典型90問 060 Chimera（★5）

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

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

        int[] AArr = InputList[1].Split(' ').Select(pX => int.Parse(pX)).ToArray();
        int UB = AArr.GetUpperBound(0);

        Dictionary<int, int> LISLenDictSei = DeriveLISLenDict(AArr);

        Array.Reverse(AArr);
        Dictionary<int, int> LISLenDictRev = DeriveLISLenDict(AArr);

        var AnswerKouho = new List<int>();
        for (int I = 0; I <= UB; I++) {
            int RevInd = UB - I;
            AnswerKouho.Add(LISLenDictSei[I] + LISLenDictRev[RevInd] - 1);
        }
        Console.WriteLine(AnswerKouho.Max());
    }

    // 配列を引数として、LIS長さ[添字]なDictを返す
    static Dictionary<int, int> DeriveLISLenDict(int[] pArr)
    {
        var WillReturn = new Dictionary<int, int>();

        // LISの最終値の最小値[LISの長さ] なDP表
        var DPSortedList = new SortedList<int, int>();

        int MaxLISLen = 1;
        for (int I = 0; I <= pArr.GetUpperBound(0); I++) {
            if (DPSortedList.Count == 0) {
                DPSortedList[1] = pArr[I];
                MaxLISLen = Math.Max(MaxLISLen, 1);
            }
            else {
                int UpsertKeyInd = ExecNibunhou(DPSortedList, pArr[I]);

                int CurrUB = DPSortedList.Count - 1;
                var Keys = DPSortedList.Keys;

                // 更新する位置によって分岐
                if (UpsertKeyInd <= CurrUB) {
                    DPSortedList[Keys[UpsertKeyInd]] = pArr[I];
                    MaxLISLen = Math.Max(MaxLISLen, Keys[UpsertKeyInd]);
                }
                else {
                    int PrevKey = Keys[CurrUB];
                    DPSortedList[PrevKey + 1] = pArr[I];
                    MaxLISLen = Math.Max(MaxLISLen, PrevKey + 1);

                }
            }
            WillReturn[I] = MaxLISLen;
        }
        return WillReturn;
    }

    // 二分法で、引数の値を設定する、キーの配列の添字を返す
    static int ExecNibunhou(SortedList<int, int> pDPSortedList, int pTargetVal)
    {
        int UB = pDPSortedList.Count - 1;
        var Keys = pDPSortedList.Keys;

        // 最小値以下の場合
        if (pTargetVal <= pDPSortedList[Keys[0]]) {
            return 0;
        }

        // 最大値より大きい場合
        if (pTargetVal > pDPSortedList[Keys[UB]]) {
            return UB + 1;
        }

        int L = 0;
        int R = UB;

        while (L + 1 < R) {
            int Mid = (L + R) / 2;
            if (pDPSortedList[Keys[Mid]] < pTargetVal) {
                L = Mid;
            }
            else {
                R = Mid;
            }
        }
        return R;
    }
}

解説

先頭と末尾からのLISの長さ合計の最長が解なので、
LISの最後の項の候補を全探索してます。