#813077 (C++14) No.315 世界のなんとか3.5

• 問題: No.315 世界のなんとか3.5
• ユーザー: 🍮かんプリン
• 提出日時: 2022-11-01 09:37:04
• 言語: C++14 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 994 ms / 2,000 ms
• コード長: 15,598 bytes
• コンパイル時間: 2,415 ms
• コンパイル使用メモリ: 196,612 KB
• 実行使用メモリ: 6,944 KB
• 最終ジャッジ日時: 2024-07-16 04:42:22
• 合計ジャッジ時間: 16,056 ms
• ジャッジサーバーID （参考情報）: judge3 / judge1

ファイルパターン	結果
other	AC * 36

ソースコード

/**
 *   @FileName	a.cpp
 *   @Author	kanpurin
 *   @Created	2022.11.01 09:37:00
**/

#include "bits/stdc++.h" 
using namespace std; 
typedef long long ll;


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;
    }
    
    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;
    }
};
 
constexpr int MOD = 1e9 + 7;
 
struct Monoid {
	using T = mint<MOD>;
    T val;
    bool undef = true;
    Monoid() { *this = zero(); }
    Monoid(T val, bool undef = true) : val(val),
                                       undef(undef) {}
    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;
    }
};

struct Automaton {
    vector<vector<int>> delta;
    vector<bool> is_accept, is_reject;
    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 bool reject(int state) const { return is_reject[state]; }
    inline int size() const {return qsize; }
};

struct IndexAutomaton {
    vector<bool> is_accept, is_reject;
    int qsize;
    int init;
    int alphabet_size = 10;
    function<int(int,int,int)> next;
    inline bool accept(int state) const { return is_accept[state]; }
    inline bool reject(int state) const { return is_reject[state]; }
    inline int size() const {return qsize; }
};

struct LeqIndexAutomaton : public IndexAutomaton {
private:
    const int tight = 0;
    const int loose = 1;
    const int dead  = 2;
    string str;
    bool eq;

    void initializer() { 
        qsize = 3;
        init = tight;
        next = [&](int state, int c, int n) -> int {
            if (n >= str.size() || state == dead) return dead;
            if (state == tight) {
                if (c == str[n]-'0') return tight;
                if (c < str[n]-'0') return loose;
                return dead;
            }
            return loose;
        };
        set_is_accept();
        set_is_reject();
    }

    void set_is_accept() {
        is_accept.resize(qsize,false);
        is_accept[tight] = eq;
        is_accept[loose] = true;
    }

    void set_is_reject() {
        is_reject.resize(qsize,false);
        is_reject[dead] = true;
    }
public:
    function<int(int,int,int)> next;

    LeqIndexAutomaton(string s, bool eq = true, int alpha_size = 10) : str(s),
                                                                  eq(eq) {
        alphabet_size = alpha_size;
        initializer();
    }
};

struct ModuloAutomaton : public Automaton {
private:
    int mod;
    
    void initializer() {
        qsize = mod;
        init = 0;
        set_delta();
        set_is_accept();
        set_is_reject();
    }

    void set_delta() {
        delta.resize(qsize,vector<int>(alphabet_size));
        for (int state = 0; state < qsize; state++) {
            for (int c = 0; c < alphabet_size; c++) {
                delta[state][c] = (state*10+c)%mod;
            }
        }
    }

    void set_is_accept() {
        is_accept.resize(qsize,false);
        is_accept[0] = true;
    }

    void set_is_reject() {
        is_reject.resize(qsize,false);
    }
public:
    ModuloAutomaton(int mod, int alpha_size = 10) : mod(mod) {
        alphabet_size = alpha_size;
        initializer();
    }
};

struct ZigZagAutomaton : public Automaton {
private:
    void initializer() {
        qsize = 2+alphabet_size*3;
        init = alphabet_size*3; 
        set_delta();
        set_is_accept();
        set_is_reject();
    }

    void set_delta() {
        delta.resize(qsize,vector<int>(alphabet_size));
        for (int state = 0; state < qsize; state++) {
            for (int c = 0; c < alphabet_size; c++) {
                if (state == alphabet_size*3) {
                    if (c == 0)
                        delta[state][c] = alphabet_size*3;
                    else
                        delta[state][c] = c;
                }
                else if (state < alphabet_size) {
                    if (c < state)
                        delta[state][c] = alphabet_size+c;
                    else if (c > state)
                        delta[state][c] = alphabet_size*2+c;
                    else
                        delta[state][c] = alphabet_size*3+1;
                }
                else if (state < alphabet_size*2) {
                    if (c > state-alphabet_size)
                        delta[state][c] = alphabet_size*2+c;
                    else
                        delta[state][c] = alphabet_size*3+1;
                }
                else if (state < alphabet_size*3) {
                    if (c < state-alphabet_size*2)
                        delta[state][c] = alphabet_size+c;
                    else
                        delta[state][c] = alphabet_size*3+1;
                }
                else {
                    delta[state][c] = alphabet_size*3+1;
                }
            }
        }
    }

    void set_is_accept() {
        is_accept.resize(qsize,false);
        for (int state = 0; state < alphabet_size*3; state++) {
            is_accept[state] = true;
        }
    }

    void set_is_reject() {
        is_reject.resize(qsize,false);
        is_reject[alphabet_size*3+1] = true;
    }
public:
    ZigZagAutomaton(int alpha_size = 10) {
        alphabet_size = alpha_size;
        initializer();
    }
};

template<class Automaton1, class Automaton2>
Automaton IntersectionAutomaton(const Automaton1 &A, const Automaton2 &B) {
    assert(A.alphabet_size == B.alphabet_size);
    Automaton M;
    M.alphabet_size = A.alphabet_size;
    vector<vector<int>> table(A.size(), vector<int>(B.size(),-1));
    vector<int> x = {A.init}, y = {B.init};
    table[x[0]][y[0]] = 0;
    M.init = 0;
    for (int i = 0; i < x.size(); ++i) {
        M.delta.push_back(vector<int>(M.alphabet_size, -1));
        M.is_accept.push_back(A.accept(x[i]) && B.accept(y[i]));
        M.is_reject.push_back(A.reject(x[i]) || B.reject(y[i]));
        for (int c = 0; c < A.alphabet_size; c++) {
            int u = A.next(x[i],c), v = B.next(y[i],c);
            if (table[u][v] == -1) {
                table[u][v] = x.size();
                x.push_back(u);
                y.push_back(v);
            }
            M.delta[i][c] = table[u][v];
        }
    }
    M.qsize = M.delta.size();
    return M;
}

template<typename Automaton>
Monoid digitDP(const string &s, const Automaton &dfa, bool eq = 1) {
    vector<vector<Monoid>> dp(2,vector<Monoid>(dfa.size(),Monoid::zero()));
    dp[1][dfa.init] = Monoid::e();
    for (int i = 0; i < s.size(); i++) {
        vector<vector<Monoid>> dp2(2,vector<Monoid>(dfa.size(),Monoid::zero()));
        for (int tight = 0; tight <= 1; tight++) {
            for (int state = 0; state < dfa.size(); state++) {
                if (dfa.reject(state) || 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);
                    if (dfa.reject(state_)) continue;
                    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;
}

Automaton Minimize(const Automaton& dfa) {
    std::vector<int> partition_0(dfa.qsize, -1);
    int accept_idx = -1, reject_idx = -1;
    for (int state = 0; state < dfa.qsize; state++) {
        if (!dfa.accept(state)) continue;
        if (accept_idx == -1) accept_idx = state;
        partition_0[state] = accept_idx;
    }
    for (int state = 0; state < dfa.qsize; state++) {
        if (partition_0[state] != -1) continue;
        if (reject_idx < 0) reject_idx = state;
        partition_0[state] = reject_idx;
    }
    auto _equivalent = [&](int i, int j) {
        for (int c = 0; c < dfa.alphabet_size; c++) {
            int dest_i = dfa.delta[i][c];
            int dest_j = dfa.delta[j][c];
            if (partition_0[dest_i] != partition_0[dest_j]) return false;
        }
        return true;
    };
    while (true) {
        vector<int> partition(dfa.qsize, -1);
        for (int i = 0; i < dfa.qsize;) {
            partition[i] = i;
            int i_next = dfa.qsize;
            for (int j = i+1; j < dfa.qsize; j++) {
                if (partition[j] >= 0) continue;  
                if (partition_0[i] == partition_0[j] && _equivalent(i, j)) {
                    partition[j] = i;   
                }
                else if (i_next == dfa.qsize) { i_next = j; }  
            }
            i = i_next;
        }
        if (partition_0 == partition) break;
        partition_0 = move(partition);
    }
    Automaton M;
    M.alphabet_size = dfa.alphabet_size;
    vector<int> idx(dfa.qsize);
    for (int state = 0; state < dfa.qsize; state++) {
        if (partition_0[state] == state) {
            idx[state] = M.delta.size();
            M.delta.push_back(vector<int>(M.alphabet_size, -1));
            M.is_accept.push_back(dfa.accept(state));
            M.is_reject.push_back(dfa.reject(state));
        }
        else {
            idx[state] = idx[partition_0[state]];
            M.is_reject[idx[state]] = M.is_reject[idx[state]] | dfa.reject(state);
        }
    }
    M.qsize = M.delta.size();
    M.init = idx[dfa.init];
    for (int state = 0; state < dfa.qsize; state++) {
        if (partition_0[state] != state) continue;
        for (int c = 0; c < M.alphabet_size; c++) {
            M.delta[idx[state]][c] = idx[dfa.delta[state][c]];
        }
    }
    return M;
}
struct IncludeAllAutomaton : public Automaton {
private:
    vector<int> elems;

    void initializer() { 
        qsize = 1+(1<<(int)elems.size());
        init = (1<<(int)elems.size());
        set_delta();
        set_is_accept();
        set_is_reject();
    }

    void set_delta() {
        delta.resize(qsize,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 {
                    delta[state][c] = state==init?0:state;
                    for (int i = 0; i < elems.size(); i++) {
                        if (c == elems[i]) {
                            delta[state][c] = delta[state][c]|1<<i;
                            break;
                        }
                    }
                }
            }
        }
    }

    void set_is_accept() {
        is_accept.resize(qsize,false);
        is_accept[(1<<(int)elems.size())-1] = true;
    }

    void set_is_reject() {
        is_reject.resize(qsize,false);
    }
public:
    IncludeAllAutomaton(vector<int> elems, int alpha_size = 10) : elems(elems) {
        alphabet_size = alpha_size;
        initializer();
    }
};

template<class Automaton1, class Automaton2>
Automaton UnionAutomaton(const Automaton1 &A, const Automaton2 &B) {
    assert(A.alphabet_size == B.alphabet_size);
    Automaton M;
    M.alphabet_size = A.alphabet_size;
    vector<vector<int>> table(A.size(), vector<int>(B.size(),-1));
    vector<int> x = {A.init}, y = {B.init};
    table[x[0]][y[0]] = 0;
    M.init = 0;
    for (int i = 0; i < x.size(); ++i) {
        M.delta.push_back(vector<int>(M.alphabet_size, -1));
        M.is_accept.push_back(A.accept(x[i]) || B.accept(y[i]));
        M.is_reject.push_back(A.reject(x[i]) && B.reject(y[i]));
        for (int c = 0; c < A.alphabet_size; c++) {
            int u = A.next(x[i],c), v = B.next(y[i],c);
            if (table[u][v] == -1) {
                table[u][v] = x.size();
                x.push_back(u);
                y.push_back(v);
            }
            M.delta[i][c] = table[u][v];
        }
    }
    M.qsize = M.delta.size();
    return M;
}

int main() {
    string a,b;cin >> a >> b;
    int p;cin >> p;
    auto M1 = Minimize(ModuloAutomaton(p));
    auto M2 = ModuloAutomaton(3);
    auto M3 = IncludeAllAutomaton({3});
    auto M4 = UnionAutomaton(M2,M3);
    auto M5 = IntersectionAutomaton(M1,M4);
    cout << digitDP(b,M4).val-digitDP(a,M4,false).val-digitDP(b,M5).val+digitDP(a,M5,false).val << endl;
    return 0;
}