期望dp+高斯消元+bfs——hdu4418

#include<bits/stdc++.h>
using namespace std;
 
const int maxn = 205;
const double esp = 1e-7;

int n,m,x,y,d;
double p[maxn],a[maxn][maxn],b[maxn];
int equ,var;

int Gauss(){
    for(int i=0;i<n;i++){
        int maxr=i;
        for(int j=i+1;j<n;j++)
            if(fabs(a[j][i])>fabs(a[maxr][i]))
                maxr=j;
        if(fabs(a[maxr][i])<esp)continue;
        if(maxr!=i)
            swap(a[maxr],a[i]);swap(b[maxr],b[i]);
        
        for(int j=i+1;j<n;j++){
            if(fabs(a[j][i])<esp)continue;
            double rate=a[j][i]/a[i][i];
            for(int k=i;k<n;k++)
                a[j][k]-=rate*a[i][k];
            b[j]-=rate*b[i];
        } 
    }
    for(int i=n-1;i>=0;i--){
        if(fabs(a[i][i])<esp)continue;
        for(int j=i+1;j<n;j++)
            b[i]-=a[i][j]*b[j];
        b[i]/=a[i][i];
    }
    return 1;
}

int id[maxn],cnt;
void bfs(int s){
    memset(id,-1,sizeof id);
    cnt=0;
    queue<int>q;
    q.push(s);id[s]=cnt++;
    while(q.size()){
        int x=q.front();q.pop();
        for(int i=1;i<=m;i++){
            if(fabs(p[i])<esp)continue;
            int y=(x+i)%n;
            if(id[y]==-1)
                q.push(y),id[y]=cnt++;
        }
    }
}

int main(){
    int t;cin>>t;
    while(t--){
        scanf("%d%d%d%d%d",&n,&m,&y,&x,&d);
        
        for(int i=1;i<=m;i++)
            scanf("%lf",&p[i]),p[i]/=100;
        if(x==y){puts("0.00");continue;}
         
        n=2*(n-1);
        if(d==1)x=n-x;        
        bfs(x); 
        if(id[y]==-1 && id[n-y]==-1){
            puts("Impossible !");continue;
        }
        equ=var=cnt;
        
        memset(a,0,sizeof a);
        memset(b,0,sizeof b);
        for(int i=0;i<n;i++){
            if(id[i]==-1)continue;
            a[id[i]][id[i]]=1;
            if(i==y || i==n-y)continue;//到了终点y 
            for(int j=1;j<=m;j++){
                int y=(i+j)%n;
                if(id[y]!=-1){
                    a[id[i]][id[y]]-=p[j];
                    b[id[i]]+=j*p[j];
                }
            } 
        }
        if(Gauss())
            printf("%.2lf\n",b[id[x]]);
        else printf("Impossible !\n");
    }
}