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第1回PAST L グラデーション


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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 1");
            WillReturn.Add("0 0 1");
            WillReturn.Add("0 1 1");
            WillReturn.Add("1 0 1");
            WillReturn.Add("1 1 1");
            //2.000000000000
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("3 1");
            WillReturn.Add("0 10 1");
            WillReturn.Add("10 0 2");
            WillReturn.Add("10 20 3");
            WillReturn.Add("10 10 1");
            //210.000000000000
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    // 塔の入力情報
    struct TowerInfoDef
    {
        internal bool IsBig;
        internal int X;
        internal int Y;
        internal int C;
    }
    static List<TowerInfoDef> mTowerInfoList = new List<TowerInfoDef>();

    // 小さい塔の添字のList
    static List<int> mSmallTowerIndList = new List<int>();

    // 無向グラフの辺の情報
    struct EdgeInfoDef
    {
        internal int FromNode;
        internal int ToNode;
        internal double Cost;
    }
    static List<EdgeInfoDef> mEdgeInfoList = new List<EdgeInfoDef>();

    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 N = wkArr[0];
        int M = wkArr[1];

        foreach (string EachStr in InputList.Skip(1).Take(N)) {
            SplitAct(EachStr);
            TowerInfoDef WillAdd;
            WillAdd.IsBig = true;
            WillAdd.X = wkArr[0];
            WillAdd.Y = wkArr[1];
            WillAdd.C = wkArr[2];
            mTowerInfoList.Add(WillAdd);
        }

        foreach (string EachStr in InputList.Skip(1 + N)) {
            SplitAct(EachStr);
            TowerInfoDef WillAdd;
            WillAdd.IsBig = false;
            WillAdd.X = wkArr[0];
            WillAdd.Y = wkArr[1];
            WillAdd.C = wkArr[2];
            mTowerInfoList.Add(WillAdd);
        }

        // 小さい塔の添字のList
        for (int I = 0; I <= mTowerInfoList.Count - 1; I++) {
            if (mTowerInfoList[I].IsBig == false) {
                mSmallTowerIndList.Add(I);
            }
        }
        List<HashSet<int>> NonUseSmallTowerSetList = DeriveNonUseSmallTowerSetList();

        for (int I = 0; I <= mTowerInfoList.Count - 1; I++) {
            for (int J = I + 1; J <= mTowerInfoList.Count - 1; J++) {
                EdgeInfoDef WillAdd;
                WillAdd.FromNode = I;
                WillAdd.ToNode = J;

                double XDiff = mTowerInfoList[I].X - mTowerInfoList[J].X;
                double YDiff = mTowerInfoList[I].Y - mTowerInfoList[J].Y;
                double Cost = Math.Sqrt(XDiff * XDiff + YDiff * YDiff);

                // 色が違う場合は、コストを10倍にする
                if (mTowerInfoList[I].C != mTowerInfoList[J].C) {
                    Cost *= 10D;
                }
                WillAdd.Cost = Cost;
                mEdgeInfoList.Add(WillAdd);
            }
        }
        // 枝をコストの昇順にソート
        mEdgeInfoList.Sort((a, b) => a.Cost.CompareTo(b.Cost));

        double Answer = double.MaxValue;
        foreach (HashSet<int> EachNonUseSmallTowerSet in NonUseSmallTowerSetList) {
            double AnswerKouho = DeriveMST(EachNonUseSmallTowerSet);
            Answer = Math.Min(Answer, AnswerKouho);
        }
        Console.WriteLine(Answer);
    }

    // 使用する小さな塔のIndSetを引数として、MSTのコストを返す
    static double DeriveMST(HashSet<int> pNonUseSmallTowerSet)
    {
        // クラスカル法で解く
        var InsUnionFind = new UnionFind();
        for (int I = 0; I <= mTowerInfoList.Count - 1; I++) {
            if (pNonUseSmallTowerSet.Contains(I)) continue;

            InsUnionFind.MakeSet(I);
        }

        double SumCost = 0;
        foreach (EdgeInfoDef EachEdgeInfo in mEdgeInfoList) {
            if (pNonUseSmallTowerSet.Contains(EachEdgeInfo.FromNode)) continue;
            if (pNonUseSmallTowerSet.Contains(EachEdgeInfo.ToNode)) continue;

            int FromNode = EachEdgeInfo.FromNode;
            int ToNode = EachEdgeInfo.ToNode;
            int RootNode1 = InsUnionFind.FindSet(EachEdgeInfo.FromNode);
            int RootNode2 = InsUnionFind.FindSet(EachEdgeInfo.ToNode);
            if (RootNode1 != RootNode2) {
                InsUnionFind.Unite(FromNode, ToNode);
                SumCost += EachEdgeInfo.Cost;
            }
        }
        return SumCost;
    }

    struct JyoutaiDef
    {
        internal int CurrInd;
        internal HashSet<int> SmallTowerSet;
    }

    //DFSで、未使用の小さい塔の候補を列挙
    static List<HashSet<int>> DeriveNonUseSmallTowerSetList()
    {
        var NonUseSmallTowerSetList = new List<HashSet<int>>();

        var Stk = new Stack<JyoutaiDef>();
        JyoutaiDef WillPush;
        WillPush.CurrInd = 0;
        WillPush.SmallTowerSet = new HashSet<int>();
        Stk.Push(WillPush);

        while (Stk.Count > 0) {
            JyoutaiDef Popped = Stk.Pop();
            NonUseSmallTowerSetList.Add(Popped.SmallTowerSet);

            for (int I = Popped.CurrInd; I <= mSmallTowerIndList.Count - 1; I++) {
                WillPush.CurrInd = I + 1;
                WillPush.SmallTowerSet = new HashSet<int>(Popped.SmallTowerSet);
                WillPush.SmallTowerSet.Add(mSmallTowerIndList[I]);
                Stk.Push(WillPush);
            }
        }
        return NonUseSmallTowerSetList;
    }
}

// UnionFindクラス
internal class UnionFind
{
    private class NodeInfoDef
    {
        internal int ParentNode;
        internal int Rank;
    }
    private Dictionary<int, NodeInfoDef> mNodeInfoDict =
        new Dictionary<int, NodeInfoDef>();

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

    // 合併処理
    internal void Unite(int pX, int pY)
    {
        int XNode = FindSet(pX);
        int YNode = FindSet(pY);
        int XRank = mNodeInfoDict[XNode].Rank;
        int YRank = mNodeInfoDict[YNode].Rank;

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

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

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

    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

小さい塔は、最大でも5個なので、
小さい塔の使う使わないの組み合わせは、最大で32通りになります。

なので、小さい塔の使う使わないの全部の組み合わせで
クラスカル法で最小全域木のコストを求めてます。