142 lines
3.8 KiB
C++
142 lines
3.8 KiB
C++
#include <functional>
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#include <algorithm>
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#include <iostream>
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#include <fstream>
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#include <sstream>
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#include <iomanip>
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#include <numeric>
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#include <cstring>
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#include <cassert>
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#include <cstdio>
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#include <string>
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#include <vector>
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#include <bitset>
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#include <queue>
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#include <stack>
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#include <cmath>
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#include <ctime>
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#include <list>
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#include <set>
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#include <map>
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using namespace std;
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#define pii pair<int,int>
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#define mem(a,b) memset(a,b,sizeof(a))
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#define lson l,mid,rt<<1
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#define rson mid+1,r,rt<<1|1
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#define PI acos(-1.0)
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typedef __int64 LL;
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typedef unsigned __int64 ULL;
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const int N=230;
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const int INF=0x3f3f3f3f;
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const LL MOD=1000000007,STA=8000010;
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const LL LNF=1LL<<55;
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const double EPS=1e-9;
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const double OO=1e30;
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const int dx[4]={-1,0,1,0};
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const int dy[4]={0,1,0,-1};
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const int day[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};
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inline int sign(double x){return (x>EPS)-(x<-EPS);}
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template<class T> T gcd(T a,T b){return b?gcd(b,a%b):a;}
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template<class T> T lcm(T a,T b){return a/gcd(a,b)*b;}
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template<class T> inline T lcm(T a,T b,T d){return a/d*b;}
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template<class T> inline T Min(T a,T b){return a<b?a:b;}
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template<class T> inline T Max(T a,T b){return a>b?a:b;}
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template<class T> inline T Min(T a,T b,T c){return min(min(a, b),c);}
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template<class T> inline T Max(T a,T b,T c){return max(max(a, b),c);}
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template<class T> inline T Min(T a,T b,T c,T d){return min(min(a, b),min(c,d));}
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template<class T> inline T Max(T a,T b,T c,T d){return max(max(a, b),max(c,d));}
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int vis[20][20],cnt[20][20],e[20][20];
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char g[20][20];
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int n,m,tot,sx,sy;
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double A[N][N];
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int gauss(int n)
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{
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int i,j,k,r;
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for(i=0;i<n;i++){
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r=i;
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for(j=i+1;j<n;j++)
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if(fabs(A[j][i]) > fabs(A[r][i]))r=j;
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if(r!=i)for(j=0;j<=n;j++)swap(A[r][j],A[i][j]);
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for(j=n;j>=i;j--){
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for(k=i+1;k<n;k++)
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A[k][j]-=A[k][i]/A[i][i]*A[i][j];
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}
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}
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for(i=0;i<n;i++)if(sign(A[i][i])==0)return 0;
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for(i=n-1;i>=0;i--){
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for(j=i+1;j<n;j++)
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A[i][n]-=A[j][n]*A[i][j];
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A[i][n]/=A[i][i];
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}
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return 1;
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}
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int bfs()
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{
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int i,j,x,y,nx,ny,t;
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queue<int> q;
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q.push(sx*m+sy);
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mem(vis,-1);mem(cnt,0);
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vis[sx][sy]=tot=0;
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tot++;
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while(!q.empty()){
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t=q.front();q.pop();
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x=t/m;y=t%m;
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for(i=0;i<4;i++){
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nx=x+dx[i];
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ny=y+dy[i];
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if(nx>=0&&nx<n && ny>=0&&ny<m && g[nx][ny]!='#'){
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cnt[x][y]++;
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if(vis[nx][ny]!=-1)continue;
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vis[nx][ny]=tot++;
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q.push(nx*m+ny);
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}
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}
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}
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for(i=0;i<n;i++){
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for(j=0;j<m;j++)
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if(vis[i][j]!=-1 && e[i][j])return 1;
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}
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return 0;
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}
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int main(){
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int i,j,k;
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while(~scanf("%d%d",&n,&m))
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{
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mem(e,0);
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for(i=0;i<n;i++){
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scanf("%s",g[i]);
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for(j=0;j<m;j++){
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if(g[i][j]=='@')sx=i,sy=j;
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else if(g[i][j]=='$')e[i][j]=1;
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}
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}
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if(!bfs()){
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printf("-1\n");
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continue;
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}
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mem(A,0);
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for(i=0;i<n;i++){
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for(j=0;j<m;j++){
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if(vis[i][j]==-1)continue;
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int u=vis[i][j];
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double p=1.0/cnt[i][j];
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if(e[i][j]){
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A[u][u]=1;
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A[u][tot]=0;
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continue;
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}
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A[u][u]=A[u][tot]=1;
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for(k=0;k<4;k++){
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int x=i+dx[k],y=j+dy[k];
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if(x>=0&&x<n && y>=0&&y<m && vis[x][y]!=-1){
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A[u][vis[x][y]]=-p;
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}
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}
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}
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}
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gauss(tot);
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printf("%.6lf\n",A[vis[sx][sy]][tot]);
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}
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return 0;
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}
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