第19回PAST K 隣接禁止

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 2");
            WillReturn.Add("1 2");
            WillReturn.Add("2 3");
            WillReturn.Add("1 4");
            WillReturn.Add("2 5");
            WillReturn.Add("3 1 4 1 5");
            //9
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("10 6");
            WillReturn.Add("7 3");
            WillReturn.Add("3 8");
            WillReturn.Add("5 1");
            WillReturn.Add("3 9");
            WillReturn.Add("2 5");
            WillReturn.Add("6 1");
            WillReturn.Add("5 4");
            WillReturn.Add("10 7");
            WillReturn.Add("7 1");
            WillReturn.Add("1 3 10 6 7 9 2 2 10 4");
            //34
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("10 6");
            WillReturn.Add("2 10");
            WillReturn.Add("1 10");
            WillReturn.Add("7 4");
            WillReturn.Add("8 9");
            WillReturn.Add("8 7");
            WillReturn.Add("4 3");
            WillReturn.Add("1 4");
            WillReturn.Add("6 7");
            WillReturn.Add("5 3");
            WillReturn.Add("2 5 1 2 3 6 2 9 9 7");
            //-1
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    // 隣接リスト
    static Dictionary<int, List<int>> mToNodeListDict = new Dictionary<int, List<int>>();

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

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

        SplitAct(InputList[0]);
        int NodeCnt = wkArr[0];
        int NeedPaintCnt = wkArr[1];

        int[] AArr = InputList.Last().Split(' ').Select(pX => int.Parse(pX)).ToArray();

        foreach (string EachStr in InputList.Skip(1).Take(NodeCnt - 1)) {
            SplitAct(EachStr);
            int FromNode = wkArr[0];
            int ToNode = wkArr[1];

            if (mToNodeListDict.ContainsKey(FromNode) == false) {
                mToNodeListDict[FromNode] = new List<int>();
            }
            if (mToNodeListDict.ContainsKey(ToNode) == false) {
                mToNodeListDict[ToNode] = new List<int>();
            }
            mToNodeListDict[FromNode].Add(ToNode);
            mToNodeListDict[ToNode].Add(FromNode);
        }
        List<DFSJyoutaiDef> DFSResult = ExecDFS(1);
        DFSResult = DFSResult.OrderByDescending(pX => pX.Level).ToList();

        var DPJyoutaiDictArr = new Dictionary<int, int>[NodeCnt + 1];
        for (int I = 1; I <= NodeCnt; I++) {
            DPJyoutaiDictArr[I] = new Dictionary<int, int>();
            DPJyoutaiDef FirstJyoutai;
            FirstJyoutai.CanPaint = 1;
            FirstJyoutai.ChildPaintCnt = 0;
            DPJyoutaiDictArr[I].Add(GetHash(FirstJyoutai), 0);
        }

        // DFSでのレベルの降順での、親ノードへの配る木DP
        foreach (DFSJyoutaiDef EachJyoutai in DFSResult) {
            int CurrNode = EachJyoutai.Node;
            int ParentNode = EachJyoutai.ParentNode;
            if (ParentNode == -1) continue;

            foreach (var EachPair1 in DPJyoutaiDictArr[ParentNode].ToArray()) {
                DPJyoutaiDef ParentJyoutai = GetDPJyoutai(EachPair1.Key);
                foreach (var EachPair2 in DPJyoutaiDictArr[CurrNode]) {
                    DPJyoutaiDef CurrJyoutai = GetDPJyoutai(EachPair2.Key);

                    // 塗る場合
                    if (CurrJyoutai.CanPaint == 1) {
                        DPJyoutaiDef NewJyoutai1;

                        NewJyoutai1.CanPaint = 0;
                        NewJyoutai1.ChildPaintCnt = ParentJyoutai.ChildPaintCnt;
                        NewJyoutai1.ChildPaintCnt += CurrJyoutai.ChildPaintCnt;
                        NewJyoutai1.ChildPaintCnt++;
                        if (NewJyoutai1.ChildPaintCnt <= NeedPaintCnt) {
                            int NewVal = EachPair1.Value + EachPair2.Value;
                            NewVal += AArr[CurrNode - 1];

                            int CurrHash = GetHash(NewJyoutai1);
                            if (DPJyoutaiDictArr[ParentNode].ContainsKey(CurrHash) == false
                             || DPJyoutaiDictArr[ParentNode][CurrHash] < NewVal) {
                                DPJyoutaiDictArr[ParentNode][CurrHash] = NewVal;
                            }
                        }
                    }

                    // 塗らない場合
                    DPJyoutaiDef NewJyoutai2;
                    NewJyoutai2.CanPaint = ParentJyoutai.CanPaint;
                    NewJyoutai2.ChildPaintCnt = ParentJyoutai.ChildPaintCnt;
                    NewJyoutai2.ChildPaintCnt += CurrJyoutai.ChildPaintCnt;
                    if (NewJyoutai2.ChildPaintCnt <= NeedPaintCnt) {
                        int NewVal = EachPair1.Value + EachPair2.Value;

                        int CurrHash = GetHash(NewJyoutai2);
                        if (DPJyoutaiDictArr[ParentNode].ContainsKey(CurrHash) == false
                         || DPJyoutaiDictArr[ParentNode][CurrHash] < NewVal) {
                            DPJyoutaiDictArr[ParentNode][CurrHash] = NewVal;
                        }
                    }
                }
            }
        }

        var AnswerList = new List<int>();
        foreach (var EachPair in DPJyoutaiDictArr[1]) {
            DPJyoutaiDef CurrJyoutai = GetDPJyoutai(EachPair.Key);
            if (CurrJyoutai.ChildPaintCnt == NeedPaintCnt) {
                AnswerList.Add(EachPair.Value);
            }
            else if (CurrJyoutai.ChildPaintCnt == NeedPaintCnt - 1) {
                if (CurrJyoutai.CanPaint == 1) {
                    // 根を塗る場合
                    AnswerList.Add(EachPair.Value + AArr[0]);
                }
            }
        }

        if (AnswerList.Count > 0) {
            Console.WriteLine(AnswerList.Max());
        }
        else {
            Console.WriteLine(-1);
        }
    }

    struct DPJyoutaiDef
    {
        internal int CanPaint;
        internal int ChildPaintCnt;
    }

    static int GetHash(DPJyoutaiDef pDPJyoutai)
    {
        return pDPJyoutai.ChildPaintCnt * 10 + pDPJyoutai.CanPaint;
    }

    static DPJyoutaiDef GetDPJyoutai(int pHash)
    {
        DPJyoutaiDef WillReturn;
        WillReturn.CanPaint = pHash % 10;
        WillReturn.ChildPaintCnt = pHash / 10;
        return WillReturn;
    }

    struct DFSJyoutaiDef
    {
        internal int Node;
        internal int ParentNode;
        internal int Level;
    }

    static List<DFSJyoutaiDef> ExecDFS(int pRootNode)
    {
        var WillReturn = new List<DFSJyoutaiDef>();

        var Stk = new Stack<DFSJyoutaiDef>();
        DFSJyoutaiDef WillPush;
        WillPush.Node = pRootNode;
        WillPush.ParentNode = -1;
        WillPush.Level = 1;
        Stk.Push(WillPush);

        var VisitedSet = new HashSet<int>();
        VisitedSet.Add(pRootNode);

        while (Stk.Count > 0) {
            DFSJyoutaiDef Popped = Stk.Pop();
            WillReturn.Add(Popped);
            if (mToNodeListDict.ContainsKey(Popped.Node)) {
                foreach (int EachToNode in mToNodeListDict[Popped.Node]) {
                    if (VisitedSet.Add(EachToNode)) {
                        WillPush.Node = EachToNode;
                        WillPush.ParentNode = Popped.Node;
                        WillPush.Level = Popped.Level + 1;
                        Stk.Push(WillPush);
                    }
                }
            }
        }
        return WillReturn;
    }
}

解説

木DPで解いてます。

木DPの後で
根を塗る場合も、考慮する必要があります。