#ifndef LOCAL
#pragma GCC optimize("O3")
#endif
#include <bits/stdc++.h>
#define FOR(i,p,k) for(int i=(p);i<=(k);++i)
#define REP(i,n) FOR(i,0,(n)-1)
#define RFOR(i,p,n) for(int i=(p);i>=(n);--i)
#define all(x) (x).begin(),(x).end()
#define rall(x) (x).rbegin(),(x).rend()
#define ssize(x) int((x).size())
#define fi first
#define se second
#define V vector
#define pb push_back
#define eb emplace_back
#define C const
#define pn printf("\n")
using namespace std;
typedef long long ll;
typedef V<int> vi;
typedef V<ll> vll;
typedef const int ci;
typedef const ll cll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
void chmin(auto &a, auto b){a=min(a,b);}
void chmax(auto &a, auto b){a=max(a,b);}
ci inf = 2.1e9;
cll infll = 4.5e18;
int I(){
int z;
scanf("%d", &z);
//cin >> z;
return z;
}
void answer(){
int n = I(), l = I();
V wej(n, vi(l, 0));// jedynki to wolne
REP(i, n){
scanf("\n");
REP(j, l){
int c = getchar();
wej[i][j] = c=='.';
}
}
REP(i, l){
int git = 0;
REP(j, n) if(wej[j][i]) git = 1;
if(!git){
printf("-1\n");
return;
}
}
if(n == 1){
printf("0/1\n");
return;
}
if(n == 2){
}
auto xd = [&](V<vi> ciag, int k){
int lmian = ssize(ciag[0]);
vi dp(1<<lmian, 0);
dp[0] = 1;
for(vi vec : ciag){
int maska_vec = 0;
REP(i, lmian) maska_vec += vec[i]<<i;
vi nowe(1<<lmian, 0);
REP(i, lmian-k+1){
int maska = maska_vec;
int git = 1;
REP(j, k){
if(!vec[i+j]){
git = 0;
break;
}
maska -= 1<<(i+j);
}
if(!git) continue;
REP(stan, 1<<lmian) nowe[stan|maska] |= dp[stan];
}
swap(dp, nowe);
}
return dp.back();
};
auto rozstrzel = [&](int mian){
int lmian = l*mian;
V ciag(n, vi(lmian, 0));
REP(i, n) REP(j, lmian) ciag[i][j] = wej[i][j/mian];
return ciag;
};
/*
if(!xd(rozstrzel(n), 1)){
printf("0/1\n");
return;
}
*/
pii wyn = {0, 1};
pii nie_wyszlo = {l*(n+1)+1, n+1};
FOR(mian, 1, n){
int lmian = l*mian;
auto ciag = rozstrzel(mian);
int mam = 0;
while((mam+1)*wyn.se <= wyn.fi*mian) ++mam;
int wiecej = mam+1;
if(!xd(ciag, wiecej)) continue;
int nie_mam = lmian+1;
while((nie_mam-1)*nie_wyszlo.se >= nie_wyszlo.fi*mian) --nie_mam;
int mniej = nie_mam-1;
for(int poc = wiecej, kon = mniej; poc <= kon;){
int sr = (poc+kon)/2;
if(xd(ciag, sr)){
pii tmp = {sr, mian};
if(tmp.fi*wyn.se > wyn.fi*tmp.se) wyn = tmp;
poc = sr+1;
}
else{
pii tmp = {sr, mian};
if(tmp.fi*nie_wyszlo.se < nie_wyszlo.fi*tmp.se) nie_wyszlo = tmp;
kon = sr-1;
}
}
}
printf("%d/%d\n", wyn.fi, wyn.se);
}
int main(){
//ios_base::sync_with_stdio(0);
//cin.tie(0);
int tt = 1;
//tt = I();
while(tt--) answer();
}
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 | #ifndef LOCAL #pragma GCC optimize("O3") #endif #include <bits/stdc++.h> #define FOR(i,p,k) for(int i=(p);i<=(k);++i) #define REP(i,n) FOR(i,0,(n)-1) #define RFOR(i,p,n) for(int i=(p);i>=(n);--i) #define all(x) (x).begin(),(x).end() #define rall(x) (x).rbegin(),(x).rend() #define ssize(x) int((x).size()) #define fi first #define se second #define V vector #define pb push_back #define eb emplace_back #define C const #define pn printf("\n") using namespace std; typedef long long ll; typedef V<int> vi; typedef V<ll> vll; typedef const int ci; typedef const ll cll; typedef pair<int, int> pii; typedef pair<ll, ll> pll; void chmin(auto &a, auto b){a=min(a,b);} void chmax(auto &a, auto b){a=max(a,b);} ci inf = 2.1e9; cll infll = 4.5e18; int I(){ int z; scanf("%d", &z); //cin >> z; return z; } void answer(){ int n = I(), l = I(); V wej(n, vi(l, 0));// jedynki to wolne REP(i, n){ scanf("\n"); REP(j, l){ int c = getchar(); wej[i][j] = c=='.'; } } REP(i, l){ int git = 0; REP(j, n) if(wej[j][i]) git = 1; if(!git){ printf("-1\n"); return; } } if(n == 1){ printf("0/1\n"); return; } if(n == 2){ } auto xd = [&](V<vi> ciag, int k){ int lmian = ssize(ciag[0]); vi dp(1<<lmian, 0); dp[0] = 1; for(vi vec : ciag){ int maska_vec = 0; REP(i, lmian) maska_vec += vec[i]<<i; vi nowe(1<<lmian, 0); REP(i, lmian-k+1){ int maska = maska_vec; int git = 1; REP(j, k){ if(!vec[i+j]){ git = 0; break; } maska -= 1<<(i+j); } if(!git) continue; REP(stan, 1<<lmian) nowe[stan|maska] |= dp[stan]; } swap(dp, nowe); } return dp.back(); }; auto rozstrzel = [&](int mian){ int lmian = l*mian; V ciag(n, vi(lmian, 0)); REP(i, n) REP(j, lmian) ciag[i][j] = wej[i][j/mian]; return ciag; }; /* if(!xd(rozstrzel(n), 1)){ printf("0/1\n"); return; } */ pii wyn = {0, 1}; pii nie_wyszlo = {l*(n+1)+1, n+1}; FOR(mian, 1, n){ int lmian = l*mian; auto ciag = rozstrzel(mian); int mam = 0; while((mam+1)*wyn.se <= wyn.fi*mian) ++mam; int wiecej = mam+1; if(!xd(ciag, wiecej)) continue; int nie_mam = lmian+1; while((nie_mam-1)*nie_wyszlo.se >= nie_wyszlo.fi*mian) --nie_mam; int mniej = nie_mam-1; for(int poc = wiecej, kon = mniej; poc <= kon;){ int sr = (poc+kon)/2; if(xd(ciag, sr)){ pii tmp = {sr, mian}; if(tmp.fi*wyn.se > wyn.fi*tmp.se) wyn = tmp; poc = sr+1; } else{ pii tmp = {sr, mian}; if(tmp.fi*nie_wyszlo.se < nie_wyszlo.fi*tmp.se) nie_wyszlo = tmp; kon = sr-1; } } } printf("%d/%d\n", wyn.fi, wyn.se); } int main(){ //ios_base::sync_with_stdio(0); //cin.tie(0); int tt = 1; //tt = I(); while(tt--) answer(); } |
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