結果
問題 | No.2303 Frog on Grid |
ユーザー |
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提出日時 | 2023-07-20 18:25:50 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 221 ms / 2,000 ms |
コード長 | 3,962 bytes |
コンパイル時間 | 2,512 ms |
コンパイル使用メモリ | 203,708 KB |
最終ジャッジ日時 | 2025-02-15 15:56:40 |
ジャッジサーバーID (参考情報) |
judge1 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 20 |
ソースコード
#include <bits/stdc++.h>using namespace std;using ll = long long;/* p = 2^m a + 1mod root998244353 3924844033 5*/const ll modc = 998244353, MAX=1000000;const ll root = 3;class mint {ll x;public:mint(ll x=0) : x((x%modc+modc)%modc) {}mint operator-() const {return mint(-x);}mint& operator+=(const mint& a) {if ((x += a.x) >= modc) x -= modc;return *this;}mint& operator-=(const mint& a) {if ((x += modc-a.x) >= modc) x -= modc;return *this;}mint& operator*=(const mint& a) {(x *= a.x) %= modc;return *this;}mint operator+(const mint& a) const {mint res(*this);return res+=a;}mint operator-(const mint& a) const {mint res(*this);return res-=a;}mint operator*(const mint& a) const {mint res(*this);return res*=a;}mint pow(ll t) const {if (!t) return 1;mint a = pow(t>>1);a *= a;if (t&1) a *= *this;return a;}mint inv() const {return pow(modc-2);}mint& operator/=(const mint& a) {return (*this) *= a.inv();}mint operator/(const mint& a) const {mint res(*this);return res/=a;}bool operator == (const mint& a) const{return x == a.x;}friend ostream& operator<<(ostream& os, const mint& m){os << m.x;return os;}friend istream& operator>>(istream& ip, mint &m) {ll t;ip >> t;m = mint(t);return ip;}ll val(){return x;}};vector<mint> ntt(vector<mint> a, bool inv = false){ll N = a.size(), m = 0, q = (modc-1)/N;// N=2^m, p=2^m q+1// g = r^q (DFT)// g = r^-q (IDFT)//p=2^m q+1//r^(p-1) = 1//r^(2^m q) = 1//(r^q) ^ (2^m) = 1//w_(2^m) = r^q//w_(2^(m-1)) = (r^q)^2//w_(2^(m-2)) = (r^q)^4for (int i=0; (1<<i)<N; i++) m++;for (int i=0; i<N; i++){int j=0;for (int k=0; k<m; k++) j |= (i>>k & 1) << (m-1-k);if (i < j) swap(a[i], a[j]);}mint g = (inv ? mint(root).pow(q).inv() : mint(root).pow(q));vector<mint> w(m+1);w[m] = g;for (int i=m-1; i>=1; i--) w[i] = w[i+1] * w[i+1];for (int b=1, i=1; b<N; b*=2, i++){for (int k=0; k<N; k += b*2){mint ww = 1;for (int j=0; j<b; j++){mint s = a[j+k], t = a[j+k+b] * ww;a[j+k] = s + t;a[j+k+b] = s - t;ww *= w[i];}}}if (inv){mint Ninv = mint(N).inv();for (int i=0; i<N; i++) a[i] *= Ninv;}return a;}//convolution c[k] = sum(i=0, k) a[i]b[k-i]vector<mint> convolution(vector<mint> a, vector<mint> b){int s = a.size() + b.size() - 1;int t = 1;while(t < s) t *= 2;a.resize(t); b.resize(t);vector<mint> A = ntt(a); //DFTvector<mint> B = ntt(b); //DFTfor (int i=0; i<t; i++) A[i] *= B[i];A = ntt(A, true); //IDFTreturn A;}vector<mint> f, finv;mint inv(mint x){mint ans = 1;ll e = modc-2;while (e > 0){if ((e & 1LL)) ans *= x;e = e >> 1LL;x *= x;}return ans;}void init(){f.resize(MAX+1); finv.resize(MAX+1);f[0] = 1;for (int i=1; i<=MAX; i++) f[i] = f[i-1]*i;finv[MAX] = inv(f[MAX]);for (int i=MAX-1; i>=0; i--) finv[i] = finv[i+1] * (i+1);}int main(){init();int H, W;mint ans=0;cin >> H >> W;vector<mint> B(H+1), D(W+1);for (int b=0; b<=H/2; b++) B[H-b] = finv[H-b*2] * finv[b];for (int d=0; d<=W/2; d++) D[W-d] = finv[W-d*2] * finv[d];vector<mint> C = convolution(B, D);for (int i=0; i<=H+W; i++){ans += f[i] * C[i];}cout << ans << endl;return 0;}