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 | 2022-11-01 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 |
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| 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;elsedelta[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;elsedelta[state][c] = alphabet_size*3+1;}else if (state < alphabet_size*2) {if (c > state-alphabet_size)delta[state][c] = alphabet_size*2+c;elsedelta[state][c] = alphabet_size*3+1;}else if (state < alphabet_size*3) {if (c < state-alphabet_size*2)delta[state][c] = alphabet_size+c;elsedelta[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;}