ABC463-E Roads and Gates

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("7 7 3");
            WillReturn.Add("1 2 1");
            WillReturn.Add("1 3 6");
            WillReturn.Add("2 3 4");
            WillReturn.Add("3 5 8");
            WillReturn.Add("3 7 4");
            WillReturn.Add("4 5 2");
            WillReturn.Add("4 7 9");
            WillReturn.Add("3 1 4 1 5 9 2");
            //1 5 6 8 14 7
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("2 0 1000000000");
            WillReturn.Add("1000000000 1000000000");
            //3000000000
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("12 20 873");
            WillReturn.Add("2 7 940");
            WillReturn.Add("6 9 444");
            WillReturn.Add("6 11 809");
            WillReturn.Add("7 8 786");
            WillReturn.Add("9 10 468");
            WillReturn.Add("7 10 234");
            WillReturn.Add("6 10 660");
            WillReturn.Add("4 12 939");
            WillReturn.Add("8 10 896");
            WillReturn.Add("1 11 953");
            WillReturn.Add("8 10 818");
            WillReturn.Add("4 8 967");
            WillReturn.Add("3 9 724");
            WillReturn.Add("6 7 929");
            WillReturn.Add("3 4 948");
            WillReturn.Add("1 3 999");
            WillReturn.Add("10 11 724");
            WillReturn.Add("7 10 338");
            WillReturn.Add("1 8 967");
            WillReturn.Add("1 12 733");
            WillReturn.Add("581 978 950 629 583 729 554 712 438 930 774 279");
            //2432 999 1672 2037 1762 1753 967 1723 1677 953 733
        }
        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 mN;
    static long mM;
    static long mY;

    struct EdgeInfoDef
    {
        internal long ToNode;
        internal long Cost;
    }
    static Dictionary<long, List<EdgeInfoDef>> mEdgeInfoListDict = new Dictionary<long, List<EdgeInfoDef>>();

    static void Main()
    {
        List<string> InputList = GetInputList();
        long[] wkArr = GetSplitArr(InputList[0]);
        mN = wkArr[0];
        mM = wkArr[1];
        mY = wkArr[2];

        Action<string> SplitAct = (pStr) => wkArr = GetSplitArr(pStr);

        for (long I = 1; I <= mN; I++) {
            mEdgeInfoListDict[I] = new List<EdgeInfoDef>();
        }

        foreach (string EachStr in InputList.Skip(1).Take((int)mM)) {
            SplitAct(EachStr);
            long FromNode = wkArr[0];
            long ToNode = wkArr[1];
            long Cost = wkArr[2];

            Action<long, long> AddAct = (pNode1, pNode2) =>
            {
                EdgeInfoDef WillAdd;
                WillAdd.ToNode = pNode2;
                WillAdd.Cost = Cost;
                mEdgeInfoListDict[pNode1].Add(WillAdd);
            };
            AddAct(FromNode, ToNode); // 正方向の辺
            AddAct(ToNode, FromNode); // 逆方向の辺
        }

        // 超頂点
        long SuperNode = mN + 1;
        mEdgeInfoListDict[SuperNode] = new List<EdgeInfoDef>();
        long[] XArr = GetSplitArr(InputList.Last());
        for (long I = 0; I <= XArr.GetUpperBound(0); I++) {
            EdgeInfoDef WillAdd1;
            WillAdd1.ToNode = SuperNode;
            WillAdd1.Cost = XArr[I] + mY;
            mEdgeInfoListDict[I + 1].Add(WillAdd1);

            EdgeInfoDef WillAdd2;
            WillAdd2.ToNode = I + 1;
            WillAdd2.Cost = XArr[I];
            mEdgeInfoListDict[SuperNode].Add(WillAdd2);
        }

        Dijkstra(1);
    }

    // ダイクストラ法で、各ノードまでの最短距離を求める
    static void Dijkstra(long pStaNode)
    {
        var InsPQueue = new PQueue_Arr();

        // 距離合計[確定ノード]なDict
        var KakuteiNodeDict = new Dictionary<long, long>();
        KakuteiNodeDict.Add(pStaNode, 0);

        // Enqueue処理
        Action<long> EnqueueAct = pFromNode =>
        {
            if (mEdgeInfoListDict.ContainsKey(pFromNode) == false) {
                return;
            }
            foreach (EdgeInfoDef EachEdge in mEdgeInfoListDict[pFromNode]) {
                // 確定ノードならContinue
                if (KakuteiNodeDict.ContainsKey(EachEdge.ToNode)) continue;

                long wkSumCost = KakuteiNodeDict[pFromNode] + EachEdge.Cost;

                PQueue_Arr.PQueueJyoutaiDef WillEnqueue;
                WillEnqueue.Node = EachEdge.ToNode;
                WillEnqueue.SumCost = wkSumCost;
                InsPQueue.Enqueue(WillEnqueue);
            }
        };
        EnqueueAct(pStaNode);

        while (InsPQueue.IsEmpty() == false) {
            PQueue_Arr.PQueueJyoutaiDef Dequeued = InsPQueue.Dequeue();

            // 確定ノードならcontinue
            if (KakuteiNodeDict.ContainsKey(Dequeued.Node)) continue;

            // 枝切り
            // if (KakuteiNodeDict.ContainsKey(pGoalNode)) break;

            KakuteiNodeDict.Add(Dequeued.Node, Dequeued.SumCost);
            EnqueueAct(Dequeued.Node);
        }

        var AnswerList = new List<long>();
        for (int I = 2; I <= mN; I++) {
            AnswerList.Add(KakuteiNodeDict[I]);
        }
        Console.WriteLine(LongEnumJoin(" ", AnswerList));
    }

    // 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 LongEnumJoin(string pSeparater, IEnumerable<long> pEnum)
    {
        string[] StrArr = Array.ConvertAll(pEnum.ToArray(), pX => pX.ToString());
        return string.Join(pSeparater, StrArr);
    }
}

#region PQueue_Arr
// 内部で配列使用の優先度付きキュー
internal class PQueue_Arr
{
    internal struct PQueueJyoutaiDef
    {
        internal long Node;
        internal long SumCost;
    }

    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;
    }

    // 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].SumCost > mHeapArr[CurrNode].SumCost) {
            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].SumCost;
        long SmallestNode = pRootNode;

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

        // 子ノードのほうが大きい場合
        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

解説

Nノードあると
ワープ辺は、N*N本ありますが、
超頂点を作ることで、ワープ辺を N*Nから 2*Nに減らすとができ、
ダイクストラ法で解くことができます。