题意:
给出一个无向图,求覆盖所有的边的路径,要求路径数最少。
思路:
在一个联通分量内,如果有多对奇数度的点,那么保留一对,其他的配对连边,再从保留的奇数度点开始找欧拉路径。
最后根据添加的辅助边分割欧拉路径,就可以得到需要的覆盖路径。
代码:
#include <iostream>
#include <iomanip>
#include <algorithm>
#include <cstring>
#include <cctype>
#include <cstdlib>
#include <cstdio>
#include <cmath>
#include <ctime>
#include <map>
#include <list>
#include <set>
#include <stack>
#include <queue>
#include <string>
#include <sstream>
#define pb push_back
#define X first
#define Y second
#define lch (o<<1)
#define rch (o<<1|1)
#define ALL(x) x.begin(),x.end()
#define INS(x) inserter(x,x.begin())
#define pii pair<int,int>
#define qclear(a) while(!a.empty())a.pop();
#define lowbit(x) (x&-x)
#define sd(n) scanf("%d",&n)
#define sdd(n,m) scanf("%d%d",&n,&m)
#define sddd(n,m,k) scanf("%d%d%d",&n,&m,&k)
#define mst(a,b) memset(a,b,sizeof(a))
#define cout3(x,y,z) cout<<x<<" "<<y<<" "<<z<<endl
#define cout2(x,y) cout<<x<<" "<<y<<endl
#define cout1(x) cout<<x<<endl
#define O2 #pragma GCC optimize(2)
#define IOS std::ios::sync_with_stdio(false)
#define SRAND srand((unsigned int)(time(0)))
typedef long long ll;
typedef unsigned long long ull;
typedef unsigned int uint;
using namespace std;
const double PI=acos(-1.0);
const int INF=0x3f3f3f3f;
const ll mod=1e9+7;
const double eps=1e-8;
const int maxn=100005;
const int maxm=500005;
struct node {
int v,dir,id;
};
int n,m;
vector<node>maps[maxn];
int oddvcur=0;
int oddv[maxn];
bool vis[maxn];
int deg[maxn];
void find_oddv(int u) {
vis[u]=1;
if(deg[u]&1)
oddv[oddvcur++]=u;
for(int i=0; i<maps[u].size(); i++) {
int v=maps[u][i].v;
if(vis[v])
continue;
find_oddv(v);
}
}
int anscnt=0;
vector<int>ans[maxn];
bool evis[maxm];
void dfs(int u) {
for(int i=0; i<maps[u].size(); i++) {
int epos=maps[u][i].id;
if(evis[epos])
continue;
evis[epos]=1;
dfs(maps[u][i].v);
if(epos<=m) {
ans[anscnt].pb(epos*maps[u][i].dir*-1);
} else {
anscnt++;
}
}
}
void init() {
for(int i=0; i<maxn; i++) {
ans[i].clear();
maps[i].clear();
}
mst(deg,0);
mst(vis,0);
mst(evis,0);
anscnt=0;
}
void solve() {
while(~sdd(n,m)) {
init();
for(int i=1; i<=m; i++) {
int u,v;
sdd(u,v);
maps[u].pb((node) {
v,1,i
});
maps[v].pb((node) {
u,-1,i
});
deg[u]++;
deg[v]++;
}
int idcnt=m+1;
for(int i=1; i<=n; i++) {
if(deg[i]==0)
continue;
if(vis[i])
continue;
oddvcur=0;
find_oddv(i);
if(oddvcur>1) {
for(int i=2; i<oddvcur; i+=2) {
int u,v;
u=oddv[i];
v=oddv[i+1];
maps[u].pb((node) {
v,0,idcnt
});
maps[v].pb((node) {
u,0,idcnt++
});
deg[u]++;
deg[v]++;
}
}
anscnt++;
if(oddvcur!=0) {
dfs(oddv[0]);
} else {
dfs(i);
}
}
printf("%d\n",anscnt);
for(int i=1; i<=anscnt; i++) {
printf("%d",ans[i].size());
for(int j=0; j<ans[i].size(); j++) {
printf(" %d",ans[i][j]);
}
printf("\n");
}
}
return ;
}
int main() {
#ifdef LOCAL
freopen("in.txt","r",stdin);
// freopen("out.txt","w",stdout);
#else
// freopen("","r",stdin);
// freopen("","w",stdout);
#endif
solve();
return 0;
}