版权声明：本文为博主原创文章，未经博主允许不得转载。 https://blog.csdn.net/Game_Acm/article/details/82498312
#include<map>
#include<set>
#include<ctime>
#include<stack>
#include<cmath>
#include<queue>
#include<vector>
#include<string>
#include<cstdio>
#include<cstring>
#include<complex>
#include<iostream>
#include<algorithm>
using namespace std;
int Min( int a , int b ){ return a<b?a:b; }
int Max( int a , int b ){ return a>b?a:b; }
typedef long long LL;
const int maxn = 620; //内存开点数的1.5倍
const int inf = 0x3f3f3f3f;
struct edge
{
int u,v,w;
}g[maxn][maxn];
int n,m,n_x,lab[maxn],match[maxn],slack[maxn],st[maxn],pa[maxn],flower_from[maxn][maxn],S[maxn],vis[maxn];
vector<int>flower[maxn]; deque<int>q;
int dist( edge e )
{
return lab[e.u]+lab[e.v]-g[e.u][e.v].w*2;
}
void update_slack( int u , int x )
{
if ( !slack[x]||dist(g[u][x])<dist(g[slack[x]][x]) ) slack[x] = u;
}
void set_slack( int x )
{
slack[x] = 0;
for ( int u=1 ; u<=n ; u++ )
if ( g[u][x].w>0&&st[u]!=x&&S[st[u]]==0 )
update_slack( u , x );
}
void q_push( int x )
{
if ( x<=n ) return q.push_back(x);
for ( int i=0 ; i<flower[x].size() ; i++ ) q_push( flower[x][i] );
}
void set_st( int x , int b )
{
st[x] = b;
if ( x<=n ) return;
for ( int i=0 ; i<flower[x].size() ; i++ ) set_st( flower[x][i] , b );
}
int get_pr( int b , int xr )
{
int pr = find( flower[b].begin() , flower[b].end() , xr )-flower[b].begin();
if ( pr%2==1 )
{
reverse( flower[b].begin()+1 , flower[b].end() );
return (int)flower[b].size()-pr;
}
else return pr;
}
void set_match( int u , int v )
{
match[u] = g[u][v].v;
if ( u<=n ) return;
edge e = g[u][v];
int xr = flower_from[u][e.u],pr = get_pr( u , xr );
for ( int i=0 ; i<pr ; i++ ) set_match( flower[u][i] , flower[u][i^1] );
set_match( xr , v );
rotate( flower[u].begin() , flower[u].begin()+pr , flower[u].end() );
}
void augment( int u , int v )
{
int xnv = st[match[u]];
set_match( u , v );
if ( !xnv ) return;
set_match( xnv , st[pa[xnv]] );
augment( st[pa[xnv]] , xnv );
}
int get_lca( int u , int v )
{
static int t = 0;
for ( ++t ; u||v ; swap( u ,v ) )
{
if ( u==0 ) continue;
if ( vis[u]==t ) return u;
vis[u] = t;
u = st[match[u]];
if ( u ) u = st[pa[u]];
}
return 0;
}
void add_blossom( int u , int lca , int v )
{
int b = n+1;
while ( b<=n_x&&st[b] ) ++b;
if ( b>n_x ) ++n_x;
lab[b] = 0,S[b] = 0;
match[b] = match[lca];
flower[b].clear();
flower[b].push_back(lca);
for ( int x=u,y ; x!=lca ; x=st[pa[y]] )
flower[b].push_back(x),flower[b].push_back(y=st[match[x]]),q_push(y);
reverse( flower[b].begin()+1 , flower[b].end() );
for ( int x=v,y ; x!=lca ; x=st[pa[y]] )
flower[b].push_back(x),flower[b].push_back(y=st[match[x]]),q_push(y);
set_st( b , b );
for ( int x=1 ; x<=n_x ; x++ ) g[b][x].w = g[x][b].w = 0;
for ( int x=1 ; x<=n ; x++ ) flower_from[b][x] = 0;
for ( int i=0 ; i<flower[b].size() ; i++ )
{
int xs = flower[b][i];
for ( int x=1 ; x<=n_x ; x++ )
if ( g[b][x].w==0||dist(g[xs][x])<dist(g[b][x]) )
g[b][x] = g[xs][x],g[x][b] = g[x][xs];
for ( int x=1 ; x<=n ; x++ )
if ( flower_from[xs][x] ) flower_from[b][x] = xs;
}
set_slack(b);
}
void expand_blossom( int b )
{
for ( int i=0 ; i<flower[b].size() ; i++ )
set_st( flower[b][i] , flower[b][i] );
int xr = flower_from[b][g[b][pa[b]].u],pr = get_pr( b , xr );
for ( int i=0 ; i<pr ; i+=2 )
{
int xs = flower[b][i],xns = flower[b][i+1];
pa[xs] = g[xns][xs].u;
S[xs] = 1,S[xns] = 0;
slack[xs] = 0,set_slack(xns);
q_push(xns);
}
S[xr] = 1,pa[xr] = pa[b];
for ( int i=pr+1 ; i<flower[b].size() ; i++ )
{
int xs = flower[b][i];
S[xs] = -1,set_slack(xs);
}
st[b] = 0;
}
bool on_found_edge( const edge &e )
{
int u =st[e.u],v = st[e.v];
if ( S[v]==-1 )
{
pa[v] = e.u,S[v] = 1;
int nu = st[match[v]];
slack[v] = slack[nu] = 0;
S[nu] = 0,q_push(nu);
}
else if ( S[v]==0 )
{
int lca = get_lca( u , v );
if ( !lca ) return augment( u , v ),augment( v , u ),1;
else add_blossom( u , lca , v );
}
return 0;
}
bool matching()
{
fill( S , S+n_x+1 , -1 ),fill( slack , slack+n_x+1 , 0 );
q.clear();
for ( int x=1 ; x<=n_x ; x++ )
if ( st[x]==x&&!match[x] ) pa[x] = 0,S[x] = 0,q_push(x);
if ( q.empty() ) return 0;
for ( ;; )
{
while ( q.size() )
{
int u = q.front();
q.pop_front();
if ( S[st[u]]==1 ) continue;
for ( int v=1 ; v<=n ; v++ )
if ( g[u][v].w>0&&st[u]!=st[v] )
{
if ( dist(g[u][v])==0 )
{
if ( on_found_edge(g[u][v]) ) return 1;
}
else update_slack( u , st[v] );
}
}
int d = inf;
for ( int b=n+1 ; b<=n_x ; b++ )
if ( st[b]==b&&S[b]==1 ) d = Min( d , lab[b]/2 );
for ( int x=1 ; x<=n_x ; x++ )
if ( st[x]==x&&slack[x] )
{
if ( S[x]==-1 ) d = Min( d , dist(g[slack[x]][x]) );
else if ( S[x]==0 ) d = Min( d , dist(g[slack[x]][x])/2 );
}
for ( int u=1 ; u<=n ; u++ )
{
if ( S[st[u]]==0 )
{
if ( lab[u]<=d ) return 0;
lab[u] -= d;
}
else if ( S[st[u]]==1 ) lab[u] += d;
}
for ( int b=n+1 ; b<=n_x ; b++ )
if ( st[b]==b )
{
if ( S[st[b]]==0 ) lab[b] += d*2;
else if ( S[st[b]]==1 ) lab[b] -= d*2;
}
q.clear();
for ( int x=1 ; x<=n_x ; x++ )
if ( st[x]==x&&slack[x]&&st[slack[x]]!=x&&dist(g[slack[x]][x])==0 )
if ( on_found_edge( g[slack[x]][x] ) ) return 1;
for ( int b=n+1 ; b<=n_x ; b++ )
if ( st[b]==b&&S[b]==1&&lab[b]==0 ) expand_blossom(b);
}
return 0;
}
pair<LL,int>weight_blossom()
{
fill(match,match+n+1,0);
n_x = n;
int n_matches = 0;
LL tot_weight = 0;
for ( int u=0 ; u<=n ; u++ ) st[u] = u,flower[u].clear();
int w_max = 0;
for ( int u=1; u<=n ; u++ )
for ( int v=1 ; v<=n ; v++ )
{
flower_from[u][v] = (u==v?u:0);
w_max = Max( w_max , g[u][v].w );
}
for ( int u=1 ; u<=n ; u++ ) lab[u] = w_max;
while ( matching() ) ++n_matches;
for ( int u=1 ; u<=n ; u++ )
if ( match[u]&&match[u]<u )
tot_weight += g[u][match[u]].w;
return make_pair( tot_weight , n_matches );
}
int main()
{
for ( ; scanf ( "%d%d" , &n , &m )==2 ; )
{
for ( int u=1 ; u<=n ; u++ )
for ( int v=1 ; v<=n ; v++ )
g[u][v] = edge{ u , v , 0 };
for ( int i=0 ; i<m ; i++ )
{
int u,v,w; scanf ( "%d%d%d" , &u , &v , &w );
g[u][v].w = g[v][u].w = w;
}
printf ( "%lld\n" , weight_blossom().first );
for ( int i=1 ; i<=n ; i++ ) printf ( "%d " , match[i] );
}
return 0;
}