AOJ 0526 Boat Travel

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("3 8");
            WillReturn.Add("1 3 1 10");
            WillReturn.Add("0 2 3");
            WillReturn.Add("1 2 3 20");
            WillReturn.Add("1 1 2 5");
            WillReturn.Add("0 3 2");
            WillReturn.Add("1 1 3 7");
            WillReturn.Add("1 2 1 9");
            WillReturn.Add("0 2 3");
            WillReturn.Add("5 16");
            WillReturn.Add("1 1 2 343750");
            WillReturn.Add("1 1 3 3343");
            WillReturn.Add("1 1 4 347392");
            WillReturn.Add("1 1 5 5497");
            WillReturn.Add("1 2 3 123394");
            WillReturn.Add("1 2 4 545492");
            WillReturn.Add("1 2 5 458");
            WillReturn.Add("1 3 4 343983");
            WillReturn.Add("1 3 5 843468");
            WillReturn.Add("1 4 5 15934");
            WillReturn.Add("0 2 1");
            WillReturn.Add("0 4 1");
            WillReturn.Add("0 3 2");
            WillReturn.Add("0 4 2");
            WillReturn.Add("0 4 3");
            WillReturn.Add("0 5 3");
            WillReturn.Add("0 0");
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

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

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

        long CurrInd = 0;
        while (true) {
            SplitAct(InputList[(int)CurrInd]);

            long N = wkArr[0];
            long M = wkArr[1];
            if (N == 0 && M == 0) break;

            string[] InputArr = InputList.Skip((int)CurrInd).Take(1 + (int)M).ToArray();
            Solve(InputArr);

            CurrInd += M + 1;
        }
    }

    static long mN;

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

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

        SplitAct(pInputArr[0]);

        mN = wkArr[0];
        mEdgeInfoListDict.Clear();

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

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

            long Type = wkArr[0];

            if (Type == 0) {
                long StaNode = wkArr[1];
                long GoalNode = wkArr[2];

                Dictionary<long, long> Result = Dijkstra(StaNode, GoalNode);
                if (Result.ContainsKey(GoalNode)) {
                    Console.WriteLine(Result[GoalNode]);
                }
                else {
                    Console.WriteLine(-1);
                }
            }
            if (Type == 1) {
                long FromNode = wkArr[1];
                long ToNode = wkArr[2];
                long Cost = wkArr[3];
                mEdgeInfoListDict[FromNode].Add(new EdgeInfoDef() { ToNode = ToNode, Cost = Cost });
                mEdgeInfoListDict[ToNode].Add(new EdgeInfoDef() { ToNode = FromNode, Cost = Cost });
            }
        }
    }

    // ダイクストラ法で、各ノードまでの最短距離を求める
    static Dictionary<long, long> Dijkstra(long pStaNode, long pGoalNode)
    {
        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);
        }

        return KakuteiNodeDict;
    }
}

#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

logを無視すると、
ダイクストラ法の計算量は、O(E+V)です。

ノードが100で辺が5000で、
ダイクストラ法を5000回実行するとしても、
5000*5000 = 25000000
で間に合います。