聪聪和可可 HYSBZ - 1415（概率 + spfa + 记忆化dp）

#include <iostream>
#include <cstdio>
#include <sstream>
#include <cstring>
#include <map>
#include <cctype>
#include <set>
#include <vector>
#include <stack>
#include <queue>
#include <algorithm>
#include <cmath>
#include <bitset>
#define rap(i, a, n) for(int i=a; i<=n; i++)
#define rep(i, a, n) for(int i=a; i<n; i++)
#define lap(i, a, n) for(int i=n; i>=a; i--)
#define lep(i, a, n) for(int i=n; i>a; i--)
#define rd(a) scanf("%d", &a)
#define rlld(a) scanf("%lld", &a)
#define rc(a) scanf("%c", &a)
#define rs(a) scanf("%s", a)
#define pd(a) printf("%d\n", a);
#define plld(a) printf("%lld\n", a);
#define pc(a) printf("%c\n", a);
#define ps(a) printf("%s\n", a);
#define MOD 2018
#define LL long long
#define ULL unsigned long long
#define Pair pair<int, int>
#define mem(a, b) memset(a, b, sizeof(a))
#define _  ios_base::sync_with_stdio(0),cin.tie(0)
//freopen("1.txt", "r", stdin);
using namespace std;
const int maxn = 1010, INF = 0x7fffffff, LL_INF = 0x7fffffffffffffff;
int n, m, ss, tt, cnt;
int head[maxn], f[maxn][maxn], vis[maxn], pre[maxn], d[maxn], out[maxn];
double p[maxn][maxn];
struct node
{
    int v, next;
}Node[maxn << 1];

void add_(int u, int v)
{
    out[u]++;
    Node[cnt].v = v;
    Node[cnt].next = head[u];
    head[u] = cnt++;
}

void add(int u, int v)
{
    add_(u, v);
    add_(v, u);
}

void spfa(int s)
{
    queue<int> Q;
    for(int i = 1; i <= n; i++) d[i] = INF;
    d[s] = 0;
    mem(vis, 0);
    Q.push(s); vis[s] = 1;
    while(!Q.empty())
    {
        int u = Q.front(); Q.pop();
        vis[u] = 0;
        for(int i = head[u]; i != -1; i = Node[i].next)
        {
            node e = Node[i];
            if(d[e.v] > d[u] + 1 || d[e.v] == d[u] + 1 && u < pre[e.v])
            {
                d[e.v] = d[u] + 1;
                pre[e.v] = u;
                if(!vis[e.v])
                {
                    vis[e.v] = 1;
                    Q.push(e.v);
                }
            }
        }
    }
    for(int i = 1; i <= n; i++)
        if(i != s)
            f[i][s] = pre[i];
}

double m_dfs(int u, int t)
{
    if(u == t) return p[u][t] = 0;
    if(f[u][t] == t) return p[u][t] = 1;
    if(f[f[u][t]][t] == t) return p[u][t] = 1;
    if(p[u][t] >= -1e-7) return p[u][t];
    int nxt = f[f[u][t]][t];
    double res = 1;
    for(int i = head[t]; i != -1; i = Node[i].next)
    {
        node e = Node[i];
        res += m_dfs(nxt, e.v) /(double) (out[t] + 1);
    }
    res += m_dfs(nxt, t) /(double) (out[t] + 1);
    return p[u][t] = res;
}

int main()
{
    mem(head, -1);
    int u, v;
    cin >> n >> m >> ss >> tt;
    rap(i, 1, m)
    {
        cin >> u >> v;
        add(u, v);
    }
    for(int i = 1; i <= n; i++)
        spfa(i);
    mem(p, -1);
    printf("%.3f\n", m_dfs(ss, tt));



    return 0;
}