digitDP

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View the Project on GitHub kanpurin/digitDP

:heavy_check_mark: test/yukicoder/1417.test.cpp

Depends on

Code

#define PROBLEM "https://yukicoder.me/problems/no/1417"
#include <bits/stdc++.h>
using namespace std;

#include "digitDP/intersection.hpp"
#include "digitDP/digit_dp_leq.hpp"
#include "digitDP/forbidden.hpp"
#include "digitDP/prod_of_digits.hpp"
#include "other/mint.hpp"

const int MOD = 1e9 + 7;

// 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() {
    string n;cin >> n;
    auto M1 = ForbiddenNumberAutomaton({1,0,0,0,0,0,0,0,0,0});
    auto M2 = ProdOfDigitsAutomaton(100);
    auto M3 = IntersectionAutomaton(M1,M2);
    cout << digitDP<Monoid>(n,M3) << endl;
    return 0;
}
#line 1 "test/yukicoder/1417.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1417"
#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 3 "digitDP/intersection.hpp"

// どちらにも受理されるような文字列を受理
Automaton IntersectionAutomaton(const Automaton &A, const Automaton &B) {
    assert(A.alphabet_size == B.alphabet_size);
    Automaton M;
    M.alphabet_size = A.alphabet_size;
    std::vector<std::vector<int>> table(A.size(), std::vector<int>(B.size(),-1));
    std::vector<int> x = {A.init}, y = {B.init};
    table[x[0]][y[0]] = 0;
    M.init = 0;
    for (int i = 0; i < (int)x.size(); ++i) {
        M.delta.emplace_back(M.alphabet_size, -1);
        M.is_accept.emplace_back(A.accept(x[i]) && B.accept(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.emplace_back(u);
                y.emplace_back(v);
            }
            M.delta[i][c] = table[u][v];
        }
    }
    M.qsize = M.delta.size();
    return M;
}
#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/forbidden.hpp"

// ある文字が現れない文字列を受理
struct ForbiddenNumberAutomaton : public Automaton {
private:
    std::vector<bool> banflg;
    
    void initializer() { 
        qsize = 3;
        init = 0;
        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 == 0) {
                    if (c == 0) delta[state][c] = 0;
                    else if (banflg[c]) delta[state][c] = 2;
                    else delta[state][c] = 1;
                }
                else if (state == 1) {
                    if (banflg[c]) delta[state][c] = 2;
                    else delta[state][c] = 1;
                }
                else {
                    delta[state][c] = 2;
                }
            }
        }
    }

    void set_is_accept() {
        is_accept.resize(qsize,false);
        is_accept[1] = true;
    }
public:
    ForbiddenNumberAutomaton(std::vector<bool> banflg, int alpha_size = 10) : banflg(banflg) {
        assert(banflg.size() == alpha_size);
        alphabet_size = alpha_size;
        initializer();
    }
};
#line 4 "digitDP/prod_of_digits.hpp"

// 桁積がNの倍数となる文字列を受理(Nの素因数は|Σ|未満)
// |Σ|=10のみの実装
// |Q|=O(log^4(N))
struct ProdOfDigitsAutomaton : public Automaton {
private:
    long long N;
    int cnt_2 = 0,cnt_3 = 0,cnt_5 = 0,cnt_7 = 0;

    inline int _tostate(int i2, int i3, int i5, int i7) {
        return std::min(i2,cnt_2)+(std::min(i3,cnt_3)+(std::min(i5,cnt_5)+std::min(i7,cnt_7)*(cnt_5+1))*(cnt_3+1))*(cnt_2+1);
    }

    int _nextstate(int i2, int i3, int i5, int i7, int c) {
        if (c == 0) return _tostate(cnt_2,cnt_3,cnt_5,cnt_7);
        else if (c == 1) return _tostate(i2,i3,i5,i7);
        else if (c == 2) return _tostate(i2+1,i3,i5,i7);
        else if (c == 3) return _tostate(i2,i3+1,i5,i7);
        else if (c == 4) return _tostate(i2+2,i3,i5,i7);
        else if (c == 5) return _tostate(i2,i3,i5+1,i7);
        else if (c == 6) return _tostate(i2+1,i3+1,i5,i7);
        else if (c == 7) return _tostate(i2,i3,i5,i7+1);
        else if (c == 8) return _tostate(i2+3,i3,i5,i7);
        else return _tostate(i2,i3+2,i5,i7);
    }

    void initializer() {
        long long M = N;
        while(M%2 == 0) M/=2,cnt_2++;
        while(M%3 == 0) M/=3,cnt_3++;
        while(M%5 == 0) M/=5,cnt_5++;
        while(M%7 == 0) M/=7,cnt_7++;
        assert(M == 1);
        qsize = (cnt_2+1)*(cnt_3+1)*(cnt_5+1)*(cnt_7+1)+1;
        init = (cnt_2+1)*(cnt_3+1)*(cnt_5+1)*(cnt_7+1);
        set_delta();
        set_is_accept();
    }

    void set_delta() {
        delta.resize(qsize,std::vector<int>(alphabet_size));
        for (int c = 0; c < alphabet_size; c++) {
            if (c == 0) delta[init][c] = init;
            else delta[init][c] = _nextstate(0,0,0,0,c);
        }
        for (int i2 = 0; i2 <= cnt_2; i2++) {
            for (int i3 = 0; i3 <= cnt_3; i3++) {
                for (int i5 = 0; i5 <= cnt_5; i5++) {
                    for (int i7 = 0; i7 <= cnt_7; i7++) {
                        int state = _tostate(i2,i3,i5,i7);
                        for (int c = 0; c < alphabet_size; c++) {
                            delta[state][c] = _nextstate(i2,i3,i5,i7,c);
                        }
                    }
                }
            }
        }
    }

    void set_is_accept() {
        is_accept.resize(qsize);
        is_accept[_tostate(cnt_2,cnt_3,cnt_5,cnt_7)] = true;
    }
public:
    ProdOfDigitsAutomaton(long long N, int alpha_size = 10) : N(N) {
        assert(alpha_size == 10);
        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 10 "test/yukicoder/1417.test.cpp"

const int MOD = 1e9 + 7;

// 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() {
    string n;cin >> n;
    auto M1 = ForbiddenNumberAutomaton({1,0,0,0,0,0,0,0,0,0});
    auto M2 = ProdOfDigitsAutomaton(100);
    auto M3 = IntersectionAutomaton(M1,M2);
    cout << digitDP<Monoid>(n,M3) << endl;
    return 0;
}
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