题目链接
题意:给你一个无向图,不存在自环和重边,现在需要把图的无向边全部变成有向边,问最多可以使多少个结点的入度等于出度,输出所有有向边集合,不考虑边的顺序
思路: 容易联想到欧拉路,求解最多可以使多少个结点的入度等于出度很简单,统计无向图的偶数度数的结点个数即可,输出边却不怎么好写,一个好的思路,添加一个结点,连接上所有的奇数度数的结点,这样整个图就由若干个欧拉图组成,跑若干次欧拉图就可以了
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
const int maxn = 205;
const int maxm = maxn * maxn;
struct Edge
{
int from,to,next;
};
Edge e[maxm];
int edgeNum,head[maxn],n,m,du[maxn];
bool vis[maxm];
void addEdge(int from,int to)
{
e[edgeNum].from = from;
e[edgeNum].to = to;
e[edgeNum].next = head[from];
head[from] = edgeNum;
edgeNum++;
}
void dfs(int rt)
{
for(int j = head[rt];j != -1; j = e[j].next)
{
if(vis[j]) continue;
int to = e[j].to;
if(rt && to) printf("%d %d\n",rt,to);
vis[j] = vis[j^1] = true;
dfs(to);
}
}
int main()
{
#ifdef LOCAL_DEBUG
freopen("input.txt","r",stdin);
#endif // LOCAL_DEBUG
int T;
scanf("%d" ,&T);
while(T--)
{
memset(head,-1,sizeof(head));
memset(du,0,sizeof(du));
memset(vis,0,sizeof(vis));
scanf("%d%d" ,&n,&m);
int from,to;
for(int i = 0; i < m; i++)
{
scanf("%d%d" ,&from,&to);
addEdge(from,to);
addEdge(to,from);
du[from]++; du[to]++;
}
int sum = 0;
for(int i = 1; i <= n; i++)
{
if(du[i]%2 != 0)
{
addEdge(i,0); addEdge(0,i);
}
else sum++;
}
printf("%d\n",sum);
for(int i = 0; i <= n; i++) dfs(i);
}
return 0;
}