二分+SPFA找负环
11090 - Going in Cycle!!Time limit: 3.000 seconds |
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I I U P C 2 0 0 6 |
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Problem G: Going in Cycle!! |
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Input: standard input Output: standard output |
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You are given a weighted directed graph with n vertices and m edges. Each cycle in the graph has a weight, which equals to sum of its edges. There are so many cycles in the graph with different weights. In this problem we want to find a cycle with the minimum mean. |
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Input |
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The first line of input gives the number of cases, N. N test cases follow. Each one starts with two numbers n and m. m lines follow, each has three positive number a, b, c which means there is an edge from vertex a to b with weight of c. |
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Output |
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For each test case output one line containing “Case #x: ” followed by a number that is the lowest mean cycle in graph with 2 digits after decimal place, if there is a cycle. Otherwise print “No cycle found.”. |
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Constraints |
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- n ≤ 50 - a, b ≤ n - c ≤ 10000000 |
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Sample Input |
Output for Sample Input |
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2 2 1 1 2 1 2 2 1 2 2 2 1 3 |
Case #1: No cycle found. Case #2: 2.50 |
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Problemsetter: Mohammad Tavakoli Ghinani Alternate Solution: Cho |
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#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <queue>
using namespace std;
const double INF=1000000000.;
struct Edge
{
int to,next;
double w;
}edge[110000];
int Adj[100],Size=0,n,m;
void init()
{
Size=0; memset(Adj,-1,sizeof(Adj));
}
void Add_Edge(int u,int v,double w)
{
edge[Size].to=v;
edge[Size].next=Adj[u];
edge[Size].w=w;
Adj[u]=Size++;
}
double dist[110];
int cq[110]; bool inq[110];
bool spfa(double mid)
{
queue<int> q;
for(int i=1;i<=n;i++)
{
q.push(i);
dist[i]=INF; cq[i]=0; inq[i]=false;
}
while(!q.empty())
{
int u=q.front(); q.pop();
inq[u]=false;
for(int i=Adj[u];~i;i=edge[i].next)
{
int v=edge[i].to;
if(dist[v]>dist[u]+edge[i].w-mid)
{
dist[v]=dist[u]+edge[i].w-mid;
if(!inq[v])
{
inq[v]=true;
cq[v]++;
if(cq[v]>=n) return false;
q.push(v);
}
}
}
}
return true;
}
int main()
{
int T_T,cas=1;
scanf("%d",&T_T);
while(T_T--)
{
scanf("%d%d",&n,&m);
init();
double ans=INF;
double low=0,high=0,mid;
for(int i=0;i<m;i++)
{
int a,b;
double c;
scanf("%d%d%lf",&a,&b,&c);
if(a==b)
ans=min(ans,c);
Add_Edge(a,b,c);
high=max(high,c);
}
printf("Case #%d: ", cas++);
if(spfa(high+10000))
{
puts("No cycle found.");
continue;
}
while(high-low>1e-3)
{
mid=(high+low)/2.;
if(spfa(mid)==false)
{
ans=min(ans,mid); high=mid;
}
else low=mid;
}
printf("%.2lf\n",ans);
}
return 0;
}
UVA 11090 - Going in Cycle!!
时间： 2024-08-28 10:02:08