• bzoj 1486: [HNOI2009]最小圈 01分数规划


    题目大意:

    求有向带权图中的最小平均值圈,平均值定义为边的权和与点数的比值

    题解:

    标准的01分数规划

    #include <cstdio>
    #include <cstring>
    #include <algorithm>
    using namespace std;
    typedef long long ll;
    inline void read(int &x){
    	x=0;char ch;bool flag = false;
    	while(ch=getchar(),ch<'!');if(ch == '-') ch=getchar(),flag = true;
    	while(x=10*x+ch-'0',ch=getchar(),ch>'!');if(flag) x=-x;
    }
    const int maxn = 3010;
    const int maxm = 10010;
    const double eps = 1e-12;
    struct Edge{
    	int to,next;
    	double dis;
    }G[maxm<<1];
    int head[maxn],cnt;
    void add(int u,int v,double d){
    	G[++cnt].to = v;
    	G[cnt].next = head[u];
    	head[u] = cnt;
    	G[cnt].dis = d;
    }
    #define v G[i].to
    bool inq[maxn];double dis[maxn];
    bool dfs(int u){
    	inq[u] = true;
    	for(int i = head[u];i;i=G[i].next){
    		if(dis[v] > dis[u] + G[i].dis){
    			dis[v] = dis[u] + G[i].dis;
    			if(inq[v]) return true;
    			if(dfs(v)) return true;
    		}
    	}inq[u] = false;
    	return false;
    }
    #undef v
    int n;
    inline bool check(double mid){
    	for(int i=1;i<=cnt;++i) G[i].dis -= mid;
    	memset(inq,0,sizeof inq);memset(dis,0,sizeof dis);
    	bool flag = false;
    	for(int i=1;i<=n;++i) if(dfs(i)){flag = true;break;}
    	for(int i=1;i<=cnt;++i) G[i].dis += mid;
    	return flag;
    }
    int main(){
    	int m;read(n);read(m);
    	double d;
    	for(int i=1,u,v;i<=m;++i){
    		read(u);read(v);scanf("%lf",&d);
    		add(u,v,d);
    	}
    	double l = -1e9,r = 1e9;
    	while(r-l > eps){
    		double mid = (l+r)/2;
    		if(check(mid)) r = mid;
    		else l = mid;
    	}printf("%.8lf
    ",r);
    	getchar();getchar();
    	return 0;
    }
    
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  • 原文地址:https://www.cnblogs.com/Skyminer/p/6477333.html
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