Submit Info #11014

Problem Lang User Status Time Memory
Hafnian of Matrix cpp Benq AC 2148 ms 1.87 MiB

ケース詳細
Name Status Time Memory
example_00 AC 3 ms 0.67 MiB
large_00 AC 22 ms 0.99 MiB
large_01 AC 43 ms 1.14 MiB
large_02 AC 208 ms 1.31 MiB
max_00 AC 2147 ms 1.87 MiB
max_01 AC 2148 ms 1.86 MiB
max_02 AC 2148 ms 1.80 MiB
small_00 AC 2 ms 0.72 MiB
small_01 AC 0 ms 0.74 MiB
small_02 AC 4 ms 0.70 MiB

// https://dl.acm.org/doi/pdf/10.5555/2095116.2095189 // inclusion-exclusion!! #include <bits/stdc++.h> using namespace std; typedef long long ll; typedef long double ld; typedef double db; typedef string str; typedef pair<int,int> pi; typedef pair<ll,ll> pl; typedef pair<db,db> pd; typedef vector<int> vi; typedef vector<ll> vl; typedef vector<db> vd; typedef vector<str> vs; typedef vector<pi> vpi; typedef vector<pl> vpl; typedef vector<pd> vpd; #define mp make_pair #define f first #define s second #define sz(x) (int)x.size() #define all(x) begin(x), end(x) #define rall(x) (x).rbegin(), (x).rend() #define rsz resize #define ins insert #define ft front() #define bk back() #define pf push_front #define pb push_back #define eb emplace_back #define lb lower_bound #define ub upper_bound #define FOR(i,a,b) for (int i = (a); i < (b); ++i) #define F0R(i,a) FOR(i,0,a) #define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i) #define R0F(i,a) ROF(i,0,a) #define trav(a,x) for (auto& a: x) const int MOD = 998244353; const int MX = 2e5+5; const ll INF = 1e18; const ld PI = acos((ld)-1); const int xd[4] = {1,0,-1,0}, yd[4] = {0,1,0,-1}; mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count()); template<class T> bool ckmin(T& a, const T& b) { return b < a ? a = b, 1 : 0; } template<class T> bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; } int pct(int x) { return __builtin_popcount(x); } int bits(int x) { return 31-__builtin_clz(x); } // floor(log2(x)) int cdiv(int a, int b) { return a/b+!(a<0||a%b == 0); } // division of a by b rounded up, assumes b > 0 int fstTrue(function<bool(int)> f, int lo, int hi) { hi ++; assert(lo <= hi); // assuming f is increasing while (lo < hi) { // find first index such that f is true int mid = (lo+hi)/2; f(mid) ? hi = mid : lo = mid+1; } return lo; } // INPUT template<class A> void re(complex<A>& c); template<class A, class B> void re(pair<A,B>& p); template<class A> void re(vector<A>& v); template<class A, size_t SZ> void re(array<A,SZ>& a); template<class T> void re(T& x) { cin >> x; } void re(db& d) { str t; re(t); d = stod(t); } void re(ld& d) { str t; re(t); d = stold(t); } template<class H, class... T> void re(H& h, T&... t) { re(h); re(t...); } template<class A> void re(complex<A>& c) { A a,b; re(a,b); c = {a,b}; } template<class A, class B> void re(pair<A,B>& p) { re(p.f,p.s); } template<class A> void re(vector<A>& x) { trav(a,x) re(a); } template<class A, size_t SZ> void re(array<A,SZ>& x) { trav(a,x) re(a); } // TO_STRING #define ts to_string str ts(char c) { return str(1,c); } str ts(bool b) { return b ? "true" : "false"; } str ts(const char* s) { return (str)s; } str ts(str s) { return s; } template<class A> str ts(complex<A> c) { stringstream ss; ss << c; return ss.str(); } str ts(vector<bool> v) { str res = "{"; F0R(i,sz(v)) res += char('0'+v[i]); res += "}"; return res; } template<size_t SZ> str ts(bitset<SZ> b) { str res = ""; F0R(i,SZ) res += char('0'+b[i]); return res; } template<class A, class B> str ts(pair<A,B> p); template<class T> str ts(T v) { // containers with begin(), end() bool fst = 1; str res = "{"; for (const auto& x: v) { if (!fst) res += ", "; fst = 0; res += ts(x); } res += "}"; return res; } template<class A, class B> str ts(pair<A,B> p) { return "("+ts(p.f)+", "+ts(p.s)+")"; } // OUTPUT template<class A> void pr(A x) { cout << ts(x); } template<class H, class... T> void pr(const H& h, const T&... t) { pr(h); pr(t...); } void ps() { pr("\n"); } // print w/ spaces template<class H, class... T> void ps(const H& h, const T&... t) { pr(h); if (sizeof...(t)) pr(" "); ps(t...); } // DEBUG void DBG() { cerr << "]" << endl; } template<class H, class... T> void DBG(H h, T... t) { cerr << ts(h); if (sizeof...(t)) cerr << ", "; DBG(t...); } #ifdef LOCAL // compile with -DLOCAL #define dbg(...) cerr << "LINE(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__) #else #define dbg(...) 0 #endif // FILE I/O void setIn(string s) { freopen(s.c_str(),"r",stdin); } void setOut(string s) { freopen(s.c_str(),"w",stdout); } void unsyncIO() { ios_base::sync_with_stdio(0); cin.tie(0); } void setIO(string s = "") { unsyncIO(); // cin.exceptions(cin.failbit); // throws exception when do smth illegal // ex. try to read letter into int if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO } /** * Description: modular arithmetic operations * Source: * KACTL * https://codeforces.com/blog/entry/63903 * https://codeforces.com/contest/1261/submission/65632855 (tourist) * https://codeforces.com/contest/1264/submission/66344993 (ksun) * Verification: * https://open.kattis.com/problems/modulararithmetic */ struct mi { typedef decay<decltype(MOD)>::type T; /// don't silently convert to T T v; explicit operator T() const { return v; } mi() { v = 0; } mi(ll _v) { v = (-MOD < _v && _v < MOD) ? _v : _v % MOD; if (v < 0) v += MOD; } friend bool operator==(const mi& a, const mi& b) { return a.v == b.v; } friend bool operator!=(const mi& a, const mi& b) { return !(a == b); } friend bool operator<(const mi& a, const mi& b) { return a.v < b.v; } friend void re(mi& a) { ll x; re(x); a = mi(x); } friend str ts(mi a) { return ts(a.v); } mi& operator+=(const mi& m) { if ((v += m.v) >= MOD) v -= MOD; return *this; } mi& operator-=(const mi& m) { if ((v -= m.v) < 0) v += MOD; return *this; } mi& operator*=(const mi& m) { v = (ll)v*m.v%MOD; return *this; } mi& operator/=(const mi& m) { return (*this) *= inv(m); } friend mi pow(mi a, ll p) { mi ans = 1; assert(p >= 0); for (; p; p /= 2, a *= a) if (p&1) ans *= a; return ans; } friend mi inv(const mi& a) { assert(a.v != 0); return pow(a,MOD-2); } mi operator-() const { return mi(-v); } mi& operator++() { return *this += 1; } mi& operator--() { return *this -= 1; } friend mi operator+(mi a, const mi& b) { return a += b; } friend mi operator-(mi a, const mi& b) { return a -= b; } friend mi operator*(mi a, const mi& b) { return a *= b; } friend mi operator/(mi a, const mi& b) { return a /= b; } }; typedef vector<mi> vmi; typedef pair<mi,mi> pmi; typedef vector<pmi> vpmi; vector<vmi> scmb; // small combinations void genComb(int SZ) { scmb.assign(SZ,vmi(SZ)); scmb[0][0] = 1; FOR(i,1,SZ) F0R(j,i+1) scmb[i][j] = scmb[i-1][j]+(j?scmb[i-1][j-1]:0); } struct haf { int n; void ad(vmi& x, const vmi& a, const vmi& b) { F0R(i,sz(a)) F0R(j,sz(b)-i-1) x[i+j+1] += a[i]*b[j]; } vmi solve(vector<vector<vmi>> v) { vmi ans(n/2+1); if (!sz(v)) { ans[0] = 1; return ans; } int m = sz(v)-2; auto V = v; V.rsz(m); vmi zero = solve(V); F0R(i,m) F0R(j,i) { ad(V[i][j],v[m][i],v[m+1][j]); ad(V[i][j],v[m+1][i],v[m][j]); } vmi one = solve(V); // do inclusion-exclusion F0R(i,sz(one)) ans[i] += one[i]-zero[i]; ad(ans,one,v[m+1][m]); // include edge connecting m w/ m+1 return ans; } mi calc(vector<vmi> m) { n = sz(m); assert(n%2 == 0); vector<vector<vmi>> v(n); F0R(i,n) { v[i].rsz(i); F0R(j,i) { v[i][j] = vmi(n/2+1); v[i][j][0] = m[i][j]; } } return solve(v)[n/2]; } }; haf H; int n; int main() { setIO(); re(n); vector<vmi> v(n,vmi(n)); re(v); ps(H.calc(v)); // you should actually read the stuff at the bottom } /* stuff you should look for * int overflow, array bounds * special cases (n=1?) * do smth instead of nothing and stay organized * WRITE STUFF DOWN */