Luogu3199 HNOI2009 最小圈 分数规划、SPFA

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可以发现它的式子是一个分数规划的式子，所以可以二分答案，将所有边权减掉当前二分值之后跑一边$SPFA$判断负环即可。

然而这道题把$BFS-SPFA$卡掉了却没卡$DFS-SPFA$

出题人：想不到吧

然而这道题目其实是有结论的，具体可以去看rqy聚聚的blog，反正我是看不懂

// luogu-judger-enable-o2
#include<bits/stdc++.h>
#define ld long double
#define eps 1e-10
//This code is written by Itst
using namespace std;

inline int read(){
    ;
    ;
    char c = getchar();
    while(c != EOF && !isdigit(c)){
        if(c == '-')
            f = ;
        c = getchar();
    }
    while(c != EOF && isdigit(c)){
        a = (a << ) + (a << ) + (c ^ ');
        c = getchar();
    }
    return f ? -a : a;
}

 , MAXM = ;
struct Edge{
    int end , upEd;
    ld w;
}Ed[MAXM];
ld minDis[MAXN];
int head[MAXN] , flo[MAXN] , N , M , cntEd;
queue < int > q;
bool inq[MAXN] , vis[MAXN];

inline void addEd(int a , int b , ld c){
    Ed[++cntEd].end = b;
    Ed[cntEd].upEd = head[a];
    head[a] = cntEd;
    Ed[cntEd].w = c;
}

/*bool SPFA(){
    memset(minDis , 0 , sizeof(minDis));
    for(int i = 1 ; i <= N ; ++i){
        if(!inq[i]){
            inq[i] = 1;
            q.push(i);
        }
        flo[i] = 1;
    }
    while(!q.empty()){
        int t = q.front();
        q.pop();
        inq[t] = 0;
        for(int i = head[t] ; i ; i = Ed[i].upEd)
            if(minDis[Ed[i].end] > minDis[t] + Ed[i].w + eps){
                minDis[Ed[i].end] = minDis[t] + Ed[i].w;
                flo[Ed[i].end] = flo[t] + 1;
                if(flo[Ed[i].end] > N)
                    return 1;
                if(!inq[Ed[i].end]){
                    inq[Ed[i].end] = 1;
                    q.push(Ed[i].end);
                }
            }
    }
    return 0;
    }*/
bool SPFA(int now){
    vis[now] = ;
    for(int i = head[now] ; i ; i = Ed[i].upEd)
        if(minDis[Ed[i].end] > minDis[now] + Ed[i].w)
            if(vis[Ed[i].end])
                ;
            else{
                minDis[Ed[i].end] = minDis[now] + Ed[i].w;
                if(SPFA(Ed[i].end))
                    ;
            }
    vis[now] = ;
    ;
}

inline void add(ld num){
     ; i <= cntEd ; ++i)
        Ed[i].w += num;
}

bool check(ld mid){
    ;
    add(-mid);
    memset(minDis ,  , sizeof(minDis));
    memset(vis ,  , sizeof(vis));
     ; !f && i <= N ; ++i)
         && minDis[i] < 1e-)
            f = SPFA(i);
    add(mid);
    return f;
}

int main(){
#ifndef ONLINE_JUDGE
    freopen("3199.in" , "r" , stdin);
    //freopen("3199.out" , "w" , stdout);
#endif
    N = read();
    M = read();
     ; i <= M ; ++i){
        int a = read() , b = read();
        ld c;
        scanf("%Lf" , &c);
        addEd(a , b , c);
    }
    ld L = -1e7 , R = 1e7;
    while(R - L > eps){
        ld mid = (L + R) / ;
        check(mid) ? R = mid : L = mid;
    }
    printf("%.8Lf" , L);
    ;
}