time limit per test : 1 second
memory limit per test : 256 megabytes
分数:2000
You are given a directed graph with
vertices and
directed edges without self-loops or multiple edges.
Let’s denote the
-coloring of a digraph as following: you color each edge in one of
colors. The
-coloring is good if and only if there no cycle formed by edges of same color.
Find a good
-coloring of given digraph with minimum possible
.
Input
The first line contains two integers
and
— the number of vertices and edges in the digraph, respectively.
Next
lines contain description of edges — one per line. Each edge is a pair of integers
and
≠
— there is directed edge from
to
in the graph.
It is guaranteed that each ordered pair
appears in the list of edges at most once.
Output
In the first line print single integer — the number of used colors in a good -coloring of given graph.
In the second line print
integers
, where ci is a color of the
-th edge (in order as they are given in the input).
If there are multiple answers print any of them (you still have to minimize
).
Examples
Input
4 5
1 2
1 3
3 4
2 4
1 4
Outpu
1
1 1 1 1 1
Input
3 3
1 2
2 3
3 1
Output
2
1 1 2
题意:
给一个有向图,给每条边染色,使得每种颜色的边不能构成环。求一种染色种数最少的方案。
题解:
最多只会染上2种颜色
考虑dfs,每次出现返祖边的时候返祖边的颜色就是第二种颜色,否则的话全是第一种颜色。
那么只要dfs即可。
#include<bits/stdc++.h>
#define ll long long
#define pa pair<int,int>
using namespace std;
int n,m;
vector<pa>G[5004];
int ans[5004];
bool flag,vis[5004],inq[5004];
void dfs(int x){
inq[x]=1;
vis[x]=1;
for(pa now:G[x]){
int to=now.first,s=now.second;
ans[s]=1;
if(!vis[to]){
dfs(to);
}
else if(inq[to]){
ans[s]=2;
flag=1;
}
else{
ans[s]=1;
}
}
inq[x]=0;
}
int main(){
scanf("%d%d",&n,&m);
for(int i=1;i<=m;i++){
int u,v;scanf("%d%d",&u,&v);
G[u].push_back({v,i});
}
flag=0;
for(int i=1;i<=n;i++){
if(!vis[i])dfs(i);
}
if(!flag){
printf("%d\n",1);
for(int i=1;i<=m;i++){
printf("%d ",ans[i]);
}
puts("");
}
else{
printf("%d\n",2);
for(int i=1;i<=m;i++){
printf("%d ",ans[i]);
}
puts("");
}
return 0;
}