最优匹配(Kuhn_Munkras算法)

最优匹配(Kuhn_Munkras算法)
// ** Start of PerfectMatch *******************************
// Name: PerfectMatch by Kuhn_Munkras O(n^3)
// Description: w is the adjacency matrix, nx,ny are the size of x and y, // lx, ly are the lables of x and y, fx[i], fy[i] is used for marking
// whether the i-th node is visited, matx[x] means x match matx[x],
// maty[y] means y match maty[y], actually, matx[x] is useless,
// all the arrays are start at 1
int nx,ny,w[MAXN][MAXN],lx[MAXN],ly[MAXN];
int fx[MAXN],fy[MAXN],matx[MAXN],maty[MAXN];
int path(int u)
{
int v;
fx[u]=1;
for(v=1;v<=ny;v++)
if((lx[u]+ly[v]==w[u][v])&&(fy[v]<0)) {
fy[v]=1;
if((maty[v]<0)||(path(maty[v]))) {
matx[u]=v;
maty[v]=u;
return(1);
} // end of if((maty[v]...
} // end of if((lx[u]...
return(0);
} // end of int path()
int PerfectMatch()
{
int ret=0,i,j,k,p;
memset(ly,0,sizeof(ly));
for(i=1;i<=nx;i++) {
lx[i]=-INF;
for(j=1;j<=ny;j++)
if(w[i][j]>lx[i])
lx[i]=w[i][j];
} // end of for(i...
memset(matx,-1,sizeof(matx));
memset(maty,-1,sizeof(maty));
for(i=1;i<=nx;i++) {
memset(fx,-1,sizeof(fx));
memset(fy,-1,sizeof(fy));
if(!path(i)) {
i--;
p=INF;
for(k=1;k<=nx;k++)
if(fx[k]>0)
for(j=1;j<=ny;j++)
if((fy[j]<0)&&(lx[k]+ly[j]-w[k][j]<p))
p=lx[k]+ly[j]-w[k][j];
for(j=1;j<=ny;j++) ly[j]+=(fy[j]<0?0:p);
for(k=1;k<=nx;k++) lx[k]-=(fx[k]<0?0:p);
} // end of if(!path(i))
} // end of for(i...
for(i=1;i<=ny;i++) ret+=w[maty[i]][i];
return ret;
} // end of int PerfectMatch()
// ** End of PerfectMatch *********************************。