#include <bits/stdc++.h> #define ll long long #define fors(u, n, s) for(ll u=(s); u < (n); u++) #define foru(u, n) fors(u, n, 0) #define ir(a, b, x) (((a) <= (x)) && ((x) <= (b))) #define vec vector #define pb push_back #define pint pair<int, int> #define f first #define s second #define mp make_pair using namespace std; #define N 200 int n; int m; struct frac{ ll a; ll b; void shorten(){ if(a==0 && b==0) return;///cout << "PANIK" << endl; ll a_=a; ll b_=b; if(a_<b_) swap(a_, b_); while(b_!=0){ a_=a_%b_; swap(a_, b_); } a/=a_; b/=a_; } frac operator+(frac rhs){ frac output; output.a=a*rhs.b+rhs.a*b; output.b=b*rhs.b; output.shorten(); return output; } frac operator-(frac rhs){ frac output; output.a=a*rhs.b-rhs.a*b; output.b=b*rhs.b; output.shorten(); return output; } frac operator*(frac rhs){ frac output; output.a=a*rhs.a; output.b=b*rhs.b; output.shorten(); return output; } frac operator/(frac rhs){ frac output; output.a=a*rhs.b; output.b=b*rhs.a; output.shorten(); return output; } bool operator<(frac rhs){ return a*rhs.b<b*rhs.a; } bool operator>(frac rhs){ return a*rhs.b>b*rhs.a; } bool operator<=(frac rhs){ return a*rhs.b<=b*rhs.a; } bool operator>=(frac rhs){ return a*rhs.b>=b*rhs.a; } bool operator==(frac rhs){ return a*rhs.b==b*rhs.a; } void print(){ shorten(); cout << a << "/" << b; } }; frac to_frac(int x){ frac output; output.a=x; output.b=1; return output; } vec<pint> adj(pint in){ vec<pint> out; if(ir(0, n-1, in.f-1)) out.pb(mp(in.f-1, in.s)); if(ir(0, n-1, in.f+1)) out.pb(mp(in.f+1, in.s)); if(ir(0, m-1, in.s-1)) out.pb(mp(in.f, in.s-1)); if(ir(0, m-1, in.s+1)) out.pb(mp(in.f, in.s+1)); return out; } char board[N][N]; char alt_board[N][N]; frac offset[N][N]; ///HOW MUCH EVAPORATED FROM PREVIOUS EDGES void save_board(){ foru(i, n) foru(j, m) alt_board[i][j]=board[i][j]; } void reload_board(){ foru(i, n) foru(j, m) board[i][j]=alt_board[i][j]; } vec<pint> unks; frac gettime(pint in){ frac c = offset[in.f][in.s]; c.shorten(); int degree = 0; for(auto i : adj(in)) degree+=(board[i.f][i.s]=='O'); frac d = to_frac(degree); if(c==to_frac(1)) return to_frac(0); if(degree==0) return to_frac(INT_MAX); return (to_frac(1)-c)/d; } struct pint_wrapper{ pint wrapped; bool operator<(const pint_wrapper rhs)const{ if(wrapped.f==-1) return true; if(rhs.wrapped.f==-1) return false; if(gettime(wrapped)==gettime(rhs.wrapped)) return wrapped.f*N+wrapped.s < rhs.wrapped.f*N+rhs.wrapped.s; return gettime(wrapped) < gettime(rhs.wrapped); } }; int main() { cin >> n >> m; foru(i, n) foru(j, m) cin >> board[i][j]; foru(i, n) foru(j, m) offset[i][j]=to_frac(0); if(n==1){ frac output = to_frac(0); foru(i, m){ frac p = to_frac(1); if(board[0][i]=='?') p.b=2; if(board[0][i]=='.') p.a=0; frac p1=to_frac(0); if(i-1>=0 && board[0][i-1]=='?') {p1.a=1; p1.b=2;} if(i-1>=0 && board[0][i-1]=='O') {p1.a=1; p1.b=1;} frac p2=to_frac(0); if(i-2>=0 && board[0][i-2]=='?') {p2.a=1; p2.b=2;} if(i-2>=0 && board[0][i-2]=='O') {p2.a=1; p2.b=1;} frac p3=to_frac(0); if(i+1<m && board[0][i+1]=='?') {p3.a=1; p3.b=2;} if(i+1<m && board[0][i+1]=='O') {p3.a=1; p3.b=1;} frac p4=to_frac(0); if(i+2<m && board[0][i+2]=='?') {p4.a=1; p4.b=2;} if(i+2<m && board[0][i+2]=='O') {p4.a=1; p4.b=1;} output = output + p*(to_frac(1)-p1)*(to_frac(1)-p3); output = output + p*(to_frac(1)-p1)*p3*p4/to_frac(2); output = output + p*p1*p2*(to_frac(1)-p3)/to_frac(2); } output.print(); return 0; } int unk_cnt=0; foru(i, n) foru(j, m) if(board[i][j]=='?') unks.pb(mp(i, j)); if(unks.size()<=5){ frac output = to_frac(0); foru(b, 1<<unks.size()){ save_board(); int b_ = b; for(auto i : unks){ if(b_ & 1) board[i.f][i.s]='O'; else board[i.f][i.s]='.'; b_=b_/2; } set<pint_wrapper> st; pint_wrapper helper; foru(i, n) foru(j, m){ helper.wrapped=mp(i, j); if(board[i][j]=='O') st.insert(helper); } while(!st.empty()){ helper.wrapped.f=-1; set<pint_wrapper>::iterator node_wrapped = st.lower_bound(helper); pint node = (*node_wrapped).wrapped; st.erase(node_wrapped); frac time = gettime(node); if(time==to_frac(INT_MAX)){ output = output + offset[node.f][node.s]; continue; } for(auto i : adj(node)){ helper.wrapped=i; st.erase(st.lower_bound(helper)); } board[node.f][node.s]='.'; for(auto i : adj(node)){ offset[i.f][i.s] = offset[i.f][i.s] + time; helper.wrapped=i; st.insert(helper); } } reload_board(); } output.print(); return 0; } return 0; }
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 | #include <bits/stdc++.h> #define ll long long #define fors(u, n, s) for(ll u=(s); u < (n); u++) #define foru(u, n) fors(u, n, 0) #define ir(a, b, x) (((a) <= (x)) && ((x) <= (b))) #define vec vector #define pb push_back #define pint pair<int, int> #define f first #define s second #define mp make_pair using namespace std; #define N 200 int n; int m; struct frac{ ll a; ll b; void shorten(){ if(a==0 && b==0) return;///cout << "PANIK" << endl; ll a_=a; ll b_=b; if(a_<b_) swap(a_, b_); while(b_!=0){ a_=a_%b_; swap(a_, b_); } a/=a_; b/=a_; } frac operator+(frac rhs){ frac output; output.a=a*rhs.b+rhs.a*b; output.b=b*rhs.b; output.shorten(); return output; } frac operator-(frac rhs){ frac output; output.a=a*rhs.b-rhs.a*b; output.b=b*rhs.b; output.shorten(); return output; } frac operator*(frac rhs){ frac output; output.a=a*rhs.a; output.b=b*rhs.b; output.shorten(); return output; } frac operator/(frac rhs){ frac output; output.a=a*rhs.b; output.b=b*rhs.a; output.shorten(); return output; } bool operator<(frac rhs){ return a*rhs.b<b*rhs.a; } bool operator>(frac rhs){ return a*rhs.b>b*rhs.a; } bool operator<=(frac rhs){ return a*rhs.b<=b*rhs.a; } bool operator>=(frac rhs){ return a*rhs.b>=b*rhs.a; } bool operator==(frac rhs){ return a*rhs.b==b*rhs.a; } void print(){ shorten(); cout << a << "/" << b; } }; frac to_frac(int x){ frac output; output.a=x; output.b=1; return output; } vec<pint> adj(pint in){ vec<pint> out; if(ir(0, n-1, in.f-1)) out.pb(mp(in.f-1, in.s)); if(ir(0, n-1, in.f+1)) out.pb(mp(in.f+1, in.s)); if(ir(0, m-1, in.s-1)) out.pb(mp(in.f, in.s-1)); if(ir(0, m-1, in.s+1)) out.pb(mp(in.f, in.s+1)); return out; } char board[N][N]; char alt_board[N][N]; frac offset[N][N]; ///HOW MUCH EVAPORATED FROM PREVIOUS EDGES void save_board(){ foru(i, n) foru(j, m) alt_board[i][j]=board[i][j]; } void reload_board(){ foru(i, n) foru(j, m) board[i][j]=alt_board[i][j]; } vec<pint> unks; frac gettime(pint in){ frac c = offset[in.f][in.s]; c.shorten(); int degree = 0; for(auto i : adj(in)) degree+=(board[i.f][i.s]=='O'); frac d = to_frac(degree); if(c==to_frac(1)) return to_frac(0); if(degree==0) return to_frac(INT_MAX); return (to_frac(1)-c)/d; } struct pint_wrapper{ pint wrapped; bool operator<(const pint_wrapper rhs)const{ if(wrapped.f==-1) return true; if(rhs.wrapped.f==-1) return false; if(gettime(wrapped)==gettime(rhs.wrapped)) return wrapped.f*N+wrapped.s < rhs.wrapped.f*N+rhs.wrapped.s; return gettime(wrapped) < gettime(rhs.wrapped); } }; int main() { cin >> n >> m; foru(i, n) foru(j, m) cin >> board[i][j]; foru(i, n) foru(j, m) offset[i][j]=to_frac(0); if(n==1){ frac output = to_frac(0); foru(i, m){ frac p = to_frac(1); if(board[0][i]=='?') p.b=2; if(board[0][i]=='.') p.a=0; frac p1=to_frac(0); if(i-1>=0 && board[0][i-1]=='?') {p1.a=1; p1.b=2;} if(i-1>=0 && board[0][i-1]=='O') {p1.a=1; p1.b=1;} frac p2=to_frac(0); if(i-2>=0 && board[0][i-2]=='?') {p2.a=1; p2.b=2;} if(i-2>=0 && board[0][i-2]=='O') {p2.a=1; p2.b=1;} frac p3=to_frac(0); if(i+1<m && board[0][i+1]=='?') {p3.a=1; p3.b=2;} if(i+1<m && board[0][i+1]=='O') {p3.a=1; p3.b=1;} frac p4=to_frac(0); if(i+2<m && board[0][i+2]=='?') {p4.a=1; p4.b=2;} if(i+2<m && board[0][i+2]=='O') {p4.a=1; p4.b=1;} output = output + p*(to_frac(1)-p1)*(to_frac(1)-p3); output = output + p*(to_frac(1)-p1)*p3*p4/to_frac(2); output = output + p*p1*p2*(to_frac(1)-p3)/to_frac(2); } output.print(); return 0; } int unk_cnt=0; foru(i, n) foru(j, m) if(board[i][j]=='?') unks.pb(mp(i, j)); if(unks.size()<=5){ frac output = to_frac(0); foru(b, 1<<unks.size()){ save_board(); int b_ = b; for(auto i : unks){ if(b_ & 1) board[i.f][i.s]='O'; else board[i.f][i.s]='.'; b_=b_/2; } set<pint_wrapper> st; pint_wrapper helper; foru(i, n) foru(j, m){ helper.wrapped=mp(i, j); if(board[i][j]=='O') st.insert(helper); } while(!st.empty()){ helper.wrapped.f=-1; set<pint_wrapper>::iterator node_wrapped = st.lower_bound(helper); pint node = (*node_wrapped).wrapped; st.erase(node_wrapped); frac time = gettime(node); if(time==to_frac(INT_MAX)){ output = output + offset[node.f][node.s]; continue; } for(auto i : adj(node)){ helper.wrapped=i; st.erase(st.lower_bound(helper)); } board[node.f][node.s]='.'; for(auto i : adj(node)){ offset[i.f][i.s] = offset[i.f][i.s] + time; helper.wrapped=i; st.insert(helper); } } reload_board(); } output.print(); return 0; } return 0; } |