ABC252-E Road Reduction

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 3");
            WillReturn.Add("1 2 1");
            WillReturn.Add("2 3 2");
            WillReturn.Add("1 3 10");
            //1 2
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("4 6");
            WillReturn.Add("1 2 1");
            WillReturn.Add("1 3 1");
            WillReturn.Add("1 4 1");
            WillReturn.Add("2 3 1");
            WillReturn.Add("2 4 1");
            WillReturn.Add("3 4 1");
            //3 1 2
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    struct EdgeInfoDef
    {
        internal long EdgeID;
        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 = { };
        Action<string> SplitAct = pStr =>
            wkArr = pStr.Split(' ').Select(pX => long.Parse(pX)).ToArray();

        long EdgeID = 1;
        foreach (string EachStr in InputList.Skip(1)) {
            SplitAct(EachStr);
            long A = wkArr[0];
            long B = wkArr[1];
            long C = wkArr[2];

            Action<long, long, long> AddEdgeAct = (pFrom, pTo, pCost) =>
            {
                if (mEdgeInfoListDict.ContainsKey(pFrom) == false) {
                    mEdgeInfoListDict[pFrom] = new List<EdgeInfoDef>();
                }
                EdgeInfoDef WillAdd;
                WillAdd.EdgeID = EdgeID;
                WillAdd.ToNode = pTo;
                WillAdd.Cost = pCost;
                mEdgeInfoListDict[pFrom].Add(WillAdd);
            };
            AddEdgeAct(A, B, C);
            AddEdgeAct(B, A, C);

            EdgeID++;
        }

        List<long> Answer = Dijkstra(1);

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

        Console.WriteLine(LongEnumJoin(" ", Answer));
    }

    // ダイクストラ法で、ダイクストラ木の枝Listを返す
    static List<long> Dijkstra(long pStaNode)
    {
        var WillReturn = new List<long>();

        var InsPQueue = new PQueue();

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

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

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

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

#region PQueue
// 優先度付きキュー
internal class PQueue
{
    internal struct PQueueJyoutaiDef
    {
        internal long EdgeID;
        internal long Node;
        internal long SumCost;
    }

    private Dictionary<int, PQueueJyoutaiDef> mHeapDict = new Dictionary<int, PQueueJyoutaiDef>();

    internal bool IsEmpty()
    {
        return mHeapDict.Count == 0;
    }

    // エンキュー処理
    internal void Enqueue(PQueueJyoutaiDef pAddJyoutai)
    {
        int CurrNode = 1 + mHeapDict.Count;
        mHeapDict[CurrNode] = pAddJyoutai;

        while (1 < CurrNode && mHeapDict[CurrNode / 2].SumCost > mHeapDict[CurrNode].SumCost) {
            PQueueJyoutaiDef Swap = mHeapDict[CurrNode];
            mHeapDict[CurrNode] = mHeapDict[CurrNode / 2];
            mHeapDict[CurrNode / 2] = Swap;

            CurrNode /= 2;
        }
    }

    // デキュー処理
    internal PQueueJyoutaiDef Dequeue()
    {
        PQueueJyoutaiDef TopNode = mHeapDict[1];
        int LastNode = mHeapDict.Count;
        mHeapDict[1] = mHeapDict[LastNode];
        mHeapDict.Remove(LastNode);

        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(int pRootNode)
    {
        if (mHeapDict.Count <= 1) {
            return;
        }

        int Left = pRootNode * 2;
        int 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 = mHeapDict[pRootNode].SumCost;
        int SmallestNode = pRootNode;

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

        // 子ノードのほうが大きい場合
        if (SmallestNode != pRootNode) {
            PQueueJyoutaiDef Swap = mHeapDict[SmallestNode];
            mHeapDict[SmallestNode] = mHeapDict[pRootNode];
            mHeapDict[pRootNode] = Swap;

            // 再帰的に呼び出し
            MinHeapify(SmallestNode);
        }
    }
}
#endregion

解説

無向グラフでダイクストラ法を行った結果をイメージすると
根付きな全域木になると分かります。
この木をダイクストラ木と言い、この木で使用してる枝が解になります。