luogu P1768 天路

嘟嘟嘟

01分数规划之最优比率环。

主要是发一下基于dfs的spfa。跑的贼快，原来总用时2000多ms还TLE了两个点，改成dfs后总用时直降43ms！

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<cstring>
#include<cmath>
#include<cstdlib>
#include<cctype>
#include<stack>
#include<queue>
#include<vector>
using namespace std;
#define enter puts("")
#define space putchar(' ')
#define Mem(a, x) memset(a, x, sizeof(a))
#define rg register
typedef long long ll;
typedef double db;
const int INF = 0x3f3f3f3f;
const db eps = 1e-4;
const int maxn = 7e3 + 5;
const int maxe = 4e4 + 5;
inline ll read()
{
  ll ans = 0;
  char ch = getchar(), las = ' ';
  while(!isdigit(ch)) las = ch, ch = getchar();
  while(isdigit(ch)) ans = (ans << 3) + (ans << 1) + ch - '0', ch = getchar();
  if(las == '-') ans = -ans;
  return ans;
}
inline void write(ll x)
{
  if(x < 0) putchar('-'), x = -x;
  if(x >= 10) write(x / 10);
  putchar(x % 10 + '0');
}

int n, m;
struct Edge
{
  int nxt, to, v, p;
}e[maxe];
int head[maxn], ecnt = -1;
void addEdge(int x, int y, int v, int p)
{
  e[++ecnt] = (Edge){head[x], y, v, p};
  head[x] = ecnt;
}

bool in[maxn];
db dis[maxn];
bool judge(db x, int now)
{
  in[now] = 1;
  for(int i = head[now]; i != -1; i = e[i].nxt)
    {
      if(dis[e[i].to] > x * (db)e[i].p - (db)e[i].v + dis[now])
    {
      if(in[e[i].to]) return 1;
      dis[e[i].to] = x * (db)e[i].p - (db)e[i].v + dis[now];
      in[e[i].to] = 1;
      if(judge(x, e[i].to)) return 1;
    }
    }
  in[now] = 0;
  return 0;
}

int main()
{
  Mem(head, -1);
  n = read(); m = read();
  for(int i = 1; i <= m; ++i)
    {
      int x = read(), y = read(), v = read(), p = read();
      addEdge(x, y, v, p);
    }
  for(int i = 1; i <= n; ++i) addEdge(0, i, 0, 0); //搞一个超级源点
  db L = 0, R = 2000;
  while(R - L > eps)
    {
      db mid = (L + R) / 2;
      Mem(dis, 0x3f); Mem(in, 0); dis[0] = 0;
      if(judge(mid, 0)) L = mid;
      else R = mid - eps;
    }
  if(L < eps) write(-1), enter;
  else printf("%.1lf
", L);
  return 0;
}