// {{{ file: opi.cpp | time: 18:41 13.03.2025 #define _USE_MATH_DEFINES #include <bits/stdc++.h> #define each(...) for (auto& __VA_ARGS__) #define rep(i, b, e) for (int i = (b); i <= (e); i++) #define rev(i, b, e) for (int i = (e); i >= (b); i--) #define mp make_pair #define mt make_tuple #define x first #define y second #define pb push_back #define all(x) (x).begin(), (x).end() #define endl '\n' #define tC template<class #define $(x) #x<<'='<<(x)<<' ' using namespace std; using ll = long long; using pii = pair<int,int>; using pll = pair<ll,ll>; using vb = vector<bool>; using vi = vector<int>; using vl = vector<ll>; using vs = vector<string>; using vpi = vector<pii>; using vpl = vector<pll>; using vvi = vector<vi>; using vvl = vector<vl>; tC T, class C=greater<T>> using min_priority_queue = priority_queue<T,vector<T>,C>; tC T> int sz(const T& a) { return (int)a.size(); } tC T> bool amin(T& a, T b) { return b < a ? a = b, 1 : 0; } tC T> bool amax(T& a, T b) { return b > a ? a = b, 1 : 0; } const int oo = 1e9+1; const ll OO = ll(1e18)+1; auto now() { return chrono::high_resolution_clock::now().time_since_epoch().count(); } mt19937 rnd(4488); tC T> T rand(T lo, T hi) { return uniform_int_distribution<T>{lo,hi}(rnd); } struct Debug { #ifdef SPONGE tC T>Debug operator<<(const T& x) { cerr<<"\033[1;33m"<<x<<"\033[0m"; return *this; } #else tC T>Debug operator<<(const T&) { return *this; } #endif } dbg; namespace { void solve(); } // }}} int main() { //freopen("input.txt","r",stdin); //freopen("output.txt","w",stdout); ios_base::sync_with_stdio(0); cin.tie(0); cout.precision(15); cout.setf(ios::fixed,ios::floatfield); cerr.precision(15); cerr.setf(ios::fixed,ios::floatfield); //rnd.seed(now()); int t=1; //cin>>t; rep(i,1,t){ //cerr<<"Case #"<<i<<": "; solve(); } } namespace { using arr_t = array<int,18>; const int N=18e5+5; int n,m,l,a[18][N],suma[N],last[19][N],wolne[18][N],wsk[18][N]; arr_t dp[1<<18]; string wej[18]; void info_pamiec() { int uzyta=0; uzyta+=sizeof(a); uzyta+=sizeof(suma); uzyta+=sizeof(last); uzyta+=sizeof(wolne); uzyta+=sizeof(wsk); uzyta+=sizeof(dp); uzyta+=sizeof(wsk); double megabajty=uzyta/1024.0/1024.0; cerr<<$(megabajty)<<endl; } void skaluj_wej(int x) { m=l*x; rep(i,0,n-1) rep(j,0,l-1) rep(k,0,x-1){ if(wej[i][j]=='X') a[i][j*x+k+1]=1; else a[i][j*x+k+1]=0; } } bool dasie(int t) { rep(j,1,m) suma[j]=0; rep(i,0,n-1) rep(j,1,m) suma[j]+=a[i][j]; rep(i,1,m) rep(x,0,18){ if(suma[i]>=x) last[x][i]=i; else last[x][i]=last[x][i-1]; } if(t==0 && last[n][m]==0) return true; if(last[n][m]>0) return false; rep(i,0,n-1) wolne[i][m+1]=0; rep(i,0,n-1) rev(j,1,m){ if(a[i][j]==1 || suma[j]==n-1) wolne[i][j]=0; else wolne[i][j]=wolne[i][j+1]+1; } rep(i,0,n-1) wsk[i][m+1]=0; rep(i,0,n-1) rev(j,0,m){ if(wolne[i][j]>=t) wsk[i][j]=j; else wsk[i][j]=wsk[i][j+1]; } rep(maska,0,(1<<n)-1) rep(i,0,n-1) dp[maska][i]=oo; rep(maska,0,(1<<n)-2){ /* dbg<<$(maska)<<endl; rep(i,0,n-1) dbg<<$(i)<<':'<<$(dp[maska][i])<<' '; dbg<<endl; */ if(maska>0 && dp[maska][0]==oo) continue; int k=0; rep(i,0,n-1) if(maska&(1<<i)) k++; int start; if(maska>0) start=dp[maska][0]; else start=0; int nowy_start=start; rep(i,0,k-1){ int koniec=dp[maska][i]+t-1; if(koniec>=start) amax(nowy_start,last[n-1-k+i][koniec]+1); } rep(i,0,n-1) if((maska&(1<<i)) == 0 && wsk[i][nowy_start]!=0){ arr_t stan=dp[maska]; stan[k]=wsk[i][nowy_start]; if(stan<dp[maska|(1<<i)]) dp[maska|(1<<i)]=stan; } } return (dp[(1<<n)-1][0] < oo); } //int nww=16*9*5*7*11*13*17; tC F>int wyszukaj(int lew,int pra,F&& fun) { int odp=-1; while(lew<=pra){ int sro=(lew+pra)/2; if(fun(sro)){ odp=sro; lew=sro+1; } else{ pra=sro-1; } } return odp; } bool porownaj(pii a1,pii b1) { return a1.y * b1.x < b1.y * a1.x; } void solve() { //info_pamiec(); cin>>n>>l; rep(i,0,n-1) cin>>wej[i]; skaluj_wej(1); int calk_odp=wyszukaj(0,l,dasie); if(calk_odp==-1){ cout<<-1<<endl; } else{ vpi ulamki; ulamki.pb(mp(1,0)); rep(mian,1,18) rep(licz,1,mian-1){ if(gcd(mian,licz)==1) ulamki.pb(mp(mian,licz)); } sort(all(ulamki),porownaj); int indeks=wyszukaj(0,sz(ulamki)-1,[&](int i){ auto [mian,licz]=ulamki[i]; skaluj_wej(mian); return dasie(calk_odp*mian+licz); }); int licz_odp=calk_odp*ulamki[indeks].x+ulamki[indeks].y; int mian_odp=ulamki[indeks].x; cout<<licz_odp<<'/'<<mian_odp<<endl; } } }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 | // {{{ file: opi.cpp | time: 18:41 13.03.2025 #define _USE_MATH_DEFINES #include <bits/stdc++.h> #define each(...) for (auto& __VA_ARGS__) #define rep(i, b, e) for (int i = (b); i <= (e); i++) #define rev(i, b, e) for (int i = (e); i >= (b); i--) #define mp make_pair #define mt make_tuple #define x first #define y second #define pb push_back #define all(x) (x).begin(), (x).end() #define endl '\n' #define tC template<class #define $(x) #x<<'='<<(x)<<' ' using namespace std; using ll = long long; using pii = pair<int,int>; using pll = pair<ll,ll>; using vb = vector<bool>; using vi = vector<int>; using vl = vector<ll>; using vs = vector<string>; using vpi = vector<pii>; using vpl = vector<pll>; using vvi = vector<vi>; using vvl = vector<vl>; tC T, class C=greater<T>> using min_priority_queue = priority_queue<T,vector<T>,C>; tC T> int sz(const T& a) { return (int)a.size(); } tC T> bool amin(T& a, T b) { return b < a ? a = b, 1 : 0; } tC T> bool amax(T& a, T b) { return b > a ? a = b, 1 : 0; } const int oo = 1e9+1; const ll OO = ll(1e18)+1; auto now() { return chrono::high_resolution_clock::now().time_since_epoch().count(); } mt19937 rnd(4488); tC T> T rand(T lo, T hi) { return uniform_int_distribution<T>{lo,hi}(rnd); } struct Debug { #ifdef SPONGE tC T>Debug operator<<(const T& x) { cerr<<"\033[1;33m"<<x<<"\033[0m"; return *this; } #else tC T>Debug operator<<(const T&) { return *this; } #endif } dbg; namespace { void solve(); } // }}} int main() { //freopen("input.txt","r",stdin); //freopen("output.txt","w",stdout); ios_base::sync_with_stdio(0); cin.tie(0); cout.precision(15); cout.setf(ios::fixed,ios::floatfield); cerr.precision(15); cerr.setf(ios::fixed,ios::floatfield); //rnd.seed(now()); int t=1; //cin>>t; rep(i,1,t){ //cerr<<"Case #"<<i<<": "; solve(); } } namespace { using arr_t = array<int,18>; const int N=18e5+5; int n,m,l,a[18][N],suma[N],last[19][N],wolne[18][N],wsk[18][N]; arr_t dp[1<<18]; string wej[18]; void info_pamiec() { int uzyta=0; uzyta+=sizeof(a); uzyta+=sizeof(suma); uzyta+=sizeof(last); uzyta+=sizeof(wolne); uzyta+=sizeof(wsk); uzyta+=sizeof(dp); uzyta+=sizeof(wsk); double megabajty=uzyta/1024.0/1024.0; cerr<<$(megabajty)<<endl; } void skaluj_wej(int x) { m=l*x; rep(i,0,n-1) rep(j,0,l-1) rep(k,0,x-1){ if(wej[i][j]=='X') a[i][j*x+k+1]=1; else a[i][j*x+k+1]=0; } } bool dasie(int t) { rep(j,1,m) suma[j]=0; rep(i,0,n-1) rep(j,1,m) suma[j]+=a[i][j]; rep(i,1,m) rep(x,0,18){ if(suma[i]>=x) last[x][i]=i; else last[x][i]=last[x][i-1]; } if(t==0 && last[n][m]==0) return true; if(last[n][m]>0) return false; rep(i,0,n-1) wolne[i][m+1]=0; rep(i,0,n-1) rev(j,1,m){ if(a[i][j]==1 || suma[j]==n-1) wolne[i][j]=0; else wolne[i][j]=wolne[i][j+1]+1; } rep(i,0,n-1) wsk[i][m+1]=0; rep(i,0,n-1) rev(j,0,m){ if(wolne[i][j]>=t) wsk[i][j]=j; else wsk[i][j]=wsk[i][j+1]; } rep(maska,0,(1<<n)-1) rep(i,0,n-1) dp[maska][i]=oo; rep(maska,0,(1<<n)-2){ /* dbg<<$(maska)<<endl; rep(i,0,n-1) dbg<<$(i)<<':'<<$(dp[maska][i])<<' '; dbg<<endl; */ if(maska>0 && dp[maska][0]==oo) continue; int k=0; rep(i,0,n-1) if(maska&(1<<i)) k++; int start; if(maska>0) start=dp[maska][0]; else start=0; int nowy_start=start; rep(i,0,k-1){ int koniec=dp[maska][i]+t-1; if(koniec>=start) amax(nowy_start,last[n-1-k+i][koniec]+1); } rep(i,0,n-1) if((maska&(1<<i)) == 0 && wsk[i][nowy_start]!=0){ arr_t stan=dp[maska]; stan[k]=wsk[i][nowy_start]; if(stan<dp[maska|(1<<i)]) dp[maska|(1<<i)]=stan; } } return (dp[(1<<n)-1][0] < oo); } //int nww=16*9*5*7*11*13*17; tC F>int wyszukaj(int lew,int pra,F&& fun) { int odp=-1; while(lew<=pra){ int sro=(lew+pra)/2; if(fun(sro)){ odp=sro; lew=sro+1; } else{ pra=sro-1; } } return odp; } bool porownaj(pii a1,pii b1) { return a1.y * b1.x < b1.y * a1.x; } void solve() { //info_pamiec(); cin>>n>>l; rep(i,0,n-1) cin>>wej[i]; skaluj_wej(1); int calk_odp=wyszukaj(0,l,dasie); if(calk_odp==-1){ cout<<-1<<endl; } else{ vpi ulamki; ulamki.pb(mp(1,0)); rep(mian,1,18) rep(licz,1,mian-1){ if(gcd(mian,licz)==1) ulamki.pb(mp(mian,licz)); } sort(all(ulamki),porownaj); int indeks=wyszukaj(0,sz(ulamki)-1,[&](int i){ auto [mian,licz]=ulamki[i]; skaluj_wej(mian); return dasie(calk_odp*mian+licz); }); int licz_odp=calk_odp*ulamki[indeks].x+ulamki[indeks].y; int mian_odp=ulamki[indeks].x; cout<<licz_odp<<'/'<<mian_odp<<endl; } } } |