2707: [SDOI2012]走迷宫

题意：求s走到t期望步数，\(n \le 10^4\)，保证\(|SCC| \le 100\)

求scc缩点，每个scc高斯消元，scc之间直接DP

注意每次清空系数矩阵

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;
typedef long long ll;
const int N=1e4+5, M=1e6+5;
const double eps=1e-8;
inline int read(){char c=getchar();int x=0,f=1;while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}while(c>='0'&&c<='9'){x=x*10+c-'0';c=getchar();}return x*f;
}int n, m, s, t, de[N], u, v;
struct edge{int v, ne;} e[M];
int cnt=1, h[N];
inline void ins(int u, int v) {e[++cnt]=(edge){v, h[u]}; h[u]=cnt;}
int dfn[N], low[N], dfc, belong[N], scc;
struct List{int a[105], n;int& operator [](int x) {return a[x];}inline void push(int x) {a[++n]=x;}
}li[N];
int st[N], top;
void dfs(int u) { //printf("dfs %d\n",u);dfn[u] = low[u] = ++dfc;st[++top] = u;for(int i=h[u];i;i=e[i].ne) {int v=e[i].v;if(!dfn[v]) dfs(v), low[u] = min(low[u], low[v]);else if(!belong[v]) low[u] = min(low[u], dfn[v]);}if(dfn[u] == low[u]) {scc++;while(true) {int x=st[top--];belong[x] = scc;li[scc].push(x);if(x == u) break;}}
}double a[105][105], f[N]; int id[N];
void gauss(int n) { //puts("\ngauss");//for(int i=1; i<=n; i++)//  for(int j=1; j<=n+1; j++) printf("%lf%c",a[i][j], j==n+1 ? '\n' : ' ');for(int i=1; i<=n; i++) {int r=i;for(int j=i; j<=n; j++) if(abs(a[j][i])>abs(a[r][i])) r=j;if(r!=i) for(int j=1; j<=n+1; j++) swap(a[r][j], a[i][j]);for(int k=i+1; k<=n; k++) if(abs(a[k][i]) > eps){double t = a[k][i]/a[i][i];for(int j=i; j<=n+1; j++) a[k][j] -= t*a[i][j];}}for(int i=n; i>=1; i--) {for(int j=n; j>i; j--) a[i][n+1] -= a[i][j]*a[j][n+1];a[i][n+1] /= a[i][i];}
}
void solve(List &q) {memset(a,0,sizeof(a));int n=0;for(int i=1; i<=q.n; i++) id[q[i]] = ++n;// printf("%d ",q[i]); puts(" q");for(int i=1; i<=q.n; i++) {int u=q[i]; a[i][i]=1; a[i][n+1]=1;if(u==t) {a[i][n+1]=0; continue;}for(int p=h[u];p;p=e[p].ne) {int v=e[p].v; if(belong[v] != belong[u]) a[i][n+1] += f[v]/de[u];else a[i][id[v]] -= 1.0/de[u];}}gauss(n);for(int i=1; i<=q.n; i++) f[q[i]] = a[i][n+1];// printf("getf %d %lf\n",q[i],f[q[i]]);
}
namespace SCC {struct edge{int v, ne;} e[M];int cnt=1, h[N];inline void ins(int u, int v) {e[++cnt]=(edge){v, h[u]}; h[u]=cnt;}int vis[N];void dfs(int u) {if(vis[u]) return; vis[u]=1;for(int i=h[u];i;i=e[i].ne) dfs(e[i].v);//printf("solveSCC %d\n",u);solve(li[u]);}
}
void build() {for(int u=1; u<=n; u++)for(int i=h[u];i;i=e[i].ne)if(belong[u] != belong[e[i].v]) SCC::ins(belong[u], belong[e[i].v]);
}
int main() {freopen("in","r",stdin);n=read(); m=read(); s=read(); t=read();for(int i=1; i<=m; i++) {u=read(), v=read();de[u]++; ins(u, v);}dfs(s);//for(int i=1; i<=n; i++) printf("scc %d  %d %d\n",i, dfn[i], belong[i]);if(!dfn[t]) {puts("INF"); return 0;}for(int i=1; i<=n; i++) if(i!=t && de[i]==0 && dfn[i]) {puts("INF"); return 0;}build();SCC::dfs(belong[s]);//for(int i=1; i<=n; i++) printf("f %d %lf\n",i,f[i]);printf("%.3lf", f[s]);
}