#include <cstdio>#include <cstdlib>#include <cstring>#include <iostream>#include <algorithm>#include <vector>#include <string>#include <cmath>using namespace std;#define print(x) cout<<x<<endl#define input(x) cin>>x#define MAT 32#define SIZE 1024#define pb push_backconst double eps=1e-8;inline bool zero(double x){return fabs(x)<eps;}struct node{ int type; int val; node(){} node(int i_type,int i_val) { type=i_type; val=i_val; }};vector<int> g[SIZE];double mat[MAT][MAT];node array[SIZE];int n;int ind;char *p;void build(int now){ int t,m; while(*p) { while(*p==' ' && *p) p++; if(!*p) break; if( (*p>='0' && *p<='9') || *p=='-') { ind++; sscanf(p,"%d%n",&t,&m); p+=m; array[ind]=node(0,t); g[now].pb(ind); } else if(*p=='(') { ind++; array[ind]=node(-1,0); p++; g[now].pb(ind); build(ind); } else if(*p==')') { p++; return; } else { ind++; array[ind]=node(1,*p-'a'); p++; g[now].pb(ind); } }}void toMatrix(int now,double tp,int var){ double p; if(g[now].size()) p=tp/g[now].size(); //写入Matrix的基本原理： //例如a = (2 , b) //a的E(a)期望等于 1/2 * 2 + 1/2 * E(b) //所以，对于Mat[ord(a)]来说，即为： // 1*E(A) -1/2*E(B) = 1/2*2 for(int i=0;i<(int)g[now].size();i++) { int x=g[now][i]; if(array[x].type==-1) { toMatrix(x,p,var); } else { if(array[x].type==0) { mat[var][n]+=array[x].val*p; } else { mat[var][array[x].val]-=p; } } }}void init(){ ind=0; memset(array,0,sizeof(array)); for(int i=0;i<SIZE;i++) g[i].clear();}void gauss_line(int a,int b,int col){ double mul_a=mat[a][col]; double mul_b=mat[b][col]; for(int i=0;i<=n;i++) { mat[b][i]=mat[b][i]-mat[a][i]*mul_b/mul_a; }}void gauss(){ for(int row=0,col=0;row<n && col<n;row++,col++) { int ptr=-1; for(int i=row;i<n;i++) { if(!zero(mat[i][col])) { ptr=i; break; } } if(ptr==-1) continue; else { for(int i=0;i<=n;i++) { swap(mat[row][i],mat[ptr][i]); } for(int i=0;i<n;i++) if(i!=row) { gauss_line(row,i,col); } } }}double getans(int x){ return mat[x][n]/mat[x][x];}bool check_exist(int x){ for(int i=0;i<n;i++) if(i!=x) { if(!zero(mat[x][i])) return false; } return !zero(mat[x][x]);}int main(){ int cas=1; char cmd[SIZE]; while(input(n) && n) { memset(mat,0,sizeof(mat)); printf("Game %dn",cas++); for(int i=0;i<n;i++) { init(); do { gets(cmd); }while(*cmd==' '); p=cmd; while(*p!='(') p++; //p++; build(0); toMatrix(0,1.,i); mat[i][i]+=1.0; } gauss(); for(int i=0;i<n;i++) { if(check_exist(i)) printf("Expected score for %c = %.3fn",i+'a',getans(i)); else printf("Expected score for %c undefinedn",i+'a'); } puts(""); } return 0;}
