結果

問題 No.2503 Typical Path Counting Problem on a Grid
ユーザー woodywoodywoodywoody
提出日時 2023-10-16 17:47:03
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 702 ms / 2,000 ms
コード長 6,250 bytes
コンパイル時間 4,443 ms
コンパイル使用メモリ 246,772 KB
実行使用メモリ 42,496 KB
最終ジャッジ日時 2024-09-16 22:15:33
合計ジャッジ時間 11,457 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 133 ms
42,240 KB
testcase_01 AC 566 ms
42,368 KB
testcase_02 AC 169 ms
42,240 KB
testcase_03 AC 506 ms
42,368 KB
testcase_04 AC 648 ms
42,496 KB
testcase_05 AC 594 ms
42,368 KB
testcase_06 AC 698 ms
42,368 KB
testcase_07 AC 702 ms
42,240 KB
testcase_08 AC 690 ms
42,368 KB
testcase_09 AC 647 ms
42,368 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include<bits/stdc++.h>
#include<atcoder/all>
#define rep(i,b) for(int i=0;i<b;i++)
#define rrep(i,b) for(int i=b-1;i>=0;i--)
#define rep1(i,b) for(int i=1;i<b;i++)
#define repx(i,x,b) for(int i=x;i<b;i++)
#define rrepx(i,x,b) for(int i=b-1;i>=x;i--)
#define fore(i,a) for(auto& i:a)
#define rng(x) (x).begin(), (x).end()
#define rrng(x) (x).rbegin(), (x).rend()
#define sz(x) ((int)(x).size())
#define pb push_back
#define fi first
#define se second
#define pcnt __builtin_popcountll

using namespace std;
using namespace atcoder;

using ll = long long;
using ld = long double;
template<typename T> using mpq = priority_queue<T, vector<T>, greater<T>>;
template<typename T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<typename T> bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
template<typename T> ll sumv(const vector<T>&a){ll res(0);for(auto&&x:a)res+=x;return res;}
bool yn(bool a) { if(a) {cout << "Yes" << endl; return true;} else {cout << "No" << endl; return false;}}
#define retval(x) {cout << #x << endl; return;}
#define cout2(x,y) cout << x << " " << y << endl;
#define coutp(p) cout << p.fi << " " << p.se << endl;
#define out cout << ans << endl;
#define outd cout << fixed << setprecision(20) << ans << endl;
#define outm cout << ans.val() << endl;
#define outv fore(yans , ans) cout << yans << "\n";
#define outdv fore(yans , ans) cout << yans.val() << "\n";
#define assertmle(x) if (!(x)) {vi v(3e8);}
#define asserttle(x) if (!(x)) {while(1){}}
#define coutv(v) {fore(vy , v) {cout << vy << " ";} cout << endl;}
#define coutv2(v) fore(vy , v) cout << vy << "\n";
#define coutvm(v) {fore(vy , v) {cout << vy.val() << " ";} cout << endl;}
#define coutvm2(v) fore(vy , v) cout << vy.val() << "\n";
using pll = pair<ll,ll>;using pil = pair<int,ll>;using pli = pair<ll,int>;using pii = pair<int,int>;using pdd = pair<ld,ld>;
using vi = vector<int>;using vd = vector<ld>;using vl = vector<ll>;using vs = vector<string>;using vb = vector<bool>;
using vpii = vector<pii>;using vpli = vector<pli>;using vpll = vector<pll>;using vpil = vector<pil>;
using vvi = vector<vector<int>>;using vvl = vector<vector<ll>>;using vvs = vector<vector<string>>;using vvb = vector<vector<bool>>;
using vvpii = vector<vector<pii>>;using vvpli = vector<vector<pli>>;using vvpll = vector<vpll>;using vvpil = vector<vpil>;
using mint = modint998244353;
//using mint = modint1000000007;
//using mint = dynamic_modint<0>;
using vm = vector<mint>;
using vvm = vector<vector<mint>>;
vector<int> dx={1,0,-1,0,1,1,-1,-1},dy={0,1,0,-1,1,-1,1,-1};
ll gcd(ll a, ll b) { return a?gcd(b%a,a):b;}
ll lcm(ll a, ll b) { return a/gcd(a,b)*b;}
#define yes {cout <<"Yes"<<endl;}
#define no {cout <<"No"<<endl;}
const double eps = 1e-10;
const ll LINF = 1001002003004005006ll;
const int INF = 1001001001;
#ifdef MY_LOCAL_DEBUG
#include "./debug/localDebug.cpp"
#define showp(p) cerr<<#p<<" = "<<p.fi<<" : "<<p.se<<endl
#define show1(a) cerr<<#a<<" = "<<a<<endl
#define show2(a,b) cerr<<#a<<" = "<<a<<" : "<<#b<<" = "<<b<<endl
#define show3(a,b,c) cerr<<#a<<" = "<<a<<" : "<<#b<<" = "<<b<<" : "<<#c<<" = "<<c<<endl
#define show4(a,b,c,d) cerr<<#a<<" = "<<a<<" : "<<#b<<" = "<<b<<" : "<<#c<<" = "<<c<<" : "<<#d<<" = "<<d<<endl
#define show5(a,b,c,d,e) cerr<<#a<<" = "<<a<<" : "<<#b<<" = "<<b<<" : "<<#c<<" = "<<c<<" : "<<#d<<" = "<<d<<" : "<<#e<<" = "<<e<<endl
#define DEBUG_LINE cout << "DEBUG_LINE : " << __LINE__ << endl
#define showv(v) {cout<<#v<<" : "; fore(vy , v) {cout << vy << " ";} cout << endl;}
#define showv2(v) {cout<<#v<<endl; fore(vy , v) cout << vy << "\n";}
#define showvm(v) {cout<<#v<<" : "; fore(vy , v) {cout << vy.val() << " ";} cout << endl;}
#define showvm2(v) {cout<<#v<<endl; fore(vy , v) cout << vy.val() << "\n";}
#define showmat(v) {cout<<#v<<endl; fore(row , v) { fore(seg , row) cout << seg << " "; cout << endl;}}
#define showmatm(v) {cout<<#v<<endl; fore(row , v) { fore(seg , row) cout << seg.val() << " "; cout << endl;}}
#else
#define showp(p)
#define show1(a)
#define show2(a,b)
#define show3(a,b,c)
#define show4(a,b,c,d)
#define show5(a,b,c,d,e)
#define DEBUG_LINE
#define showv(v)
#define showv2(v)
#define showvm(v)
#define showvm2(v)
#define showmat(v)
#define showmatm(v)
#endif
#define overload5(a,b,c,d,e,f, ...) f
#define show(...) overload5(__VA_ARGS__, show5, show4, show3, show2, show1)(__VA_ARGS__)

vm dp;

struct matexp{
    int n;
    const int logmax = 64;
    vector<vvm> exp;

    matexp(int n) : n(n){
        exp.resize(logmax,vvm(n,vm(n)));
    }

    vvm mat_product(vvm& a,vvm& b){
        int n1 = sz(a);
        int m1 = sz(a[0]);
        int n2 = sz(b);
        int m2 = sz(b[0]);
        assert(m1 == n2);
        vvm ret(n1,vm(m2));
        rep(i,n1) rep(j,m2) rep(k,m1) ret[i][j] += a[i][k]*b[k][j];
        return ret;
    }

    void init(vvm a){
        exp[0] = a;
        rep1(i,logmax) exp[i] = mat_product(exp[i-1],exp[i-1]);
    }

    vvm getexp_k(ll k){
        vvm ret(n,vm(n));
        rep(i,n) ret[i][i] = 1;
        rep(i,logmax) if ((k >> i & 1) == 1) ret = mat_product(ret,exp[i]);
        return ret;
    }
};

// A^k (Aは行列)を計算

// matexp(n) : n(行列の次元)を初期化
// mat_product(a,b) : 行列積a*bを返す 
// init(a) : 行列Aを初期化
// getexp_k : A^kを返す 

void solve(){
    ll n,m; cin>>n>>m;
    if (n > m) swap(n,m);
    if (n==0) retval(1);
    mint ans = 0;
    if (n==m){
        ans += dp[n]*dp[n];
        ans += dp[n-1]*dp[n-1]*n;
    }else{
        matexp mt(2);
        vvm a(2,vm(2));
        a[0][0] = n*2 + 1;
        a[0][1] = n;
        a[1][0] = 1;
        a[1][1] = 0;
        mt.init(a);
        a = mt.getexp_k(m-n-1);
        mint fir = dp[n-1]*n + dp[n]*(2*n+1);
        mint sec = dp[n];
        mint fir2 = a[0][0]*fir + a[0][1]*sec;
        mint sec2 = a[1][0]*fir + a[1][1]*sec;
        ans += fir2 * sec;
        ans += sec2 * dp[n-1]*n;
    }
    outm;

    return;
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);

    int t = 1;
    cin>>t;

    const int nmax = (int)1e7 + 1;
    dp.resize(nmax);
    dp[0] = 1;
    dp[1] = 2;
    repx(i,2,nmax){
        dp[i] = dp[i-1]*2*i + dp[i-2]*(i-1);
    }

    rep(i,t){
        solve();
    }

    return 0;
}
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