https://codeforces.com/contest/1144/problem/F
题意:给定一个无向图,要求添加方向使得图变为有向图并且不存在长度大于1的路径
C++版本一
题解:二分匹配
对于一个点的所有有关系的边中只能有指向它的或者背向它的;
所有二分匹配,标记这个点是什么情况。然后枚举边的出发点,输出出发点的情况就行了
/*
*@Author: STZG
*@Language: C++
*/
#include <bits/stdc++.h>
#include<iostream>
#include<algorithm>
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<string>
#include<vector>
#include<bitset>
#include<queue>
#include<deque>
#include<stack>
#include<cmath>
#include<list>
#include<map>
#include<set>
//#define DEBUG
#define RI register int
#define endl "\n"
using namespace std;
typedef long long ll;
//typedef __int128 lll;
const int N=200000+10;
const int M=100000+10;
const int MOD=1e9+7;
const double PI = acos(-1.0);
const double EXP = 1E-8;
const int INF = 0x3f3f3f3f;
int t,n,m,k,p,l,r,u,v;
int ans,cnt,flag,temp,sum;
int color[N];
int a[N];
char str;
vector<int>G[N];
void dfs(int u,int c){
color[u]=c;
for(int i=0,j=G[u].size();i<j;i++){
int v=G[u][i];
if(color[u]==color[v]){
flag=0;
}
if(color[v]==-1)
dfs(v,!c);
}
}
int main()
{
#ifdef DEBUG
freopen("input.in", "r", stdin);
//freopen("output.out", "w", stdout);
#endif
//ios::sync_with_stdio(false);
//cin.tie(0);
//cout.tie(0);
//scanf("%d",&t);
//while(t--){
scanf("%d%d",&n,&m);
for(int i=1;i<=m;i++){
scanf("%d%d",&u,&v);
G[u].push_back(v);
G[v].push_back(u);
a[i]=u;
}
memset(color,-1,sizeof(color));
flag=1;
for(int i=1;i<=n;i++){
if(color[i]==-1)
dfs(i,0);
}
if(flag){
cout<<"YES"<<endl;
for(int i=1;i<=m;i++){
cout<<!color[a[i]];
}
}else{
cout<<"No"<<endl;
}
//}
#ifdef DEBUG
printf("Time cost : %lf s\n",(double)clock()/CLOCKS_PER_SEC);
#endif
//cout << "Hello world!" << endl;
return 0;
}
C++版本二
#include<bits/stdc++.h>
#define fi first
#define sf scanf
#define se second
#define pf printf
#define pb push_back
#define mp make_pair
#define sz(x) ((int)(x).size())
#define all(x) (x).begin(),(x).end()
#define mem(x,y) memset((x),(y),sizeof(x))
#define fup(i,x,y) for(int i=(x);i<=(y);++i)
#define fdn(i,x,y) for(int i=(x);i>=(y);--i)
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
typedef std::pair<int,int> pii;
using namespace std;
const int __=2e5+5;
struct node
{
int x,c,id;
};
vector<node>G[__];
int col[__],ans[__];
void dfs(int x,int fa=-1,int c=0)
{
if(col[x])
{
if(col[x]!=c)
{
puts("NO");
exit(0);
}
return;
}
col[x]=c;
for(int i=0;i<sz(G[x]);++i)
{
node y=G[x][i];
if(y.x!=fa)
{
ans[y.id]=y.c^c;
dfs(y.x,x,1-c);
}
}
}
int main()
{
int n,m;sf("%d%d",&n,&m);
fup(i,1,m)
{
int x,y;sf("%d%d",&x,&y);
G[x].pb({y,1,i});
G[y].pb({x,0,i});
}
dfs(1);
puts("YES");
fup(i,1,m)
pf("%d",ans[i]);
return 0;
}