(CurrFromNode);
            int Root2 = InsUnionFind.FindSet(CurrToNode);
            if (Root1 == Root2) continue;
            InsUnionFind.Unite(CurrFromNode, CurrToNode);

            if (mToNodeListDict.ContainsKey(CurrFromNode) == false) {
                mToNodeListDict[CurrFromNode] = new List<EdgeInfoDef>();
            }
            if (mToNodeListDict.ContainsKey(CurrToNode) == false) {
                mToNodeListDict[CurrToNode] = new List<EdgeInfoDef>();
            }
            mToNodeListDict[CurrFromNode].Add(
                new EdgeInfoDef() { EdgeID = CurrEdgeID, ToNode = CurrToNode });
            mToNodeListDict[CurrToNode].Add(
                new EdgeInfoDef() { EdgeID = CurrEdgeID, ToNode = CurrFromNode });
        }
        Solve();
    }

    static void Solve()
    {
        var AnswerList = new List<int>();
        while (true) {
            // 枝が全部なくなるまで無限ループ
            if (mToNodeListDict.Count == 0) {
                break;
            }

            // 任意の葉ノードを探す
            int LeafNode = -1;
            int LeafNodeConnNode = -1;
            foreach (var EachPair in mToNodeListDict) {
                if (EachPair.Value.Count == 1) {
                    LeafNode = EachPair.Key;
                    LeafNodeConnNode = EachPair.Value[0].ToNode;
                    break;
                }
            }

            // 葉ノードから該当値をDFSで探して、経路上の値交換を行う
            bool IsOK;
            List<int> EdgeIDList = DFS(LeafNode, out IsOK);
            if (IsOK == false) {
                Console.WriteLine(-1);
                return;
            }
            AnswerList.AddRange(EdgeIDList);

            // 葉ノードに接続する枝を削除
            mToNodeListDict.Remove(LeafNode);
            mToNodeListDict[LeafNodeConnNode].RemoveAll(pX => pX.ToNode == LeafNode);
            if (mToNodeListDict[LeafNodeConnNode].Count == 0) {
                mToNodeListDict.Remove(LeafNodeConnNode);
            }
        }

        Console.WriteLine(AnswerList.Count);
        string[] AnswerStr = Array.ConvertAll(AnswerList.ToArray(), pX => pX.ToString());
        Console.WriteLine(string.Join(" ", AnswerStr));
    }

    struct JyoutaiDef
    {
        internal int CurrInd;
        internal List<int> EdgeIDList;
        internal List<int> CurrIndList;
    }

    static List<int> DFS(int pLeafNode, out bool pIsOK)
    {
        pIsOK = true;
        var Stk = new Stack<JyoutaiDef>();
        JyoutaiDef WillPush;
        WillPush.CurrInd = pLeafNode;
        WillPush.EdgeIDList = new List<int>();
        WillPush.CurrIndList = new List<int>();
        WillPush.CurrIndList.Add(WillPush.CurrInd);
        Stk.Push(WillPush);

        int GoalInd = Array.IndexOf(mPArr, pLeafNode);

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

            // クリア判定
            if (Popped.CurrInd == GoalInd) {

                // 逆順にする
                Popped.EdgeIDList.Reverse();

                // 配列の交換を行う
                for (int I = Popped.CurrIndList.Count - 1; 1 <= I; I--) {
                    int Ind1 = Popped.CurrIndList[I];
                    int Ind2 = Popped.CurrIndList[I - 1];

                    // 三角交換
                    int Saved = mPArr[Ind1];
                    mPArr[Ind1] = mPArr[Ind2];
                    mPArr[Ind2] = Saved;
                }
                return Popped.EdgeIDList;
            }

            if (mToNodeListDict.ContainsKey(Popped.CurrInd) == false) {
                continue;
            }
            foreach (EdgeInfoDef EachEdgeInfo in mToNodeListDict[Popped.CurrInd]) {
                // 再訪防止
                if (Popped.CurrIndList.Contains(EachEdgeInfo.ToNode)) continue;

                WillPush.CurrInd = EachEdgeInfo.ToNode;
                WillPush.EdgeIDList = new List<int>(Popped.EdgeIDList);
                WillPush.EdgeIDList.Add(EachEdgeInfo.EdgeID);

                WillPush.CurrIndList = new List<int>(Popped.CurrIndList);
                WillPush.CurrIndList.Add(EachEdgeInfo.ToNode);

                Stk.Push(WillPush);
            }
        }
        pIsOK = false;
        return null;
    }
}

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

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

    // 合併処理
    internal void Unite(int pX, int pY)
    {
        int XNode = FindSet(pX);
        int YNode = FindSet(pY);
        int XRank = mNodeInfoDict[XNode].Rank;
        int 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 int FindSet(int pTargetNode)
    {
        // 根までの経路上のノードのList
        var PathNodeList = new List<int>();

        int 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 (int EachPathNode in PathNodeList) {
            NodeInfoDef wkNodeInfo = mNodeInfoDict[EachPathNode];
            wkNodeInfo.ParentNode = CurrNode;
            mNodeInfoDict[EachPathNode] = wkNodeInfo;
        }
        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

連結成分内でサイクルができると後が大変なので、
UnionFindを使って、全域木を作ります。

後は、全域木の葉ノードからDFSを行い、
バブルソートの要領で、値を交換していってます。