#787265 (C#(csc)) No.2019 Digits Filling for All Substrings

• 問題: No.2019 Digits Filling for All Substrings
• ユーザー: Lily89164763
• 提出日時: 2022-08-12 00:52:47
• 言語: C#(csc) (csc 3.9.0)
• 結果: AC
• 実行時間: 82 ms / 2,000 ms
• コード長: 12,786 bytes
• コンパイル時間: 1,234 ms
• コンパイル使用メモリ: 122,160 KB
• 実行使用メモリ: 30,844 KB
• 最終ジャッジ日時: 2024-09-22 06:57:22
• 合計ジャッジ時間: 4,139 ms
• ジャッジサーバーID （参考情報）: judge4 / judge3

ファイルパターン	結果
sample	AC * 4
other	AC * 30

コンパイルメッセージ

Microsoft (R) Visual C# Compiler version 3.9.0-6.21124.20 (db94f4cc)
Copyright (C) Microsoft Corporation. All rights reserved.

ソースコード

using System;
using System.Linq;
using CompLib.Util;
using System.Threading;
using System.IO;
using System.Collections.Generic;
using System.Text;
using CompLib.Collections.Generic;
using CompLib.Mathematics;

public class Program
{
    int N;
    string S;
    public void Solve()
    {
        var sc = new Scanner();
        N = sc.NextInt();
        S = sc.Next();

        ModInt ans = 0;
        var dp = new ModInt[N + 1, 3];
        dp[0, 0] = 1;
        for (int i = 0; i < N; i++)
        {
            for (int p = 0; p < 3; p++)
            {
                var cur = dp[i, p];
                if (S[i] == '?')
                {
                    for (int q = 0; q <= 9; q++)
                    {
                        dp[i + 1, (p + q) % 3] += cur;
                    }
                }
                else
                {
                    dp[i + 1, (p + S[i] - '0') % 3] += cur;
                }
            }

            ans += dp[i + 1, 0];
            dp[i + 1, 0] += 1;
        }

        Console.WriteLine(ans);
    }

    public static void Main(string[] args) => new Program().Solve();
    // public static void Main(string[] args) => new Thread(new Program().Solve, 1 << 27).Start();
}

// https://bitbucket.org/camypaper/complib
namespace CompLib.Mathematics
{
    #region ModInt
    /// <summary>
    /// [0,<see cref="Mod"/>) までの値を取るような数
    /// </summary>
    public struct ModInt
    {
        /// <summary>
        /// 剰余を取る値．
        /// </summary>
        // public const long Mod = (int)1e9 + 7;
        public const long Mod = 998244353;

        /// <summary>
        /// 実際の数値．
        /// </summary>
        public long num;
        /// <summary>
        /// 値が <paramref name="n"/> であるようなインスタンスを構築します．
        /// </summary>
        /// <param name="n">インスタンスが持つ値</param>
        /// <remarks>パフォーマンスの問題上，コンストラクタ内では剰余を取りません．そのため，<paramref name="n"/> ∈ [0,<see cref="Mod"/>) を満たすような <paramref name="n"/> を渡してください．このコンストラクタは O(1) で実行されます．</remarks>
        public ModInt(long n) { num = n; }
        /// <summary>
        /// このインスタンスの数値を文字列に変換します．
        /// </summary>
        /// <returns>[0,<see cref="Mod"/>) の範囲内の整数を 10 進表記したもの．</returns>
        public override string ToString() { return num.ToString(); }
        public static ModInt operator +(ModInt l, ModInt r) { l.num += r.num; if (l.num >= Mod) l.num -= Mod; return l; }
        public static ModInt operator -(ModInt l, ModInt r) { l.num -= r.num; if (l.num < 0) l.num += Mod; return l; }
        public static ModInt operator *(ModInt l, ModInt r) { return new ModInt(l.num * r.num % Mod); }
        public static implicit operator ModInt(long n) { n %= Mod; if (n < 0) n += Mod; return new ModInt(n); }

        /// <summary>
        /// 与えられた 2 つの数値からべき剰余を計算します．
        /// </summary>
        /// <param name="v">べき乗の底</param>
        /// <param name="k">べき指数</param>
        /// <returns>繰り返し二乗法により O(N log N) で実行されます．</returns>
        public static ModInt Pow(ModInt v, long k) { return Pow(v.num, k); }

        /// <summary>
        /// 与えられた 2 つの数値からべき剰余を計算します．
        /// </summary>
        /// <param name="v">べき乗の底</param>
        /// <param name="k">べき指数</param>
        /// <returns>繰り返し二乗法により O(N log N) で実行されます．</returns>
        public static ModInt Pow(long v, long k)
        {
            long ret = 1;
            for (k %= Mod - 1; k > 0; k >>= 1, v = v * v % Mod)
                if ((k & 1) == 1) ret = ret * v % Mod;
            return new ModInt(ret);
        }
        /// <summary>
        /// 与えられた数の逆元を計算します．
        /// </summary>
        /// <param name="v">逆元を取る対象となる数</param>
        /// <returns>逆元となるような値</returns>
        /// <remarks>法が素数であることを仮定して，フェルマーの小定理に従って逆元を O(log N) で計算します．</remarks>
        public static ModInt Inverse(ModInt v) { return Pow(v, Mod - 2); }
    }
    #endregion
    #region Binomial Coefficient
    public class BinomialCoefficient
    {
        public ModInt[] fact, ifact;
        public BinomialCoefficient(int n)
        {
            fact = new ModInt[n + 1];
            ifact = new ModInt[n + 1];
            fact[0] = 1;
            for (int i = 1; i <= n; i++)
                fact[i] = fact[i - 1] * i;
            ifact[n] = ModInt.Inverse(fact[n]);
            for (int i = n - 1; i >= 0; i--)
                ifact[i] = ifact[i + 1] * (i + 1);
            ifact[0] = ifact[1];
        }
        public ModInt this[int n, int r]
        {
            get
            {
                if (n < 0 || n >= fact.Length || r < 0 || r > n) return 0;
                return fact[n] * ifact[n - r] * ifact[r];
            }
        }
        public ModInt RepeatedCombination(int n, int k)
        {
            if (k == 0) return 1;
            return this[n + k - 1, k];
        }
    }
    #endregion
}



namespace CompLib.Collections.Generic
{
    using System;
    using System.Diagnostics;

    public class SegmentTree<T>
    {
        // 見かけ上の大きさ、実際の大きさ
        private readonly int _n, _size;
        private T[] _array;

        private T _identity;
        private Func<T, T, T> _operation;

        public SegmentTree(int n, Func<T, T, T> operation, T identity)
        {
            _n = n;
            _size = 1;
            while (_size < _n)
            {
                _size *= 2;
            }

            _identity = identity;
            _operation = operation;
            _array = new T[_size * 2];
            for (int i = 1; i < _size * 2; i++)
            {
                _array[i] = _identity;
            }
        }

        public SegmentTree(T[] a, Func<T, T, T> operation, T identity)
        {
            _n = a.Length;
            _size = 1;
            while (_size < _n)
            {
                _size *= 2;
            }

            _identity = identity;
            _operation = operation;
            _array = new T[_size * 2];
            for (int i = 0; i < a.Length; i++)
            {
                _array[i + _size] = a[i];
            }
            for (int i = a.Length; i < _size; i++)
            {
                _array[i + _size] = identity;
            }

            for (int i = _size - 1; i >= 1; i--)
            {
                _array[i] = operation(_array[i * 2], _array[i * 2 + 1]);
            }
        }

        /// <summary>
        /// A[i]をnに更新 O(log N)
        /// </summary>
        /// <param name="i"></param>
        /// <param name="n"></param>
        public void Update(int i, T n)
        {
            Debug.Assert(0 <= i && i < _n);
            i += _size;
            _array[i] = n;
            while (i > 1)
            {
                i /= 2;
                _array[i] = _operation(_array[i * 2], _array[i * 2 + 1]);
            }
        }

        /// <summary>
        /// A[left] op A[left+1] ... op A[right-1]を求める
        /// </summary>
        /// <param name="left"></param>
        /// <param name="right"></param>
        /// <returns></returns>
        public T Query(int left, int right)
        {
            Debug.Assert(0 <= left && left <= right && right <= _n);
            T sml = _identity;
            T smr = _identity;

            left += _size;
            right += _size;
            while (left < right)
            {
                if ((left & 1) != 0) sml = _operation(sml, _array[left++]);
                if ((right & 1) != 0) smr = _operation(_array[--right], smr);
                left >>= 1;
                right >>= 1;
            }
            return _operation(sml, smr);
        }

        /// <summary>
        /// op(a[0],a[1],...,a[n-1])を返します
        /// </summary>
        /// <returns></returns>
        public T All()
        {
            return _array[1];
        }

        /// <summary>
        /// f(op(a[l],a[l+1],...a[r-1])) = trueとなる最大のrを返します
        /// </summary>
        /// <param name="l"></param>
        /// <param name="f"></param>
        /// <returns></returns>
        public int MaxRight(int l, Func<T, bool> f)
        {
            Debug.Assert(0 <= l && l <= _n);
#if DEBUG
            Debug.Assert(f(_identity));
#endif
            if (l == _n) return _n;
            l += _size;
            T sm = _identity;
            do
            {
                while (l % 2 == 0) l >>= 1;
                if (!f(_operation(sm, _array[l])))
                {
                    while (l < _size)
                    {
                        l <<= 1;
                        if (f(_operation(sm, _array[l])))
                        {
                            sm = _operation(sm, _array[l]);
                            l++;
                        }
                    }
                    return l - _size;
                }
                sm = _operation(sm, _array[l]);
                l++;
            } while ((l & -l) != l);
            return _n;
        }
        /// <summary>
        /// f(op(a[l],a[l+1],...a[r-1])) = trueとなる最小のlを返します
        /// </summary>
        /// <param name="r"></param>
        /// <param name="f"></param>
        /// <returns></returns>
        public int MinLeft(int r, Func<T, bool> f)
        {
            Debug.Assert(0 <= r && r <= _n);
#if DEBUG
            Debug.Assert(f(_identity));
#endif
            if (r == 0) return 0;
            r += _size;
            T sm = _identity;

            do
            {
                r--;
                while (r > 1 && (r % 2 != 0)) r >>= 1;
                if (!f(_operation(_array[r], sm)))
                {
                    while (r < _size)
                    {
                        r = (2 * r + 1);
                        if (f(_operation(_array[r], sm)))
                        {
                            sm = _operation(_array[r], sm);
                            r--;
                        }
                    }
                    return r + 1 - _size;
                }
                sm = _operation(_array[r], sm);
            } while ((r & -r) != r);
            return 0;
        }

        public T this[int i]
        {
            set { Update(i, value); }
            get
            {
                Debug.Assert(0 <= i && i < _n);
                return _array[i + _size];
            }
        }
    }
}

namespace CompLib.Util
{
    using System;
    using System.Linq;

    class Scanner
    {
        private string[] _line;
        private int _index;
        private const char Separator = ' ';

        public Scanner()
        {
            _line = new string[0];
            _index = 0;
        }

        public string Next()
        {
            if (_index >= _line.Length)
            {
                string s;
                do
                {
                    s = Console.ReadLine();
                } while (s.Length == 0);

                _line = s.Split(Separator);
                _index = 0;
            }

            return _line[_index++];
        }

        public string ReadLine()
        {
            _index = _line.Length;
            return Console.ReadLine();
        }

        public int NextInt() => int.Parse(Next());
        public int NextInt1() => NextInt() - 1;
        public long NextLong() => long.Parse(Next());
        public double NextDouble() => double.Parse(Next());
        public decimal NextDecimal() => decimal.Parse(Next());
        public char NextChar() => Next()[0];
        public char[] NextCharArray() => Next().ToCharArray();

        public string[] Array()
        {
            string s = Console.ReadLine();
            _line = s.Length == 0 ? new string[0] : s.Split(Separator);
            _index = _line.Length;
            return _line;
        }

        public int[] IntArray() => Array().Select(int.Parse).ToArray();
        public int[] IntArray1() => Array().Select(s => int.Parse(s) - 1).ToArray();
        public long[] LongArray() => Array().Select(long.Parse).ToArray();
        public double[] DoubleArray() => Array().Select(double.Parse).ToArray();
        public decimal[] DecimalArray() => Array().Select(decimal.Parse).ToArray();
    }
}