digitDP

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View the Project on GitHub kanpurin/digitDP

:heavy_check_mark: test/yukicoder/0362.test.cpp

Depends on

Code

#define PROBLEM "https://yukicoder.me/problems/no/362"
#include <bits/stdc++.h>
using namespace std;

#include "digitDP/digit_dp_leq.hpp"
#include "digitDP/intersection.hpp"
#include "digitDP/count_number.hpp"
#include "digitDP/kadomatsu.hpp"

// 受理する文字列の数
struct Monoid {
    using T = long long;
    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 t;cin >> t;
    auto M = KadomatsuAutomaton();
    auto M2 = IntersectionAutomaton(M,CountNumberAutomaton({1,1,1,1,1,1,1,1,1,1},2));
    while(t--) {
        long long k;cin >> k;
        long long l = 0, r = 37294859064823;
        while(r-l>1) {
            long long mid = (l+r)/2;
            string sm = to_string(mid);
            if (k <= digitDP<Monoid>(sm,M).val-digitDP<Monoid>(sm,M2).val) {
                r = mid;
            }
            else {
                l = mid;
            }
        }
        cout << r << endl;
    }
    return 0;
}
#line 1 "test/yukicoder/0362.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/362"
#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 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/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 4 "digitDP/kadomatsu.hpp"

#line 6 "digitDP/kadomatsu.hpp"

// 門松文字列を受理
struct KadomatsuAutomaton : public Automaton {
private:
    void initializer() { 
        qsize = 11*11+1;
        init = 0;
        set_delta();
        set_is_accept();
    }

    void set_delta() {
        delta.resize(qsize,std::vector<int>(alphabet_size,0));
        for (int i = -1; i < 10; i++) {
            for (int j = -1; j < 10; j++) {
                for (int k = 0; k < 10; k++) {
                    if (i == -1 && j == -1 && k == 0) {
                        delta[(i+1)*11+(j+1)][k] = 0;
                    }
                    else if (i != -1 && j == -1) {
                        delta[(i+1)*11+(j+1)][k] = qsize-1;
                    }
                    else if (i == -1 && j != -1 && j != k) {
                        delta[(i+1)*11+(j+1)][k] = (j+1)*11+(k+1);
                    }
                    else if (i == -1 && j != -1) {
                        delta[(i+1)*11+(j+1)][k] = qsize-1;
                    }
                    else if (i == -1) {
                        delta[(i+1)*11+(j+1)][k] = (j+1)*11+(k+1);
                    }
                    else if (i != j && j != k && i != k && (j==std::min({i,j,k})||j==std::max({i,j,k}))) {
                        delta[(i+1)*11+(j+1)][k] = (j+1)*11+(k+1);
                    }
                    else {
                        delta[(i+1)*11+(j+1)][k] = qsize-1;
                    }
                }
            }
        }
        for (int c = 0; c < alphabet_size; c++) {
            delta[qsize-1][c] = qsize-1;
        }
    }

    void set_is_accept() {
        is_accept.resize(qsize,false);
        for (int i = 0; i < 10; i++) {
            for (int j = 0; j < 10; j++) {
                is_accept[(i+1)*11+(j+1)] = true;
            }
        }
    }
public:
    KadomatsuAutomaton(int alpha_size = 10) {
        alphabet_size = alpha_size;
        initializer();
    }
};
#line 9 "test/yukicoder/0362.test.cpp"

// 受理する文字列の数
struct Monoid {
    using T = long long;
    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 t;cin >> t;
    auto M = KadomatsuAutomaton();
    auto M2 = IntersectionAutomaton(M,CountNumberAutomaton({1,1,1,1,1,1,1,1,1,1},2));
    while(t--) {
        long long k;cin >> k;
        long long l = 0, r = 37294859064823;
        while(r-l>1) {
            long long mid = (l+r)/2;
            string sm = to_string(mid);
            if (k <= digitDP<Monoid>(sm,M).val-digitDP<Monoid>(sm,M2).val) {
                r = mid;
            }
            else {
                l = mid;
            }
        }
        cout << r << endl;
    }
    return 0;
}
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