結果
問題 | No.2503 Typical Path Counting Problem on a Grid |
ユーザー |
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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 |
ソースコード
#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;}}