BZOJ 1415 聪聪和可可

\(N^2\)
DP[C][M]
废状态多
不好确定顺序
记忆化搜索
注意聪聪走编号小的点

#include <iostream>
#include <iomanip>

using namespace std;

const int MAXN=1011;
const int MAXM=1011;
const int INF=1034567890;

int N, M;
int S, T;

int Dis[MAXN][MAXN];
double F[MAXN][MAXN];
bool Vis[MAXN][MAXN];

struct Vert{
	int FE;
	int Dis;
	int Bfn;
	int Deg;
} V[MAXN];

struct Edge{
	int x, y, next;
} E[MAXM<<1];

int Ecnt=0;

void addE(int a, int b){
	++Ecnt;
	E[Ecnt].x=a;E[Ecnt].y=b;E[Ecnt].next=V[a].FE;V[a].FE=Ecnt;
}

int Q[MAXN], Head, Tail;
int BFN=0;

void BFS_init(){
	Head=1;Tail=1;
	++BFN;
}

void BFS(int at){
	BFS_init();
	V[at].Dis=0;
	Q[Tail++]=at;
	V[at].Bfn=BFN;
	while(Head<Tail){
		at=Q[Head++];
		for(int k=V[at].FE, to;k>0;k=E[k].next){
			to=E[k].y;
			if(V[to].Bfn==BFN)	continue;
			V[to].Dis=V[at].Dis+1;
			Q[Tail++]=to;
			V[to].Bfn=BFN;
		}
	}
}

double DP(int s, int t){
	if(s==t)	return 0.0;
	if(Dis[s][t]<=2)	return 1.0;
	if(Vis[s][t])	return F[s][t];
	int s1=N+1, s1d=INF;
	for(int k=V[s].FE, to;k>0;k=E[k].next){
		to=E[k].y;
		if(Dis[to][t]<s1d || (Dis[to][t]==s1d && to<s1)){
			s1=to;
			s1d=Dis[to][t];
		}
	}
	if(s1d>=INF)	return 1e9;
	int s2=N+1, s2d=INF;
	for(int k=V[s1].FE, to;k>0;k=E[k].next){
		to=E[k].y;
		if(Dis[to][t]<s2d || (Dis[to][t]==s2d && to<s2)){
			s2=to;
			s2d=Dis[to][t];
		}
	}
	if(s2d>=INF)	return 1e9;
	double ret=1.0, p=1.0/(double)(V[t].Deg+1);
	for(int k=V[t].FE, to;k>0;k=E[k].next){
		to=E[k].y;
		ret+=p*DP(s2, to);
	}
	ret+=p*DP(s2, t);
	Vis[s][t]=true;F[s][t]=ret;
	return ret;
}

int main(){
	ios_base::sync_with_stdio(false);
	
	cin >> N >> M;
	cin >> S >> T;
	
	for(int i=1, a, b;i<=M;++i){
		cin >> a >> b;
		addE(a, b);addE(b, a);
		++V[a].Deg;++V[b].Deg;
	}
	
	for(int i=1;i<=N;++i)
		for(int j=1;j<=N;++j)
			Dis[i][j]=INF;
	
	for(int i=1;i<=N;++i){
		BFS(i);
		for(int j=1;j<=N;++j)
			Dis[i][j]=V[j].Dis;
	}
	
	cout << fixed << setprecision(3) << DP(S, T) << endl;
	
	return 0;
}

/*
4 3
1 4
1 2
2 3
3 4

1.500

*/

/*
9 9
9 3
1 2
2 3
3 4
4 5
3 6
4 6
4 7
7 8
8 9

2.167

*/