結果
| 問題 | No.1241 Eternal Tours |
| コンテスト | |
| ユーザー |
 hitonanode
|
| 提出日時 | 2020-09-06 12:28:46 |
| 言語 | C++17 (gcc 15.2.0 + boost 1.89.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 8,632 bytes |
| 記録 | |
| コンパイル時間 | 1,382 ms |
| コンパイル使用メモリ | 91,996 KB |
| 最終ジャッジ日時 | 2025-01-14 07:39:05 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge5 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 23 WA * 17 |
ソースコード
#include <cassert>
#include <chrono>
#include <iostream>
#include <vector>
using namespace std;
// Berlekamp-Massey 解法（与える項の数が足りず想定WA）
template <int mod>
struct ModInt
{
using lint = long long;
int val;
constexpr ModInt() : val(0) {}
constexpr ModInt &_setval(lint v) { val = (v >= mod ? v - mod : v); return *this; }
constexpr ModInt(lint v) { _setval(v % mod + mod); }
explicit operator bool() const { return val != 0; }
constexpr ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); }
constexpr ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + mod); }
constexpr ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % mod); }
constexpr ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % mod); }
constexpr ModInt operator-() const { return ModInt()._setval(mod - val); }
constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % mod + x.val); }
friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % mod - x.val + mod); }
friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.val % mod); }
friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.inv() % mod); }
constexpr bool operator==(const ModInt &x) const { return val == x.val; }
constexpr bool operator!=(const ModInt &x) const { return val != x.val; }
bool operator<(const ModInt &x) const { return val < x.val; } // To use std::map<ModInt, T>
friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; is >> t; x = ModInt(t); return is; }
friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { os << x.val; return os; }
constexpr lint power(lint n) const {
lint ans = 1, tmp = this->val;
while (n) {
if (n & 1) ans = ans * tmp % mod;
tmp = tmp * tmp % mod;
n /= 2;
}
return ans;
}
constexpr ModInt pow(lint n) const {
return power(n);
}
constexpr lint inv() const { return this->power(mod - 2); }
};
constexpr int md = 998244353;
using mint = ModInt<md>;
// Berlekamp–Massey algorithm
// <https://en.wikipedia.org/wiki/Berlekamp%E2%80%93Massey_algorithm>
// Complexity: O(N^2)
// input: S = sequence from field K
// return: L = degree of minimal polynomial,
// C_reversed = monic min. polynomial (size = L + 1, reversed order, C_reversed[0] = 1))
// Formula: convolve(S, C_reversed)[i] = 0 for i >= L
// Example:
// - [1, 2, 4, 8, 16] -> (1, [1, -2])
// - [1, 1, 2, 3, 5, 8] -> (2, [1, -1, -1])
// - [0, 0, 0, 0, 1] -> (5, [1, 0, 0, 0, 0, 998244352]) (mod 998244353)
// - [] -> (0, [1])
// - [0, 0, 0] -> (0, [1])
// - [-2] -> (1, [1, 2])
template <typename Tfield>
std::pair<int, std::vector<Tfield>> linear_recurrence(const std::vector<Tfield> &S)
{
int N = S.size();
using poly = std::vector<Tfield>;
poly C_reversed{1}, B{1};
int L = 0, m = 1;
Tfield b = 1;
// adjust: C(x) <- C(x) - (d / b) x^m B(x)
auto adjust = [](poly C, const poly &B, Tfield d, Tfield b, int m) -> poly {
C.resize(std::max(C.size(), B.size() + m));
Tfield a = d / b;
for (unsigned i = 0; i < B.size(); i++) C[i + m] -= a * B[i];
return C;
};
for (int n = 0; n < N; n++) {
Tfield d = S[n];
for (int i = 1; i <= L; i++) d += C_reversed[i] * S[n - i];
if (d == 0) m++;
else if (2 * L <= n) {
poly T = C_reversed;
C_reversed = adjust(C_reversed, B, d, b, m);
L = n + 1 - L;
B = T;
b = d;
m = 1;
}
else C_reversed = adjust(C_reversed, B, d, b, m++);
}
return std::make_pair(L, C_reversed);
}
// Calculate x^N mod f(x)
// Known as `Kitamasa method`
// Input: f_reversed: monic, reversed (f_reversed[0] = 1)
// Complexity: O(K^2 lgN) (K: deg. of f)
// Example: (4, [1, -1, -1]) -> [2, 3]
// ( x^4 = (x^2 + x + 2)(x^2 - x - 1) + 3x + 2 )
// Reference: <http://misawa.github.io/others/fast_kitamasa_method.html>
// <http://sugarknri.hatenablog.com/entry/2017/11/18/233936>
template <typename Tfield>
std::vector<Tfield> monomial_mod_polynomial(long long N, const std::vector<Tfield> &f_reversed)
{
assert(!f_reversed.empty() and f_reversed[0] == 1);
int K = f_reversed.size() - 1;
if (!K) return {};
int D = 64 - __builtin_clzll(N);
std::vector<Tfield> ret(K, 0);
ret[0] = 1;
auto self_conv = [](std::vector<Tfield> x) -> std::vector<Tfield> {
int d = x.size();
std::vector<Tfield> ret(d * 2 - 1);
for (int i = 0; i < d; i++)
{
ret[i * 2] += x[i] * x[i];
for (int j = 0; j < i; j++) ret[i + j] += x[i] * x[j] * 2;
}
return ret;
};
for (int d = D; d--;)
{
ret = self_conv(ret);
for (int i = 2 * K - 2; i >= K; i--)
{
for (int j = 1; j <= K; j++) ret[i - j] -= ret[i] * f_reversed[j];
}
ret.resize(K);
if ((N >> d) & 1)
{
std::vector<Tfield> c(K);
c[0] = -ret[K - 1] * f_reversed[K];
for (int i = 1; i < K; i++)
{
c[i] = ret[i - 1] - ret[K - 1] * f_reversed[K - i];
}
ret = c;
}
}
return ret;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &vec)
{
os << '[';
for (auto v : vec)
os << v << ',';
os << ']';
return os;
}
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl
int main()
{
int X, Y;
long long T;
long long a, b, c, d;
cin >> X >> Y >> T >> a >> b >> c >> d;
auto START = std::chrono::system_clock::now();
T = (T - 1) % (md - 1) + 1;
long long dist = abs(a - c) + abs(b - d);
if (dist > T)
{
puts("0");
return 0;
}
mint primitive_root = 3;
mint rx = primitive_root.pow((md - 1) / (1 << (X + 1))), rxi = rx.inv();
mint ry = primitive_root.pow((md - 1) / (1 << (Y + 1))), ryi = ry.inv();
mint rxa = rx.pow(a), rxai = rxa.inv();
mint ryb = ry.pow(b), rybi = ryb.inv();
mint rxc = rx.pow(c), rxci = rxc.inv();
mint ryd = ry.pow(d), rydi = ryd.inv();
mint rxpow = 1, rxpowi = 1, rypow, rypowi;
mint rxapow = 1, rxapowi = 1, rybpow, rybpowi;
mint rxcpow = 1, rxcpowi = 1, rydpow, rydpowi;
vector<mint> coeffs;
vector<mint> fkls;
for (int k = 0; k < 1 << X; k++)
{
rypow = 1, rypowi = 1;
rybpow = 1, rybpowi = 1;
rydpow = 1, rydpowi = 1;
for (int l = 0; l < 1 << Y; l++)
{
fkls.emplace_back(rxpow + rxpowi + rypow + rypowi + 1);
coeffs.emplace_back((rxapow - rxapowi) * (rybpow - rybpowi) * (rxcpow - rxcpowi) * (rydpow - rydpowi) * mint(1 << (X + Y + 2)).inv());
rypow *= ry, rypowi *= ryi;
rybpow *= ryb, rybpowi *= rybi;
rydpow *= ryd, rydpowi *= rydi;
}
rxpow *= rx, rxpowi *= rxi;
rxapow *= rxa, rxapowi *= rxai;
rxcpow *= rxc, rxcpowi *= rxci;
}
vector<mint> fklpow;
dbg(dist);
dbg(T);
for (auto x : fkls) fklpow.emplace_back(x.pow(dist));
vector<mint> seq;
for (long long t = dist; t - dist <= 10000; t++)
{
if (chrono::duration_cast<std::chrono::milliseconds>(std::chrono::system_clock::now() - START).count() > 2000) break;
mint tmp = 0;
for (int kl = 0; kl < 1 << (X + Y); kl++) {
tmp += coeffs[kl] * fklpow[kl];
fklpow[kl] *= fkls[kl];
}
if (t == T)
{
cout << tmp << '\n';
return 0;
}
seq.emplace_back(tmp);
}
dbg(seq.size());
auto [L, poly_reversed] = linear_recurrence(seq);
dbg(L);
auto g = monomial_mod_polynomial(T - dist, poly_reversed);
mint ret = 0;
for (int i = 0; i < int(g.size()); i++) ret += seq.at(i) * g.at(i);
cout << ret << '\n';
}