3993: [SDOI2015]星际战争

题意：略

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R1D2T1考了裸二分答案+二分图最大匹配...

#include <iostream>

#include <cstdio>

#include <cstring>

#include <algorithm>

#include <cmath>

using namespace std;

typedef long long ll;

const int N=105, M=1e5+5, INF=1e9+5;

const double eps=1e-12;

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, a[N], b[N], g[55][55], sum;

struct edge{int v, ne; double c, f;}e[M];

int cnt=1, h[N];

inline void ins(int u, int v, double c) { //printf("ins %d %d %lf\n",u,v,c);

	e[++cnt]=(edge){v, h[u], c, 0}; h[u]=cnt;

	e[++cnt]=(edge){u, h[v], 0, 0}; h[v]=cnt;

}

int q[N], head, tail, d[N], vis[N];

bool bfs() { //puts("bfs");

	memset(vis, 0, sizeof(vis));

	head=tail=1;

	q[tail++]=s; d[s]=0; vis[s]=1;

	while(head != tail) {

		int u=q[head++]; //printf("u %d\n",u);

		for(int i=h[u];i;i=e[i].ne)

			if(!vis[e[i].v] && e[i].c>e[i].f) {

				vis[e[i].v]=1; d[e[i].v]=d[u]+1;

				q[tail++]=e[i].v;

				if(e[i].v == t) return true;

			}

	}

	return false;

}

int cur[N];

double dfs(int u, double a) {

	if(u==t || a==0) return a;

	double flow=0, f;

	for(int &i=cur[u];i;i=e[i].ne)

		if(d[e[i].v] == d[u]+1 && (f = dfs(e[i].v, min(a, e[i].c-e[i].f)))>0 ) {

			flow += f;

			e[i].f += f;

			e[i^1].f -= f;

			a -= f;

			if(a==0) break;

		}

	if(a) d[u]=-1;

	return flow;

}

double dinic() {

	double flow=0;

	while(bfs()) {

		for(int i=s; i<=t; i++) cur[i]=h[i];

		flow += dfs(s, INF); //printf("flow %lf\n",flow);

	}

	//printf("flow %lf\n", flow);

	return flow;

}

bool check(double mid) {

	cnt=1; memset(h, 0, sizeof(h));

	for(int i=1; i<=m; i++) ins(s, i, b[i]*mid);

	for(int i=1; i<=n; i++) ins(m+i, t, a[i]);

	for(int i=1; i<=m; i++)

		for(int j=1; j<=n; j++) if(g[i][j]) ins(i, m+j, INF);

	double flow=dinic();

	return abs(flow-sum) < eps ? 1 : 0;

}

double l, r;

void solve() {

	while(r-l > 1e-4) {

		double mid=(l+r)/2.0;

		if(check(mid)) r=mid;

		else l=mid;

	}

	printf("%lf", l);

}

int main() {

	freopen("in","r",stdin);

	n=read(); m=read(); s=0; t=n+m+1;

	for(int i=1; i<=n; i++) a[i]=read(), r+=a[i], sum+=a[i];

	for(int i=1; i<=m; i++) b[i]=read();

	for(int i=1; i<=m; i++) for(int j=1; j<=n; j++) g[i][j]=read();

	solve();

}