ABC259-F Select Edges

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");
            WillReturn.Add("1 2 1 0 2 1 1");
            WillReturn.Add("1 2 8");
            WillReturn.Add("2 3 9");
            WillReturn.Add("2 4 10");
            WillReturn.Add("2 5 -3");
            WillReturn.Add("5 6 8");
            WillReturn.Add("5 7 3");
            //28
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("20");
            WillReturn.Add("0 2 0 1 2 1 0 0 3 0 1 1 1 1 0 0 3 0 1 2");
            WillReturn.Add("4 9 583");
            WillReturn.Add("4 6 -431");
            WillReturn.Add("5 9 325");
            WillReturn.Add("17 6 131");
            WillReturn.Add("17 2 -520");
            WillReturn.Add("2 16 696");
            WillReturn.Add("5 7 662");
            WillReturn.Add("17 15 845");
            WillReturn.Add("7 8 307");
            WillReturn.Add("13 7 849");
            WillReturn.Add("9 19 242");
            WillReturn.Add("20 6 909");
            WillReturn.Add("7 11 -775");
            WillReturn.Add("17 18 557");
            WillReturn.Add("14 20 95");
            WillReturn.Add("18 10 646");
            WillReturn.Add("4 3 -168");
            WillReturn.Add("1 3 -917");
            WillReturn.Add("11 12 30");
            //2184
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static long[] mDArr;

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

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

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

        // スコア[枝のハッシュ値]
        var ScoreDict = new Dictionary<long, long>();

        foreach (string EachStr in InputList.Skip(2)) {
            SplitAct(EachStr);
            long FromNode = wkArr[0];
            long ToNode = wkArr[1];
            long Score = wkArr[2];

            if (mToNodeListDict.ContainsKey(FromNode) == false) {
                mToNodeListDict[FromNode] = new List<long>();
            }
            if (mToNodeListDict.ContainsKey(ToNode) == false) {
                mToNodeListDict[ToNode] = new List<long>();
            }
            mToNodeListDict[FromNode].Add(ToNode);
            mToNodeListDict[ToNode].Add(FromNode);

            ScoreDict[FromNode * 1000000 + ToNode] = Score;
            ScoreDict[ToNode * 1000000 + FromNode] = Score;
        }

        // 枝をスコアの降順にソートしておく
        foreach (long EachKey in mToNodeListDict.Keys.ToArray()) {
            List<long> CurrList = mToNodeListDict[EachKey];

            CurrList = CurrList.OrderByDescending(pX => ScoreDict[EachKey * 1000000 + pX]).ToList();
            mToNodeListDict[EachKey] = CurrList;
        }

        List<JyoutaiDef> DFSResult = ExecDFS();
        DFSResult.Reverse();

        // 削除した辺のスコア合計の最大値[ノード][削除辺の数]なDP表
        var DPDict = new Dictionary<long, Dictionary<long, long>>();
        for (long I = 1; I <= mDArr.Length; I++) {
            DPDict[I] = new Dictionary<long, long>();
            DPDict[I][0] = 0;
        }

        // 根から葉に向かって配るDP
        foreach (JyoutaiDef EachJyoutai in DFSResult) {
            if (EachJyoutai.Node == 1) break;

            long EdgeScore = ScoreDict[EachJyoutai.Node * 1000000 + EachJyoutai.ParentNode];

            var CurrDPDict = new Dictionary<long, long>();
            foreach (var EachPairFrom in DPDict[EachJyoutai.Node]) {
                foreach (var EachPairTo in DPDict[EachJyoutai.ParentNode]) {

                    Action<long, long> UpdateAct = (pNewKey, pNewVal) =>
                    {
                        if (pNewKey > mDArr[EachJyoutai.ParentNode - 1]) {
                            return;
                        }

                        if (CurrDPDict.ContainsKey(pNewKey)) {
                            if (CurrDPDict[pNewKey] >= pNewVal) {
                                return;
                            }
                        }
                        CurrDPDict[pNewKey] = pNewVal;
                    };

                    // 間の辺を切断する場合
                    if (EdgeScore > 0) {
                        if (mDArr[EachJyoutai.Node - 1] > EachPairFrom.Key) {
                            UpdateAct(EachPairTo.Key + 1, EdgeScore + EachPairFrom.Value + EachPairTo.Value);
                        }
                    }

                    // 間の辺を切断しない場合
                    UpdateAct(EachPairTo.Key, EachPairFrom.Value + EachPairTo.Value);
                }
            }

            var RemoveList = new List<long>();
            foreach (var EachPair in CurrDPDict.OrderByDescending(pX => pX.Value).Skip(10)) {
                RemoveList.Add(EachPair.Key);
            }
            RemoveList.ForEach(pX => CurrDPDict.Remove(pX));

            DPDict[EachJyoutai.ParentNode] = CurrDPDict;
        }

        long Answer = 0;
        foreach (var EachPair in DPDict[1]) {
            Answer = Math.Max(Answer, EachPair.Value);
        }

        Console.WriteLine(Answer);
    }

    struct JyoutaiDef
    {
        internal long Node;
        internal long ParentNode;
    }

    static List<JyoutaiDef> ExecDFS()
    {
        var WillReturn = new List<JyoutaiDef>();

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

        var VisitedSet = new HashSet<long>();
        VisitedSet.Add(1);

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

解説

木DPで配るDPで解いてます。