結果

問題 No.315 世界のなんとか3.5
ユーザー 🍮かんプリン🍮かんプリン
提出日時 2022-11-04 09:58:05
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
WA  
実行時間 -
コード長 10,828 bytes
コンパイル時間 4,274 ms
コンパイル使用メモリ 228,672 KB
実行使用メモリ 4,500 KB
最終ジャッジ日時 2023-09-25 14:10:31
合計ジャッジ時間 12,460 ms
ジャッジサーバーID
（参考情報） 		judge13 / judge14
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
4,384 KB
testcase_01 AC 3 ms
4,380 KB
testcase_02 AC 7 ms
4,380 KB
testcase_03 AC 3 ms
4,384 KB
testcase_04 AC 2 ms
4,384 KB
testcase_05 AC 3 ms
4,376 KB
testcase_06 AC 7 ms
4,380 KB
testcase_07 AC 3 ms
4,380 KB
testcase_08 AC 3 ms
4,380 KB
testcase_09 AC 2 ms
4,376 KB
testcase_10 AC 2 ms
4,380 KB
testcase_11 AC 3 ms
4,376 KB
testcase_12 WA -
testcase_13 WA -
testcase_14 WA -
testcase_15 WA -
testcase_16 WA -
testcase_17 WA -
testcase_18 WA -
testcase_19 WA -
testcase_20 WA -
testcase_21 WA -
testcase_22 WA -
testcase_23 WA -
testcase_24 WA -
testcase_25 WA -
testcase_26 WA -
testcase_27 WA -
testcase_28 WA -
testcase_29 WA -
testcase_30 WA -
testcase_31 WA -
testcase_32 WA -
testcase_33 WA -
testcase_34 AC 506 ms
4,380 KB
testcase_35 AC 531 ms
4,376 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: メンバ関数 ‘void PartitionRefinement::print()’ 内:
main.cpp:159:19: 警告: structured bindings only available with ‘-std=c++17’ or ‘-std=gnu++17’ [-Wc++17-extensions]
  159 |         for (auto [i,st] : block) {
      |                   ^
main.cpp: 関数 ‘Automaton Minimize(const Automaton&)’ 内:
main.cpp:189:14: 警告: structured bindings only available with ‘-std=c++17’ or ‘-std=gnu++17’ [-Wc++17-extensions]
  189 |         auto [c,b_id] = que.front(); que.pop();
      |              ^

ソースコード

diff # 

/**
 *   @FileName	a.cpp
 *   @Author	kanpurin
 *   @Created	2022.11.04 09:57:54
**/

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


struct Monoid {
    using T = ll;
    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});
            }
        }
    }
    pr.print();
    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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