ABC340-D Super Takahashi Bros.

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");
            WillReturn.Add("100 200 3");
            WillReturn.Add("50 10 1");
            WillReturn.Add("100 200 5");
            WillReturn.Add("150 1 2");
            //350
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("10");
            WillReturn.Add("1000 10 9");
            WillReturn.Add("1000 10 10");
            WillReturn.Add("1000 10 2");
            WillReturn.Add("1000 10 3");
            WillReturn.Add("1000 10 4");
            WillReturn.Add("1000 10 5");
            WillReturn.Add("1000 10 6");
            WillReturn.Add("1000 10 7");
            WillReturn.Add("1000 10 8");
            //90
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("6");
            WillReturn.Add("1000000000 1000000000 1");
            WillReturn.Add("1000000000 1000000000 1");
            WillReturn.Add("1000000000 1000000000 1");
            WillReturn.Add("1000000000 1000000000 1");
            WillReturn.Add("1000000000 1000000000 1");
            //5000000000
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static long mN;

    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();
        mN = long.Parse(InputList[0]);

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

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

        for (int I = 1; I <= InputList.Count - 1; I++) {
            SplitAct(InputList[I]);

            EdgeInfoDef WillAdd1;
            WillAdd1.ToNode = I + 1;
            WillAdd1.Cost = wkArr[0];
            mEdgeInfoListDict[I].Add(WillAdd1);

            EdgeInfoDef WillAdd2;
            WillAdd2.ToNode = wkArr[2];
            WillAdd2.Cost = wkArr[1];
            mEdgeInfoListDict[I].Add(WillAdd2);
        }

        Dictionary<long, long> Result = Dijkstra(1);
        Console.WriteLine(Result[mN]);
    }

    // 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)
    {
        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(mN)) 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

ダイクストラ法を使ってます。