#813690 (C++14) No.315 世界のなんとか3.5

提出ソース

結果

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	2022-11-04 10:12:47
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	547 ms / 2,000 ms
コード長	13,628 bytes
コンパイル時間	3,045 ms
コンパイル使用メモリ	229,892 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-07-18 11:16:49
合計ジャッジ時間	11,151 ms
ジャッジサーバーID （参考情報）	judge1 / judge3

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 6,812 KB
testcase_01	AC	2 ms 6,820 KB
testcase_02	AC	4 ms 6,812 KB
testcase_03	AC	2 ms 6,940 KB
testcase_04	AC	2 ms 6,944 KB
testcase_05	AC	2 ms 6,940 KB
testcase_06	AC	4 ms 6,944 KB
testcase_07	AC	2 ms 6,940 KB
testcase_08	AC	2 ms 6,940 KB
testcase_09	AC	2 ms 6,944 KB
testcase_10	AC	2 ms 6,944 KB
testcase_11	AC	2 ms 6,940 KB
testcase_12	AC	119 ms 6,944 KB
testcase_13	AC	119 ms 6,940 KB
testcase_14	AC	234 ms 6,944 KB
testcase_15	AC	237 ms 6,944 KB
testcase_16	AC	252 ms 6,940 KB
testcase_17	AC	252 ms 6,944 KB
testcase_18	AC	128 ms 6,940 KB
testcase_19	AC	128 ms 6,944 KB
testcase_20	AC	141 ms 6,944 KB
testcase_21	AC	139 ms 6,940 KB
testcase_22	AC	272 ms 6,940 KB
testcase_23	AC	272 ms 6,940 KB
testcase_24	AC	252 ms 6,940 KB
testcase_25	AC	272 ms 6,940 KB
testcase_26	AC	251 ms 6,944 KB
testcase_27	AC	234 ms 6,940 KB
testcase_28	AC	268 ms 6,940 KB
testcase_29	AC	535 ms 6,944 KB
testcase_30	AC	488 ms 6,940 KB
testcase_31	AC	450 ms 6,940 KB
testcase_32	AC	541 ms 6,940 KB
testcase_33	AC	275 ms 6,944 KB
testcase_34	AC	512 ms 6,940 KB
testcase_35	AC	547 ms 6,940 KB

権限があれば一括ダウンロードができます

コンパイルメッセージ

main.cpp: In member function 'void PartitionRefinement::print()':
main.cpp:261:19: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17' [-Wc++17-extensions]
  261 |         for (auto [i,st] : block) {
      |                   ^
main.cpp: In function 'Automaton Minimize(const Automaton&)':
main.cpp:291:14: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17' [-Wc++17-extensions]
  291 |         auto [c,b_id] = que.front(); que.pop();
      |              ^

ソースコード

raw source code

/**
 *   @FileName	a.cpp
 *   @Author	kanpurin
 *   @Created	2022.11.04 09:59:29
**/

#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; }
};

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;
}

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 PartitionRefinement {
    unordered_map<int,unordered_set<int>> block;
    vector<int> block_id;
    int t;

    PartitionRefinement(int k) : block_id(k) {
        for (int i = 0; i < k; i++) {
            block[0].insert(i);
            block_id[i] = 0;
        }
        t = 1;
    }
    
    vector<pair<int,int>> partition(vector<int> &v) {
        unordered_map<int,int> split;
        for (int i = 0; i < v.size(); i++) {
            if (block[block_id[v[i]]].size() == 1) {
                if (split.find(block_id[v[i]]) == split.end()) continue;
                for (int p : block[split[block_id[v[i]]]]) {
                    block_id[p] = block_id[v[i]];
                    block[block_id[v[i]]].insert(p);
                }
                block.erase(split[block_id[v[i]]]);
                continue;
            }
            block[block_id[v[i]]].erase(v[i]);
            if (split.find(block_id[v[i]]) != split.end()) {
                block_id[v[i]] = split[block_id[v[i]]];
                block[block_id[v[i]]].insert(v[i]);
            }
            else {
                split[block_id[v[i]]] = t;
                block_id[v[i]] = t++;
                block[block_id[v[i]]].insert(v[i]);
            }
        }
        vector<pair<int,int>> res;
        for (auto p : split) {
            res.push_back(p);
        }
        return res;
    }

    void print() {
        for (auto [i,st] : block) {
            cerr << i << " [ ";
            for (int v : st) {
                cerr << v << " ";
            }
            cerr << "]" << endl;
        }
    }
};

Automaton Minimize(const Automaton& dfa) {
    vector<vector<vector<int>>> inv_delta(dfa.size(),vector<vector<int>>(dfa.alphabet_size));
    for (int state = 0; state < dfa.size(); state++) {
        for (int c = 0; c < dfa.alphabet_size; c++) {
            int t = dfa.delta[state][c];
            inv_delta[t][c].push_back(state);
        }
    }
    PartitionRefinement pr(dfa.size());
    vector<int> f;
    for (int state = 0; state < dfa.size(); state++) {
        if (dfa.accept(state)) f.push_back(state);
    }
    pr.partition(f);
    queue<pair<int,int>> que;
    for (int c = 0; c < dfa.alphabet_size; c++) {
        que.push({c,0});
        que.push({c,1});
    }
    while(!que.empty()) {
        auto [c,b_id] = que.front(); que.pop();
        vector<int> v;
        for (int state : pr.block[b_id]) {
            for (int p : inv_delta[state][c]) {
                v.push_back(p);
            }
        }
        if (v.size() == 0) continue;
        auto par = pr.partition(v);
        for (auto p : par) {
            if (pr.block[p.first].size() > pr.block[p.second].size()) {
                swap(p.first,p.second);
            }
            if (pr.block[p.first].size() == 0) continue;
            for (int c2 = 0; c2 < dfa.alphabet_size; c2++) {
                que.push({c2,p.first});
            }
        }
    }
    map<int,int> mp;
    for (int state = 0; state < dfa.size(); state++) {
        int b_id = pr.block_id[state];
        if (mp.find(b_id) != mp.end()) continue;
        mp[b_id] = mp.size();
    }
    vector<int> to_state(dfa.size());
    for (int state = 0; state < dfa.size(); state++) {
        to_state[state] = mp[pr.block_id[state]];
    }
    Automaton M;
    M.init = to_state[dfa.init];
    M.alphabet_size = dfa.alphabet_size;
    M.qsize = mp.size();
    M.delta.resize(M.qsize,vector<int>(M.alphabet_size));
    M.is_accept.resize(M.qsize);
    M.is_reject.resize(M.qsize);
    for (int state = 0; state < dfa.size(); state++) {
        for (int c = 0; c < dfa.alphabet_size; c++) {
            M.delta[to_state[state]][c] = to_state[dfa.next(state,c)];
        }
        if (dfa.accept(state)) M.is_accept[to_state[state]] = true;
        if (dfa.reject(state)) M.is_reject[to_state[state]] = true;
    }
    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;
}

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;
}

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 = Minimize(UnionAutomaton(M2,M3));
    auto M5 = Minimize(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;
}

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結果

テストケース

コンパイルメッセージ

ソースコード