結果
問題 | No.2164 Equal Balls |
ユーザー | 👑 emthrm |
提出日時 | 2022-12-15 02:06:22 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
TLE
|
実行時間 | - |
コード長 | 10,732 bytes |
コンパイル時間 | 2,682 ms |
コンパイル使用メモリ | 214,128 KB |
実行使用メモリ | 10,084 KB |
最終ジャッジ日時 | 2024-04-26 05:52:44 |
合計ジャッジ時間 | 18,728 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge3 |
(要ログイン)
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
5,248 KB |
testcase_01 | AC | 2 ms
5,376 KB |
testcase_02 | AC | 3 ms
5,376 KB |
testcase_03 | AC | 2 ms
5,376 KB |
testcase_04 | AC | 2 ms
5,376 KB |
testcase_05 | AC | 3 ms
5,376 KB |
testcase_06 | AC | 2 ms
5,376 KB |
testcase_07 | AC | 2 ms
5,376 KB |
testcase_08 | AC | 4,138 ms
5,376 KB |
testcase_09 | AC | 4,092 ms
5,376 KB |
testcase_10 | AC | 774 ms
5,376 KB |
testcase_11 | TLE | - |
testcase_12 | -- | - |
testcase_13 | -- | - |
testcase_14 | -- | - |
testcase_15 | -- | - |
testcase_16 | -- | - |
testcase_17 | -- | - |
testcase_18 | -- | - |
testcase_19 | -- | - |
testcase_20 | -- | - |
testcase_21 | -- | - |
testcase_22 | -- | - |
testcase_23 | -- | - |
testcase_24 | -- | - |
testcase_25 | -- | - |
testcase_26 | -- | - |
testcase_27 | -- | - |
testcase_28 | -- | - |
testcase_29 | -- | - |
testcase_30 | -- | - |
testcase_31 | -- | - |
testcase_32 | -- | - |
testcase_33 | -- | - |
testcase_34 | -- | - |
testcase_35 | -- | - |
testcase_36 | -- | - |
testcase_37 | -- | - |
testcase_38 | -- | - |
testcase_39 | -- | - |
testcase_40 | -- | - |
testcase_41 | -- | - |
testcase_42 | -- | - |
testcase_43 | -- | - |
testcase_44 | -- | - |
testcase_45 | -- | - |
testcase_46 | -- | - |
testcase_47 | -- | - |
testcase_48 | -- | - |
testcase_49 | -- | - |
testcase_50 | -- | - |
testcase_51 | -- | - |
testcase_52 | -- | - |
testcase_53 | -- | - |
ソースコード
#define _USE_MATH_DEFINES #include <bits/stdc++.h> using namespace std; #define FOR(i,m,n) for(int i=(m);i<(n);++i) #define REP(i,n) FOR(i,0,n) #define ALL(v) (v).begin(),(v).end() using ll = long long; constexpr int INF = 0x3f3f3f3f; constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL; constexpr double EPS = 1e-8; constexpr int MOD = 998244353; // constexpr int MOD = 1000000007; constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1}; constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1}; constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1}; template <typename T, typename U> inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; } template <typename T, typename U> inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; } struct IOSetup { IOSetup() { std::cin.tie(nullptr); std::ios_base::sync_with_stdio(false); std::cout << fixed << setprecision(20); } } iosetup; template <int M> struct MInt { unsigned int v; MInt() : v(0) {} MInt(const long long x) : v(x >= 0 ? x % M : x % M + M) {} static constexpr int get_mod() { return M; } static void set_mod(const int divisor) { assert(divisor == M); } static void init(const int x = 10000000) { inv(x, true); fact(x); fact_inv(x); } static MInt inv(const int n, const bool init = false) { // assert(0 <= n && n < M && std::__gcd(n, M) == 1); static std::vector<MInt> inverse{0, 1}; const int prev = inverse.size(); if (n < prev) { return inverse[n]; } else if (init) { // "n!" and "M" must be disjoint. inverse.resize(n + 1); for (int i = prev; i <= n; ++i) { inverse[i] = -inverse[M % i] * (M / i); } return inverse[n]; } int u = 1, v = 0; for (unsigned int a = n, b = M; b;) { const unsigned int q = a / b; std::swap(a -= q * b, b); std::swap(u -= q * v, v); } return u; } static MInt fact(const int n) { static std::vector<MInt> factorial{1}; const int prev = factorial.size(); if (n >= prev) { factorial.resize(n + 1); for (int i = prev; i <= n; ++i) { factorial[i] = factorial[i - 1] * i; } } return factorial[n]; } static MInt fact_inv(const int n) { static std::vector<MInt> f_inv{1}; const int prev = f_inv.size(); if (n >= prev) { f_inv.resize(n + 1); f_inv[n] = inv(fact(n).v); for (int i = n; i > prev; --i) { f_inv[i - 1] = f_inv[i] * i; } } return f_inv[n]; } static MInt nCk(const int n, const int k) { if (n < 0 || n < k || k < 0) return 0; return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) : fact_inv(n - k) * fact_inv(k)); } static MInt nPk(const int n, const int k) { return n < 0 || n < k || k < 0 ? 0 : fact(n) * fact_inv(n - k); } static MInt nHk(const int n, const int k) { return n < 0 || k < 0 ? 0 : (k == 0 ? 1 : nCk(n + k - 1, k)); } static MInt large_nCk(long long n, const int k) { if (n < 0 || n < k || k < 0) return 0; inv(k, true); MInt res = 1; for (int i = 1; i <= k; ++i) { res *= inv(i) * n--; } return res; } MInt pow(long long exponent) const { MInt res = 1, tmp = *this; for (; exponent > 0; exponent >>= 1) { if (exponent & 1) res *= tmp; tmp *= tmp; } return res; } MInt& operator+=(const MInt& x) { if ((v += x.v) >= M) v -= M; return *this; } MInt& operator-=(const MInt& x) { if ((v += M - x.v) >= M) v -= M; return *this; } MInt& operator*=(const MInt& x) { v = static_cast<unsigned long long>(v) * x.v % M; return *this; } MInt& operator/=(const MInt& x) { return *this *= inv(x.v); } bool operator==(const MInt& x) const { return v == x.v; } bool operator!=(const MInt& x) const { return v != x.v; } bool operator<(const MInt& x) const { return v < x.v; } bool operator<=(const MInt& x) const { return v <= x.v; } bool operator>(const MInt& x) const { return v > x.v; } bool operator>=(const MInt& x) const { return v >= x.v; } MInt& operator++() { if (++v == M) v = 0; return *this; } MInt operator++(int) { const MInt res = *this; ++*this; return res; } MInt& operator--() { v = (v == 0 ? M - 1 : v - 1); return *this; } MInt operator--(int) { const MInt res = *this; --*this; return res; } MInt operator+() const { return *this; } MInt operator-() const { return MInt(v ? M - v : 0); } MInt operator+(const MInt& x) const { return MInt(*this) += x; } MInt operator-(const MInt& x) const { return MInt(*this) -= x; } MInt operator*(const MInt& x) const { return MInt(*this) *= x; } MInt operator/(const MInt& x) const { return MInt(*this) /= x; } friend std::ostream& operator<<(std::ostream& os, const MInt& x) { return os << x.v; } friend std::istream& operator>>(std::istream& is, MInt& x) { long long v; is >> v; x = MInt(v); return is; } }; using ModInt = MInt<MOD>; template <int T> struct NumberTheoreticTransform { using ModInt = MInt<T>; NumberTheoreticTransform() { for (int i = 0; i < 23; ++i) { if (primes[i][0] == ModInt::get_mod()) { n_max = 1 << primes[i][2]; root = ModInt(primes[i][1]).pow((primes[i][0] - 1) >> primes[i][2]); return; } } assert(false); } template <typename U> std::vector<ModInt> dft(const std::vector<U>& a) { const int n = a.size(); int lg = 1; while ((1 << lg) < n) ++lg; std::vector<ModInt> b(1 << lg, 0); std::copy(a.begin(), a.end(), b.begin()); calc(&b); return b; } void idft(std::vector<ModInt>* a) { const int n = a->size(); assert(__builtin_popcount(n) == 1); calc(a); std::reverse(std::next(a->begin()), a->end()); const ModInt inv_n = ModInt::inv(n); for (int i = 0; i < n; ++i) { (*a)[i] *= inv_n; } } template <typename U> std::vector<ModInt> convolution(const std::vector<U>& a, const std::vector<U>& b) { const int a_size = a.size(), b_size = b.size(); const int c_size = a_size + b_size - 1; int lg = 1; while ((1 << lg) < c_size) ++lg; const int n = 1 << lg; std::vector<ModInt> c(n, 0), d(n, 0); std::copy(a.begin(), a.end(), c.begin()); calc(&c); std::copy(b.begin(), b.end(), d.begin()); calc(&d); for (int i = 0; i < n; ++i) { c[i] *= d[i]; } idft(&c); c.resize(c_size); return c; } private: const int primes[23][3]{ {16957441, 329, 14}, {17006593, 26, 15}, {19529729, 770, 17}, {167772161, 3, 25}, {469762049, 3, 26}, {645922817, 3, 23}, {897581057, 3, 23}, {924844033, 5, 21}, {935329793, 3, 22}, {943718401, 7, 22}, {950009857, 7, 21}, {962592769, 7, 21}, {975175681, 17, 21}, {976224257, 3, 20}, {985661441, 3, 22}, {998244353, 3, 23}, {1004535809, 3, 21}, {1007681537, 3, 20}, {1012924417, 5, 21}, {1045430273, 3, 20}, {1051721729, 6, 20}, {1053818881, 7, 20}, {1224736769, 3, 24} }; int n_max; ModInt root; std::vector<int> butterfly{0}; std::vector<std::vector<ModInt>> omega{{1}}; void calc(std::vector<ModInt>* a) { const int n = a->size(), prev_n = butterfly.size(); if (n > prev_n) { assert(n <= n_max); butterfly.resize(n); const int prev_lg = omega.size(), lg = __builtin_ctz(n); for (int i = 1; i < prev_n; ++i) { butterfly[i] <<= lg - prev_lg; } for (int i = prev_n; i < n; ++i) { butterfly[i] = (butterfly[i >> 1] >> 1) | ((i & 1) << (lg - 1)); } omega.resize(lg); for (int i = prev_lg; i < lg; ++i) { omega[i].resize(1 << i); const ModInt tmp = root.pow((ModInt::get_mod() - 1) >> (i + 1)); for (int j = 0; j < (1 << (i - 1)); ++j) { omega[i][j << 1] = omega[i - 1][j]; omega[i][(j << 1) + 1] = omega[i - 1][j] * tmp; } } } const int shift = __builtin_ctz(butterfly.size()) - __builtin_ctz(n); for (int i = 0; i < n; ++i) { const int j = butterfly[i] >> shift; if (i < j) std::swap((*a)[i], (*a)[j]); } for (int block = 1, den = 0; block < n; block <<= 1, ++den) { for (int i = 0; i < n; i += (block << 1)) { for (int j = 0; j < block; ++j) { const ModInt tmp = (*a)[i + j + block] * omega[den][j]; (*a)[i + j + block] = (*a)[i + j] - tmp; (*a)[i + j] += tmp; } } } } }; int main() { constexpr int M = 300; NumberTheoreticTransform<MOD> ntt; int n, m; cin >> n >> m; vector<int> a(n), b(n); REP(i, n) cin >> a[i]; REP(i, n) cin >> b[i]; vector<ModInt> dp_(M * m * 2 + 1, 0); auto dp = next(dp_.begin(), M * m); dp[0] = 1; REP(i, m) { int lb = -M, ub = M; for (int k = i; k < n; k += m) { chmax(lb, -b[k]); chmin(ub, a[k]); } vector<ModInt> ways(ub - lb + 1, 1); for (int k = i; k < n; k += m) { vector<ModInt> c(a[k] + b[k] + 1, 0), d(a[k] + b[k] + 1, 0); for (int j = 0; j <= a[k]; ++j) { c[j + b[k]] = ModInt::nCk(a[k], j); } for (int j = 0; j <= b[k]; ++j) { d[b[k] - j] = ModInt::nCk(b[k], j); } const vector<ModInt> e = ntt.convolution(c, d); for (int j = lb; j <= ub; ++j) { ways[j - lb] *= e[j + b[k] * 2]; } } vector<ModInt> nxt_(M * m * 2 + 1, 0); auto nxt = next(nxt_.begin(), M * m); for (int j = -M * m; j <= M * m; ++j) { REP(k, ub - lb + 1) { if (-M * m <= j + k + lb && j + k + lb <= M * m) nxt[j + k + lb] += dp[j] * ways[k]; } } dp_.swap(nxt_); dp = next(dp_.begin(), M * m); } cout << dp[0] << '\n'; // ModInt ans = 0; // const auto f = [&](auto&& f, vector<int>& c, vector<int>& d, ModInt ways) -> void { // if (c.size() < n) { // const int i = c.size(); // for (int j = 0; j <= a[i]; ++j) { // c.emplace_back(j); // f(f, c, d, ways * ModInt::nCk(a[i], j)); // c.pop_back(); // } // } else if (d.size() < n) { // const int i = d.size(); // for (int j = 0; j <= b[i]; ++j) { // d.emplace_back(j); // f(f, c, d, ways * ModInt::nCk(b[i], j)); // d.pop_back(); // } // } else { // REP(i, n - m + 1) { // int c_sum = 0, d_sum = 0; // REP(j, m) c_sum += c[i + j]; // REP(j, m) d_sum += d[i + j]; // if (c_sum != d_sum) return; // } // ans += ways; // } // }; // vector<int> c, d; // c.reserve(n); // d.reserve(n); // f(f, c, d, 1); // assert(dp[0] == ans); return 0; }