二分图匹配模板

虽然说这玩意似乎没什么好写的.....

但是不经常用....时不时就忘了....还是记一些东西吧...

首先是Hungary算法.....邻接矩阵实现.....

bool M[205][205];bool used[205];int mat[205];bool DFS(int x){for(int i=0;i<m;i++)if(M[x][i] && !used[i]){used[i]=true;if( mat[i]==-1 || DFS(mat[i]) ){mat[i]=x;return true;}}return false;}.....int res=0;memset(mat,0xFF,sizeof(mat));for(int i=0;i<n;i++){memset(used,0,sizeof(used));res+=DFS(i);}.....

M是边表,存储集合A到集合B的有向边.

使用used来使得对于每次搜索,集合B只访问一次.

mat[i]表示集合B中元素i,在A中对应的元素是哪个.

要点:

1.注意对应关系.我们只存储从集合A到集合B的边.used的tag打在集合B的元素上.

2.千万别忘了初始化....

3.由于算法复杂度比较高,所以一般不会吝啬地用链表邻接表.如果可匹配得边数比较少而点数比较多,就用链表邻接表.

下面是邻接表写的Hungary.没什么区别...

struct edge{int in;edge*nxt;}pool[50000];edge*et=pool;edge*eds[205];void addedge(int i,int j){ et->in=j; et->nxt=eds[i]; eds[i]=et++; }#define FOREACH_EDGE(i,j) for(edge*i=eds[j];i;i=i->nxt)bool used[205];int mat[205];bool DFS(int x){FOREACH_EDGE(i,x)if(!used[i->in]){used[i->in]=true;if( mat[i->in]==-1 || DFS(mat[i->in]) ){mat[i->in]=x;return true;}}return false;}..........int res=0;memset(mat,0xFF,sizeof(mat));for(int i=0;i<n;i++){memset(used,0,sizeof(used));res+=DFS(i);}........

如果是带权匹配的话.....

果断网络流!

不就是120行嘛!

顺便贴了新的文件头.....

#include <cstdio>#include <fstream>#include <iostream>#include <cstdlib>#include <cstring>#include <algorithm>#include <cmath>#include <queue>#include <vector>#include <map>#include <set>#include <stack>#include <list>typedef unsigned int uint;typedef long long int ll;typedef unsigned long long int ull;typedef double db;#define DBG printf("*")using namespace std;int getint(){int res=0;char c=getchar();bool mi=false;while( (c<'0' || c>'9') && !feof(stdin) ) mi=(c=='-'),c=getchar();while( ('0'<=c && c<='9') && !feof(stdin) ) res=res*10+c-'0',c=getchar();return mi ? -res : res;}ll getll(){ll res=0;char c=getchar();bool mi=false;while( (c<'0' || c>'9') && !feof(stdin) ) mi=(c=='-'),c=getchar();while( ('0'<=c && c<='9') && !feof(stdin) ) res=res*10+c-'0',c=getchar();return mi ? -res : res;}void fillarray(int*k,int v,int size){ for(int i=0;i<size;i++) k[i]=v; }void fillarray(ll*k,ll v,int size){ for(int i=0;i<size;i++) k[i]=v; }void fillarray(char*k,char v,int size){ for(int i=0;i<size;i++) k[i]=v; }void fillarray(db*k,db v,int size){ for(int i=0;i<size;i++) k[i]=v; }//==============================================================================//==============================================================================//==============================================================================//==============================================================================db INF=1e20;db eps=1e-11;bool fequal(db a,db b){ return fabs(a-b)<eps; }//maxflowstruct edge{int in;int c;db v;edge*nxt;edge*ptr;}pool[100000];edge*et=pool;edge*eds[1000];void addedge(int i,int j,int c,db v){et->ptr=et+1;et->in=j; et->c=c; et->v=v; et->nxt=eds[i]; eds[i]=et++;et->ptr=et-1;et->in=i; et->c=0; et->v=-v; et->nxt=eds[j]; eds[j]=et++;}#define FOREACH_EDGE(i,j) for(edge*i=eds[j];i;i=i->nxt)int n;int st,ed;db cost;db dist[1000];bool used[1000];int DFS(int x,int mi){if(x==ed) return mi;used[x]=true;int res=0; int c;FOREACH_EDGE(i,x)if(i->c>0 && !used[i->in] && fequal(dist[x]+i->v,dist[i->in]) && ( c=DFS(i->in,min(i->c,mi)) )){res+=c;i->c-=c;i->ptr->c+=c;mi-=c;cost+=db(c)*i->v;if(mi==0) break; }used[x]=false;if(res==0) dist[x]=INF;return res;}int qh,qt;int q[4000000];db DINIC(){db res=0.0;while(true){fillarray(dist,INF,n);qh=qt=0;q[qt++]=st;dist[st]=0;while(qh!=qt){int&cur=q[qh];FOREACH_EDGE(i,cur)if( i->c>0 && dist[i->in] > dist[cur] + i->v ){dist[i->in]=dist[cur]+i->v;q[qt++]=i->in;}qh++;}if(dist[ed]>=INF) break;cost=0;if(0==DFS(st,(1<<28)-1)) break;res+=cost;}return res;}//=================================================int ptot;int mx[1050];int my[1050];int ex[1050];int ey[1050];db dst(int i,int j){ return sqrt(db(mx[i]-ex[j])*db(mx[i]-ex[j])+db(my[i]-ey[j])*db(my[i]-ey[j])); }//blocks define#define MISSILE(i) (i)#define ENEMY(i) ((i)+ptot)int main(){ptot=getint();for(int i=0;i<ptot;i++)mx[i]=getint(),my[i]=getint();for(int i=0;i<ptot;i++)ex[i]=getint(),ey[i]=getint();st=ptot*2;ed=st+1;n=ed+1;for(int i=0;i<ptot;i++)for(int j=0;j<ptot;j++)addedge(MISSILE(i),ENEMY(j),1,dst(i,j));for(int i=0;i<ptot;i++)addedge(st,MISSILE(i),1,0.0);for(int i=0;i<ptot;i++)addedge(ENEMY(i),ed,1,0.0);printf("%.3lf\n",DINIC());return 0;}