結果

問題 No.2503 Typical Path Counting Problem on a Grid
ユーザー milanis48663220milanis48663220
提出日時 2023-10-14 01:40:03
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 701 ms / 2,000 ms
コード長 4,377 bytes
コンパイル時間 1,169 ms
コンパイル使用メモリ 121,316 KB
最終ジャッジ日時 2025-02-17 07:45:10
ジャッジサーバーID
(参考情報)
judge4 / judge2
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ファイルパターン 結果
other AC * 10
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ソースコード

diff #
プレゼンテーションモードにする

#include <iostream>
#include <algorithm>
#include <iomanip>
#include <vector>
#include <queue>
#include <deque>
#include <set>
#include <map>
#include <tuple>
#include <cmath>
#include <numeric>
#include <functional>
#include <cassert>
#include <atcoder/modint>
#define debug_value(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << #x << "=" << x << endl;
#define debug(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << x << endl;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
using namespace std;
typedef long long ll;
template<typename T>
vector<vector<T>> vec2d(int n, int m, T v){
return vector<vector<T>>(n, vector<T>(m, v));
}
template<typename T>
vector<vector<vector<T>>> vec3d(int n, int m, int k, T v){
return vector<vector<vector<T>>>(n, vector<vector<T>>(m, vector<T>(k, v)));
}
template<typename T>
void print_vector(vector<T> v, char delimiter=' '){
if(v.empty()) {
cout << endl;
return;
}
for(int i = 0; i+1 < v.size(); i++) cout << v[i] << delimiter;
cout << v.back() << endl;
}
using mint = atcoder::modint998244353;
ostream& operator<<(ostream& os, const mint& m){
os << m.val();
return os;
}
template<typename T, int N, int M>
class Matrix {
public:
array<array<T, M>, N> dat;
Matrix(T val=0) {
for(int i = 0; i < N; i++){
for(int j = 0; j < M; j++){
dat[i][j] = val;
}
}
}
Matrix(array<array<T, M>, N> dat): dat(dat){ }
array<T, M>& operator[](int x) {
return dat[x];
}
};
template<typename T, int N, int M, int K>
Matrix<T, N, K> operator*(Matrix<T, N, M> a, Matrix<T, M, K> b){
Matrix<T, N, K> c(T(0));
for(int i = 0; i < N; i++){
for(int j = 0; j < K; j++){
for(int k = 0; k < M; k++){
c.dat[i][j] += a.dat[i][k]*b.dat[k][j];
}
}
}
return c;
}
template<typename T, int N>
Matrix<T, N, N> operator^(Matrix<T, N, N> m, long long r){
Matrix<T, N, N> ans(T(0));
for(int i = 0; i < N; i++) ans[i][i] = T(1);
while (r > 0) {
if (r&1) ans = (ans*m);
m = (m*m);
r >>= 1;
}
return ans;
}
template <typename T, int N, int M>
void print_mat(Matrix<T, N, M> a){
for(int i = 0; i < N; i++){
for(int j = 0; j < M; j++){
cout << a.dat[i][j] << ' ';
}
cout << endl;
}
}
template <typename T, int N, int M>
ostream& operator<<(ostream& os, const Matrix<T, N, M>& m){
print_mat<T, N, M>(m);
return os;
}
mint naive(ll n, ll m){
if(n > m) swap(n, m);
if(n == 0) return mint(1);
vector<mint> dp(n+m+1);
dp[0] = 1;
dp[1] = 2;
for(ll x = 2; x <= n+m; x++){
if(x <= n){
dp[x] += dp[x-1]*2*x;
dp[x] += dp[x-2]*(x-1);
}else if(x <= m){
dp[x] += dp[x-1]*(2*n+1);
dp[x] += dp[x-2]*n;
}else{
int c = n+m-x+1;
dp[x] += dp[x-1]*2*c;
dp[x] += dp[x-2]*c;
}
}
// print_vector(dp);
return dp[n+m];
}
const int N = 10000000;
using M = Matrix<mint, 2, 2>;
using V = Matrix<mint, 2, 1>;
M f0[N+1];
M f1[N+1];
void init(){
f0[1] = M({{
{mint(1), mint(0)},
{mint(0), mint(1)},
}});
for(int x = 2; x <= N; x++){
f0[x] = M({{
{mint(2*x), mint(x-1)},
{mint(1), mint(0)},
}})*f0[x-1];
}
f1[0] = M({{
{mint(1), mint(0)},
{mint(0), mint(1)},
}});
for(int x = 1; x <= N; x++){
f1[x] = f1[x-1]*M({{
{mint(2*x), mint(x)},
{mint(1), mint(0)},
}});
}
}
mint solve(ll n, ll m){
if(n > m) swap(n, m);
if(n == 0) return mint(1);
mint dp1 = 2;
mint dp0 = 1;
V v({{
{dp1},
{dp0}
}});
v = f0[n]*v;
M A({{
{mint(2*n+1), mint(n)},
{mint(1), mint(0)},
}});
v = (A^(m-n))*v;
v = f1[n]*v;
return v[0][0];
}
int main(){
ios::sync_with_stdio(false);
cin.tie(0);
cout << setprecision(10) << fixed;
init();
int t; cin >> t;
while(t--) {
ll n, m; cin >> n >> m;
cout << solve(n, m) << endl;
}
}
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