SDOI2015第1轮第2试星际战争

Posted 2021-03-08 leiyuanze

#include<cstdio>
#include<queue>
using namespace std;

const int M = 10000;
const double inf = 1e18;
int n , m , h[505] , cur[505] , dep[505] , s , t , tot = 1;
double a[55] , b[55] , ans , Max;
struct edge{
    int to , nxt;
    double w;
}e[M + 5] , ee[M + 5];

inline double min(double x , double y) {return x < y ? x : y;};

inline void add(int x , int y , double w)
{
    e[++tot].to = y;
    e[tot].w = w;
    e[tot].nxt = h[x];
    h[x] = tot;
}

inline int bfs(int s , int t)
{
    for(register int i = s; i <= t; i++) dep[i] = 0 , cur[i] = h[i];
    queue<int> Q;
    dep[s] = 1;
    Q.push(s);
    while (!Q.empty())
    {
        int now = Q.front();
        Q.pop();
        for(register int i = h[now]; i; i = ee[i].nxt)
        {
            int v = ee[i].to;
            if (ee[i].w <= 0 || dep[v] != 0) continue;
            dep[v] = dep[now] + 1;
            Q.push(v);
        }
    }
    return dep[t];
}

inline double dfs(int x , int fa , double mi)
{
    if (x == t || mi <= 0) return mi;
    double flow = 0;
    for(register int i = cur[x]; i; i = ee[i].nxt)
    {
        cur[x] = i;
        int v = ee[i].to;
        if (v == fa || dep[x] + 1 != dep[v] || ee[i].w <= 0) continue;
        double f = dfs(v , x , min(mi , ee[i].w));
        if (f <= 0) continue;
        mi -= f , ee[i].w -= f , ee[i ^ 1].w += f , flow += f;
        if (mi <= 0) break;
    }
    return flow;
}

inline bool check(double mid)
{
    for(register int i = 1; i <= tot; i++) ee[i] = e[i];
    for(register int i = h[s]; i; i = ee[i].nxt)
        ee[i].w = b[ee[i].to] * mid;
    double res = 0;
    while (bfs(s , t)) res += dfs(s , 0 , inf);
    return res >= Max;
}

int main()
{
//  freopen("星际战争.in" , "r" , stdin);
    scanf("%d%d" , &n , &m);
    t = n + m + 5;
    for(register int i = 1; i <= n; i++)
    {
        scanf("%lf" , &a[i]);
        Max += a[i];
        add(i + m , t , a[i]);
        add(t , i + m , 0); 
    }
    for(register int i = 1; i <= m; i++) 
    {
        scanf("%lf" , &b[i]);
        add(s , i , b[i]);
        add(i , s , 0);
    }
    int x;
    for(register int i = 1; i <= m; i++)
        for(register int j = 1; j <= n; j++)
        {
            scanf("%d" , &x);
            if (x == 1) add(i , j + m , inf) , add(j + m , i , 0);
        }
    double l = 0 , r = 1e9 , mid;
    for(register int i = 1; i <= 60; i++)
    {
        mid = (l + r) * 0.5;
        if (check(mid)) r = mid , ans = mid;
        else l = mid;
    }
    printf("%.6lf" , ans);
}