結果
| 問題 | No.2503 Typical Path Counting Problem on a Grid |
| ユーザー |
 torisasami4
|
| 提出日時 | 2023-10-12 01:11:02 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 477 ms / 2,000 ms |
| コード長 | 10,973 bytes |
| コンパイル時間 | 2,676 ms |
| コンパイル使用メモリ | 244,012 KB |
| 最終ジャッジ日時 | 2025-02-17 06:46:12 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 10 |
ソースコード
// #define _GLIBCXX_DEBUG
#pragma GCC optimize("O2,no-stack-protector,unroll-loops,fast-math")
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < int(n); i++)
#define per(i, n) for (int i = (n)-1; 0 <= i; i--)
#define rep2(i, l, r) for (int i = (l); i < int(r); i++)
#define per2(i, l, r) for (int i = (r)-1; int(l) <= i; i--)
#define each(e, v) for (auto& e : v)
#define MM << " " <<
#define pb push_back
#define eb emplace_back
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define sz(x) (int)x.size()
template <typename T> void print(const vector<T>& v, T x = 0) {
int n = v.size();
for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
if (v.empty()) cout << '\n';
}
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
template <typename T> bool chmax(T& x, const T& y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T> bool chmin(T& x, const T& y) {
return (x > y) ? (x = y, true) : false;
}
template <class T>
using minheap = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template <class T> using maxheap = std::priority_queue<T>;
template <typename T> int lb(const vector<T>& v, T x) {
return lower_bound(begin(v), end(v), x) - begin(v);
}
template <typename T> int ub(const vector<T>& v, T x) {
return upper_bound(begin(v), end(v), x) - begin(v);
}
template <typename T> void rearrange(vector<T>& v) {
sort(begin(v), end(v));
v.erase(unique(begin(v), end(v)), end(v));
}
// __int128_t gcd(__int128_t a, __int128_t b) {
// if (a == 0)
// return b;
// if (b == 0)
// return a;
// __int128_t cnt = a % b;
// while (cnt != 0) {
// a = b;
// b = cnt;
// cnt = a % b;
// }
// return b;
// }
struct Union_Find_Tree {
vector<int> data;
const int n;
int cnt;
Union_Find_Tree(int n) : data(n, -1), n(n), cnt(n) {}
int root(int x) {
if (data[x] < 0) return x;
return data[x] = root(data[x]);
}
int operator[](int i) { return root(i); }
bool unite(int x, int y) {
x = root(x), y = root(y);
if (x == y) return false;
if (data[x] > data[y]) swap(x, y);
data[x] += data[y], data[y] = x;
cnt--;
return true;
}
int size(int x) { return -data[root(x)]; }
int count() { return cnt; };
bool same(int x, int y) { return root(x) == root(y); }
void clear() {
cnt = n;
fill(begin(data), end(data), -1);
}
};
template <int mod> struct Mod_Int {
int x;
Mod_Int() : x(0) {}
Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
static int get_mod() { return mod; }
Mod_Int& operator+=(const Mod_Int& p) {
if ((x += p.x) >= mod) x -= mod;
return *this;
}
Mod_Int& operator-=(const Mod_Int& p) {
if ((x += mod - p.x) >= mod) x -= mod;
return *this;
}
Mod_Int& operator*=(const Mod_Int& p) {
x = (int)(1LL * x * p.x % mod);
return *this;
}
Mod_Int& operator/=(const Mod_Int& p) {
*this *= p.inverse();
return *this;
}
Mod_Int& operator++() { return *this += Mod_Int(1); }
Mod_Int operator++(int) {
Mod_Int tmp = *this;
++*this;
return tmp;
}
Mod_Int& operator--() { return *this -= Mod_Int(1); }
Mod_Int operator--(int) {
Mod_Int tmp = *this;
--*this;
return tmp;
}
Mod_Int operator-() const { return Mod_Int(-x); }
Mod_Int operator+(const Mod_Int& p) const { return Mod_Int(*this) += p; }
Mod_Int operator-(const Mod_Int& p) const { return Mod_Int(*this) -= p; }
Mod_Int operator*(const Mod_Int& p) const { return Mod_Int(*this) *= p; }
Mod_Int operator/(const Mod_Int& p) const { return Mod_Int(*this) /= p; }
bool operator==(const Mod_Int& p) const { return x == p.x; }
bool operator!=(const Mod_Int& p) const { return x != p.x; }
Mod_Int inverse() const {
assert(*this != Mod_Int(0));
return pow(mod - 2);
}
Mod_Int pow(long long k) const {
Mod_Int now = *this, ret = 1;
for (; k > 0; k >>= 1, now *= now) {
if (k & 1) ret *= now;
}
return ret;
}
friend ostream& operator<<(ostream& os, const Mod_Int& p) {
return os << p.x;
}
friend istream& operator>>(istream& is, Mod_Int& p) {
long long a;
is >> a;
p = Mod_Int<mod>(a);
return is;
}
};
ll mpow2(ll x, ll n, ll mod) {
ll ans = 1;
x %= mod;
while (n != 0) {
if (n & 1) ans = ans * x % mod;
x = x * x % mod;
n = n >> 1;
}
ans %= mod;
return ans;
}
template <typename T> T modinv(T a, const T& m) {
T b = m, u = 1, v = 0;
while (b > 0) {
T t = a / b;
swap(a -= t * b, b);
swap(u -= t * v, v);
}
return u >= 0 ? u % m : (m - (-u) % m) % m;
}
ll divide_int(ll a, ll b) {
if (b < 0) a = -a, b = -b;
return (a >= 0 ? a / b : (a - b + 1) / b);
}
// const int MOD = 1000000007;
const int MOD = 998244353;
using mint = Mod_Int<MOD>;
// ----- library -------
template <typename T>
struct Matrix {
vector<vector<T>> A;
int n, m;
Matrix(int n, int m) : A(n, vector<T>(m, 0)), n(n), m(m) {}
inline const vector<T> &operator[](int k) const { return A[k]; }
inline vector<T> &operator[](int k) { return A[k]; }
static Matrix I(int l) {
Matrix ret(l, l);
for (int i = 0; i < l; i++) ret[i][i] = 1;
return ret;
}
Matrix &operator*=(const Matrix &B) {
assert(m == B.n);
Matrix ret(n, B.m);
for (int i = 0; i < n; i++) {
for (int k = 0; k < m; k++) {
for (int j = 0; j < B.m; j++) ret[i][j] += A[i][k] * B[k][j];
}
}
swap(A, ret.A);
m = B.m;
return *this;
}
Matrix operator*(const Matrix &B) const { return Matrix(*this) *= B; }
Matrix pow(long long k) const {
assert(n == m);
Matrix now = *this, ret = I(n);
for (; k > 0; k >>= 1, now *= now) {
if (k & 1) ret *= now;
}
return ret;
}
bool eq(const T &a, const T &b) const {
return a == b;
// return abs(a-b) <= EPS;
}
// 行基本変形を用いて簡約化を行い、(rank, det) の組を返す
pair<int, T> row_reduction(vector<T> &b) {
assert((int)b.size() == n);
if (n == 0) return make_pair(0, m > 0 ? 0 : 1);
int check = 0, rank = 0;
T det = (n == m ? 1 : 0);
for (int j = 0; j < m; j++) {
int pivot = check;
for (int i = check; i < n; i++) {
if (A[i][j] != 0) pivot = i;
// if(abs(A[i][j]) > abs(A[pivot][j])) pivot = i; // T が小数の場合はこちら
}
if (check != pivot) det *= T(-1);
swap(A[check], A[pivot]), swap(b[check], b[pivot]);
if (eq(A[check][j], T(0))) {
det = T(0);
continue;
}
rank++;
det *= A[check][j];
T r = T(1) / A[check][j];
for (int k = j + 1; k < m; k++) A[check][k] *= r;
b[check] *= r;
A[check][j] = T(1);
for (int i = 0; i < n; i++) {
if (i == check) continue;
if (!eq(A[i][j], 0)) {
for (int k = j + 1; k < m; k++) A[i][k] -= A[i][j] * A[check][k];
b[i] -= A[i][j] * b[check];
}
A[i][j] = T(0);
}
if (++check == n) break;
}
return make_pair(rank, det);
}
pair<int, T> row_reduction() {
vector<T> b(n, T(0));
return row_reduction(b);
}
// 行基本変形を行い、逆行列を求める
pair<bool, Matrix> inverse() {
if (n != m) return make_pair(false, Matrix(0, 0));
if (n == 0) return make_pair(true, Matrix(0, 0));
Matrix ret = I(n);
for (int j = 0; j < n; j++) {
int pivot = j;
for (int i = j; i < n; i++) {
if (A[i][j] != 0) pivot = i;
// if(abs(A[i][j]) > abs(A[pivot][j])) pivot = i; // T が小数の場合はこちら
}
swap(A[j], A[pivot]), swap(ret[j], ret[pivot]);
if (eq(A[j][j], T(0))) return make_pair(false, Matrix(0, 0));
T r = T(1) / A[j][j];
for (int k = j + 1; k < n; k++) A[j][k] *= r;
for (int k = 0; k < n; k++) ret[j][k] *= r;
A[j][j] = T(1);
for (int i = 0; i < n; i++) {
if (i == j) continue;
if (!eq(A[i][j], T(0))) {
for (int k = j + 1; k < n; k++) A[i][k] -= A[i][j] * A[j][k];
for (int k = 0; k < n; k++) ret[i][k] -= A[i][j] * ret[j][k];
}
A[i][j] = T(0);
}
}
return make_pair(true, ret);
}
// Ax = b の解の 1 つと解空間の基底の組を返す
vector<vector<T>> Gaussian_elimination(vector<T> b) {
row_reduction(b);
vector<vector<T>> ret;
vector<int> p(n, m);
vector<bool> is_zero(m, true);
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
if (!eq(A[i][j], T(0))) {
p[i] = j;
break;
}
}
if (p[i] < m) {
is_zero[p[i]] = false;
} else if (!eq(b[i], T(0))) {
return {};
}
}
vector<T> x(m, T(0));
for (int i = 0; i < n; i++) {
if (p[i] < m) x[p[i]] = b[i];
}
ret.push_back(x);
for (int j = 0; j < m; j++) {
if (!is_zero[j]) continue;
x[j] = T(1);
for (int i = 0; i < n; i++) {
if (p[i] < m) x[p[i]] = -A[i][j];
}
ret.push_back(x);
x[j] = T(0);
}
return ret;
}
};
// ----- library -------
int main() {
ios::sync_with_stdio(false);
std::cin.tie(nullptr);
cout << fixed << setprecision(15);
const int si = 1e7 + 10;
vector<mint> f(si);
f[0] = 1, f[1] = 2;
rep2(i, 2, si) f[i] = f[i - 1] * i * 2 + f[i - 2] * (i - 1);
int T;
cin >> T;
while (T--) {
ll n, m;
cin >> n >> m;
if (n > m)
swap(n, m);
if (n == 0) {
cout << 1 << '\n';
continue;
}
Matrix<mint> a(2, 2), b(2, 1);
a[0][0] = n * 2 + 1, a[0][1] = n;
a[1][0] = 1, a[1][1] = 0;
b[0][0] = f[n];
b[1][0] = f[n - 1];
auto ret = a.pow(m - n) * b;
cout << ret[0][0] * f[n] + ret[1][0] * f[n - 1] * n << '\n';
}
}