ABC234-F Reordering

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("aab");
            //8
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("aaa");
            //3
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("abcdefghijklmnopqrstuvwxyz");
            //149621752
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    const long Hou = 998244353;

    static void Main()
    {
        List<string> InputList = GetInputList();
        string S = InputList[0];

        // 度数のList
        var CntList = new List<long>();
        foreach (var EachItem in S.ToCharArray().GroupBy(pX => pX)) {
            CntList.Add(EachItem.LongCount());
        }

        long UB = S.Length;

        ChooseMod InsChooseMod = new ChooseMod(S.Length, Hou);

        // 場合の数[文字数]なDP表
        long[] DPArr = new long[UB + 1];
        DPArr[0] = 1;

        foreach (var EachCnt in CntList) {
            for (long I = UB; 0 <= I; I--) {
                if (DPArr[I] == 0) continue;

                for (long J = 1; J <= EachCnt; J++) {
                    long PatternCnt = InsChooseMod.DeriveChoose(I + J, J);
                    DPArr[I + J] += DPArr[I] * PatternCnt;
                    DPArr[I + J] %= Hou;
                }
            }
        }

        long Answer = 0;
        for (long I = 1; I <= UB; I++) {
            Answer += DPArr[I];
            Answer %= Hou;
        }
        Console.WriteLine(Answer);
    }
}

#region ChooseMod
// 二項係数クラス
internal class ChooseMod
{
    private long mHou;

    private long[] mFacArr;
    private long[] mFacInvArr;
    private long[] mInvArr;

    // コンストラクタ
    internal ChooseMod(long pCnt, long pHou)
    {
        mHou = pHou;
        mFacArr = new long[pCnt + 1];
        mFacInvArr = new long[pCnt + 1];
        mInvArr = new long[pCnt + 1];

        mFacArr[0] = mFacArr[1] = 1;
        mFacInvArr[0] = mFacInvArr[1] = 1;
        mInvArr[1] = 1;
        for (int I = 2; I <= pCnt; I++) {
            mFacArr[I] = mFacArr[I - 1] * I % mHou;
            mInvArr[I] = mHou - mInvArr[mHou % I] * (mHou / I) % mHou;
            mFacInvArr[I] = mFacInvArr[I - 1] * mInvArr[I] % mHou;
        }
    }

    // nCrを返す
    internal long DeriveChoose(long pN, long pR)
    {
        if (pN < pR) return 0;
        if (pN < 0 || pR < 0) return 0;
        return mFacArr[pN] * (mFacInvArr[pR] * mFacInvArr[pN - pR] % mHou) % mHou;
    }
}
#endregion

解説

3文字の文字列に、同じ2文字を追加するのは、
既存文字を縦棒、追加する同じ2文字を○で表せば、
○○|||
と表せるので、重複組み合わせの考え方が使えます。

このことをふまえて、DPで解いてます。

類題

ABC358-E Alphabet Tiles