test/yukicoder/1740.test.cpp

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• Last update: 2022-11-06 06:14:50+09:00
• Problem: https://yukicoder.me/problems/no/1740

Depends on

• オートマトン (digitDP/automaton.hpp)
• digitDP/count_number.hpp
• digitDP/digit_dp_leq.hpp
• other/mint.hpp

Code

#define PROBLEM "https://yukicoder.me/problems/no/1740"
#include <bits/stdc++.h>
using namespace std;

#include "digitDP/digit_dp_leq.hpp"
#include "digitDP/count_number.hpp"
#include "other/mint.hpp"

const int MOD = 998244353;

// 受理する文字列の数
struct Monoid {
    using T = mint<MOD>;
    T val;
    bool undef = true;
    Monoid() { *this = zero(); }
    Monoid(T val, bool undef = true) : val(val),
                                       undef(undef) {}
    // 単位元(和)
    static Monoid zero() { return Monoid(0); }
    static Monoid e() { return Monoid(1,false); }
    Monoid& operator+=(const Monoid &a) {
        if (this->undef) *this = a;
        else if (!a.undef) this->val += a.val;
        return *this;
    }
    Monoid& operator*=(int c) {
        return *this;
    }
    friend Monoid operator+(const Monoid& a, const Monoid& b) {
        return Monoid(a) += b;
    }
    friend Monoid operator*(const Monoid& a, int c) {
        return Monoid(a) *= c;
    }
    friend std::ostream& operator<<(std::ostream &os, const Monoid &x) {
        return os << x.val;
    }
};

int main() {
    int n;cin >> n;
    string s;cin >> s;
    for (int i = 0; i < n; i++) s[i] = s[i]-'a'+'0';
    s = "1"+s;
    string t(n+1,'0'); t[0] = '1';
    vector<bool> flg(26,false); flg[0] = true;
    auto M = CountNumberAutomaton(flg,1,true,26);
    cout << digitDP<Monoid>(s,M,false).val-digitDP<Monoid>(t,M,false).val << endl;
}

#line 1 "test/yukicoder/1740.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1740"
#include <bits/stdc++.h>
using namespace std;

#line 3 "digitDP/automaton.hpp"

struct Automaton {
    std::vector<std::vector<int>> delta;
    std::vector<bool> is_accept;
    int qsize;
    int init;
    int alphabet_size = 10;
    inline int next(int state, int c) const { return delta[state][c]; }
    inline bool accept(int state) const { return is_accept[state]; }
    inline int size() const {return qsize; }
};
#line 4 "digitDP/digit_dp_leq.hpp"

// LeqAutomaton付き桁DP
template<typename Monoid>
Monoid digitDP(const std::string &s, const Automaton &dfa, bool eq = 1) {
    std::vector<std::vector<Monoid>> dp(2,std::vector<Monoid>(dfa.size(),Monoid::zero()));
    dp[1][dfa.init] = Monoid::e();
    for (int i = 0; i < (int)s.size(); i++) {
        std::vector<std::vector<Monoid>> dp2(2,std::vector<Monoid>(dfa.size(),Monoid::zero()));
        for (int tight = 0; tight <= 1; tight++) {
            for (int state = 0; state < dfa.size(); state++) {
                if (dp[tight][state].undef) continue;
                int lim = (tight ? s[i] - '0' : dfa.alphabet_size - 1);
                for (int c = 0; c <= lim; c++) {
                    int tight_ = tight && c == lim;
                    int state_ = dfa.next(state,c);
                    dp2[tight_][state_] += dp[tight][state]*c;
                }
            }
        }
        dp = move(dp2);
    }
    Monoid ans = Monoid::zero();
    for (int tight = 0; tight <= eq; tight++)
        for (int state = 0; state < dfa.size(); state++)
            if (dfa.accept(state)) ans += dp[tight][state];
    return ans;
}
#line 4 "digitDP/count_number.hpp"

// 特定の数字がN回(eq?丁度:以下)含まれる文字列を受理
struct CountNumberAutomaton : public Automaton {
private:
    std::vector<bool> flg;
    int num;
    bool eq;

    void initializer() { 
        assert(flg.size() == alphabet_size);
        qsize = num+3;
        init = num+2;
        set_delta();
        set_is_accept();
    }

    void set_delta() {
        delta.resize(qsize,std::vector<int>(alphabet_size));
        for (int state = 0; state < qsize; state++) {
            for (int c = 0; c < alphabet_size; c++) {
                if (state == init && c == 0) delta[state][c] = init;
                else if (state == init) delta[state][c] = flg[c]?1:0;
                else if (state == num+1) delta[state][c] = state;
                else delta[state][c] = flg[c]?state+1:state;
            }
        }
    }

    void set_is_accept() {
        is_accept.resize(qsize,false);
        if (eq) is_accept[num] = true;
        else {
            for (int state = 0; state <= num; state++) {
                is_accept[state] = true;
            }
            is_accept[num+2] = true;
        }
    }
public:
    CountNumberAutomaton(std::vector<bool> flg, int num, bool eq = false, int alpha_size = 10) : flg(flg),
                                                                                                 num(num),
                                                                                                 eq(eq) {
        alphabet_size = alpha_size;
        initializer();
    }
};
#line 2 "other/mint.hpp"

template< int MOD >
struct mint {
public:
    unsigned int x;
    mint() : x(0) {}
    mint(long long v) {
        long long w = (long long)(v % (long long)(MOD));
        if (w < 0) w += MOD;
        x = (unsigned int)(w);
    }
    mint(std::string &s) {
        unsigned int z = 0;
        for (int i = 0; i < s.size(); i++) {
            z *= 10;
            z += s[i] - '0';
            z %= MOD;
        }
        x = z;
    }
    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }
    mint& operator+=(const mint &a) {
        if ((x += a.x) >= MOD) x -= MOD;
        return *this;
    }
    mint& operator-=(const mint &a) {
        if ((x -= a.x) >= MOD) x += MOD;
        return *this;
    }
    mint& operator*=(const mint &a) {
        unsigned long long z = x;
        z *= a.x;
        x = (unsigned int)(z % MOD);
        return *this;
    }
    mint& operator/=(const mint &a) {return *this = *this * a.inv(); }
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs.x == rhs.x;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs.x != rhs.x;
    }
    friend std::ostream& operator<<(std::ostream &os, const mint &n) {
        return os << n.x;
    }
    friend std::istream &operator>>(std::istream &is, mint &n) {
        unsigned int x;
        is >> x;
        n = mint(x);
        return is;
    }
    mint inv() const {
        assert(x);
        return pow(MOD-2);
    }
    mint pow(long long n) const {        
        assert(0 <= n);
        mint p = *this, r = 1;
        while (n) {
            if (n & 1) r *= p;
            p *= p;
            n >>= 1;
        }
        return r;
    }
    
    // 存在しない場合0を返す(二乗して確認).
    // O(log^2MOD)
    mint sqrt() const {
        if (this->x < 2) return *this;
        if (this->pow((MOD-1)>>1).x != 1) return mint(0);
        mint b = 1, one = 1;
        while (b.pow((MOD-1) >> 1) == 1) b += one;
        long long m = MOD-1, e = 0;
        while (m % 2 == 0) m >>= 1, e += 1;
        mint x = this->pow((m - 1) >> 1);
        mint y = (*this) * x * x;
        x *= (*this);
        mint z = b.pow(m);
        while (y.x != 1) {
            int j = 0;
            mint t = y;
            while (t != one) j += 1, t *= t;
            z = z.pow(1LL << (e-j-1));
            x *= z; z *= z; y *= z; e = j;
        }
        return x;
    }
};
#line 8 "test/yukicoder/1740.test.cpp"

const int MOD = 998244353;

// 受理する文字列の数
struct Monoid {
    using T = mint<MOD>;
    T val;
    bool undef = true;
    Monoid() { *this = zero(); }
    Monoid(T val, bool undef = true) : val(val),
                                       undef(undef) {}
    // 単位元(和)
    static Monoid zero() { return Monoid(0); }
    static Monoid e() { return Monoid(1,false); }
    Monoid& operator+=(const Monoid &a) {
        if (this->undef) *this = a;
        else if (!a.undef) this->val += a.val;
        return *this;
    }
    Monoid& operator*=(int c) {
        return *this;
    }
    friend Monoid operator+(const Monoid& a, const Monoid& b) {
        return Monoid(a) += b;
    }
    friend Monoid operator*(const Monoid& a, int c) {
        return Monoid(a) *= c;
    }
    friend std::ostream& operator<<(std::ostream &os, const Monoid &x) {
        return os << x.val;
    }
};

int main() {
    int n;cin >> n;
    string s;cin >> s;
    for (int i = 0; i < n; i++) s[i] = s[i]-'a'+'0';
    s = "1"+s;
    string t(n+1,'0'); t[0] = '1';
    vector<bool> flg(26,false); flg[0] = true;
    auto M = CountNumberAutomaton(flg,1,true,26);
    cout << digitDP<Monoid>(s,M,false).val-digitDP<Monoid>(t,M,false).val << endl;
}

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