ABC414-D Transmission Mission

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 3");
            WillReturn.Add("5 10 15 20 8 14 15");
            //6
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("7 7");
            WillReturn.Add("5 10 15 20 8 14 15");
            //0
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("7 1");
            WillReturn.Add("5 10 15 20 8 14 15");
            //15
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static void Main()
    {
        List<string> InputList = GetInputList();
        long[] wkArr = InputList[0].Split(' ').Select(pX => long.Parse(pX)).ToArray();
        long M = wkArr[1];

        long[] XArr = InputList[1].Split(' ').Select(pX => long.Parse(pX)).ToArray();
        XArr = XArr.Distinct().ToArray();

        Array.Sort(XArr);

        if (XArr.Length <= M) {
            Console.WriteLine(0);
            return;
        }

        long UB = XArr.GetUpperBound(0);

        for (long I = 1; I <= UB; I++) {
            EdgeInfo WillAdd;
            WillAdd.FromNode = XArr[I - 1];
            WillAdd.ToNode = XArr[I];
            WillAdd.Cost = XArr[I] - XArr[I - 1];
            mEdgeList.Add(WillAdd);
        }

        var InsUnionFindWithAnyInfo = new UnionFindWithAnyInfo();
        foreach (long EachNode in XArr) {
            InsUnionFindWithAnyInfo.MakeSet(EachNode);
        }

        // 枝のコストの昇順に、枝を接続
        long NeedRootCnt = M;
        foreach (EdgeInfo EachEdge in mEdgeList.OrderBy(pX => pX.Cost)) {
            if (InsUnionFindWithAnyInfo.TreeCnt == NeedRootCnt) {
                break;
            }
            InsUnionFindWithAnyInfo.Unite(EachEdge.FromNode, EachEdge.ToNode);
        }

        long Answer = 0;
        var AppearRootSet = new HashSet<long>();
        foreach (long EachNode in XArr) {
            long CurrRoot = InsUnionFindWithAnyInfo.FindSet(EachNode);
            if (AppearRootSet.Add(CurrRoot)) {
                long MaxNode = InsUnionFindWithAnyInfo.GetMaxNode(CurrRoot);
                long MinNode = InsUnionFindWithAnyInfo.GetMinNode(CurrRoot);
                Answer += MaxNode - MinNode;
            }
        }
        Console.WriteLine(Answer);
    }

    struct EdgeInfo
    {
        internal long FromNode;
        internal long ToNode;
        internal long Cost;
    }
    static List<EdgeInfo> mEdgeList = new List<EdgeInfo>();
}

// UnionFindWithAnyInfoクラス
internal class UnionFindWithAnyInfo
{
    private class NodeInfoDef
    {
        internal long ParentNode;
        internal long Rank;
        internal long Size;    // 木のノード数
        internal long EdgeCnt; // 木の枝の数
        internal long MinNode;
        internal long MaxNode;
    }
    private Dictionary<long, NodeInfoDef> mNodeInfoDict =
        new Dictionary<long, NodeInfoDef>();

    // 森にある木の数
    private long mTreeCnt = 0;

    // 森にある木の数を返す
    internal long TreeCnt
    {
        get { return mTreeCnt; }
    }

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

    // 合併処理
    internal void Unite(long pX, long pY)
    {
        long XNode = FindSet(pX);
        long YNode = FindSet(pY);

        // 既に同じ木の場合
        if (XNode == YNode) {
            mNodeInfoDict[XNode].EdgeCnt++;
            return;
        }
        mTreeCnt--;

        long XRank = mNodeInfoDict[XNode].Rank;
        long YRank = mNodeInfoDict[YNode].Rank;

        var NodeList = new List<long>();
        NodeList.Add(mNodeInfoDict[XNode].MinNode);
        NodeList.Add(mNodeInfoDict[XNode].MaxNode);
        NodeList.Add(mNodeInfoDict[YNode].MinNode);
        NodeList.Add(mNodeInfoDict[YNode].MaxNode);

        if (XRank > YRank) {
            mNodeInfoDict[YNode].ParentNode = XNode;
            mNodeInfoDict[XNode].Size += mNodeInfoDict[YNode].Size;

            mNodeInfoDict[XNode].EdgeCnt++;
            mNodeInfoDict[XNode].EdgeCnt += mNodeInfoDict[YNode].EdgeCnt;

            mNodeInfoDict[XNode].MinNode = NodeList.Min();
            mNodeInfoDict[XNode].MaxNode = NodeList.Max();
        }
        else {
            mNodeInfoDict[XNode].ParentNode = YNode;
            mNodeInfoDict[YNode].Size += mNodeInfoDict[XNode].Size;

            mNodeInfoDict[YNode].EdgeCnt++;
            mNodeInfoDict[YNode].EdgeCnt += mNodeInfoDict[XNode].EdgeCnt;
            if (XRank == YRank) {
                mNodeInfoDict[YNode].Rank++;
            }

            mNodeInfoDict[YNode].MinNode = NodeList.Min();
            mNodeInfoDict[YNode].MaxNode = NodeList.Max();
        }
    }

    // ノードを引数として、木の根を取得
    internal long FindSet(long pTargetNode)
    {
        // 根までの経路上のノードのList
        var PathNodeList = new List<long>();

        long 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 (long EachPathNode in PathNodeList) {
            mNodeInfoDict[EachPathNode].ParentNode = CurrNode;
        }
        return CurrNode;
    }

    // ノードを引数として、木のサイズを取得
    internal long GetSize(long pNode)
    {
        long RootNode = FindSet(pNode);
        return mNodeInfoDict[RootNode].Size;
    }

    // ノードを引数として、木の枝数を取得
    internal long GetEdgeCnt(long pNode)
    {
        long RootNode = FindSet(pNode);
        return mNodeInfoDict[RootNode].EdgeCnt;
    }

    // ノードを引数として、木の最小ノードを取得
    internal long GetMinNode(long pNode)
    {
        long RootNode = FindSet(pNode);
        return mNodeInfoDict[RootNode].MinNode;
    }

    // ノードを引数として、木の最大ノードを取得
    internal long GetMaxNode(long pNode)
    {
        long RootNode = FindSet(pNode);
        return mNodeInfoDict[RootNode].MaxNode;
    }

    internal void DebugPrint()
    {
        foreach (var EachPair in mNodeInfoDict.OrderBy(pX => pX.Key)) {
            Console.WriteLine("mNodeInfoDict[{0}].ParentNode={1}",
                EachPair.Key, EachPair.Value.ParentNode);
        }
    }
}

解説

木の数と、木ごとの最小ノードと最大ノードを取れるUnionFindで
木の数が必要数になるまで
距離の小さい枝から接続してます。