匈牙利算法与KM算法

匈牙利算法

var
  i,j,k,l,n,m,mm,ans:longint;
  a:array[0..501,0..501]of longint;
  p,f:array[0..501]of longint;
function xyl(x,y:longint):boolean;
var i,j,k,l:longint;
begin
  if f[x]=y then exit(false);
  f[x]:=y;
  for i:=1 to m do
  if(a[x,i]=1)and((p[i]=0)or(xyl(p[i],y)))then
  begin p[i]:=x; exit(true); end;
  exit(false);
end;
begin
  readln(n,m,mm);
  for i:=1 to mm do
  begin
    readln(j,k);
    a[j,k]:=1;
  end;
  for i:=1 to n do if xyl(i,i) then inc(ans);
  writeln(ans);
end.

#include<bits/stdc++.h>
using namespace std;
int a[502][502],p[502],f[502],n,m,mm,j,k,ans;
bool xyl(int x,int y)
{
    if(f[x]==y)return 0; f[x]=y;
    for(int i=1;i<=m;i++)if((a[x][i]==1)and((p[i]==0)or(xyl(p[i],y)))){p[i]=x; return 1;}
    return 0;
}
int main()
{
    scanf("%d%d%d",&n,&m,&mm);
    for(int i=1;i<=mm;i++){scanf("%d%d",&j,&k); a[j][k]=1;}
    for(int i=1;i<=n;i++)if(xyl(i,i))ans++;
    printf("%d",ans);
}

KM算法

uses math;
var
  ii,i,j,k,l,n,m,v,mm,down:longint;
  a:array[0..501,0..501]of longint;
  p,v1,v2,d1,d2,s:array[0..501]of longint;
  ans:int64;
function km(x:longint):boolean;
var i,j,k,l:longint;
begin
  v1[x]:=1;
  for i:=1 to m do
  if(v2[i]=0)and(d1[x]+d2[i]=a[x,i])then
  begin
    v2[i]:=1;
    if(p[i]=0)or(km(p[i]))then
    begin p[i]:=x; exit(true); end;
  end else
  begin
    if v2[i]=0 then s[i]:=min(s[i],d2[i]+d1[x]-a[x,i]);
  end;
  exit(false);
end;
begin
  readln(n,m,mm);
  for i:=1 to mm do
  begin
    readln(j,k,l);
    a[j,k]:=max(a[j,k],l);
    d1[j]:=max(d1[j],a[j,k]);
  end;
  if m<n then m:=n;
  for ii:=1 to n do
  begin
    while true do
    begin
      for i:=1 to n do v1[i]:=0;
      for i:=1 to m do begin v2[i]:=0; s[i]:=maxlongint; end;
      if km(ii) then break;
      down:=maxlongint;
      for i:=1 to m do if v2[i]=0 then down:=min(s[i],down);
      for i:=1 to n do if v1[i]=1 then d1[i]:=d1[i]-down;
      for i:=1 to m do if v2[i]=1 then d2[i]:=d2[i]+down;
    end;
  end;
  for i:=1 to n do ans:=ans+d1[i];
  for i:=1 to m do if p[i]>0 then ans:=ans+d2[i];
  writeln(ans);
end.

#include<bits/stdc++.h>
using namespace std;
int lb[505][3],f[505],f2[505],p[505];
int n,l,r,x,bo[505],bo2[505],n1,p1[505],m;
long long ans,a[505][505],d[505],d2[505];
void workback(int x)
{
    while(x>1){ int y=lb[x][0]; x=lb[x][2]; p[y]=lb[x][1]; }
}
int main()
{
    scanf("%d%d%d",&n1,&n,&m); n=max(n,n1);
    for(int i=1;i<=m;i++)
    {
        int j,k,l; scanf("%d%d%d",&j,&k,&l);
        a[j][k]=l; d[j]=max(d[j],a[j][k]);
    }
    for(int ii=1;ii<=n;ii++)
    {
        for(int i=1;i<=n;i++)f[i]=f2[i]=0;
        l=0; r=1; lb[r][1]=ii;
        while(r>0)
        {
            int flag=-1;
            while(l<r)
            {
                l++; x=lb[l][1]; bo[x]=ii;
                for(int i=1;i<=n;i++)if(bo2[i]<ii)
                {
                    if(d[x]+d2[i]-a[x][i]==0)
                    {
                        bo2[i]=ii;
                        if(p[i]==0){ p[i]=x; flag=l; break; }
                        r++; lb[r][0]=i; lb[r][1]=p[i]; lb[r][2]=l;
                    }else 
                    if((f[i]==0)or(d[x]+d2[i]-a[x][i]<d[f[i]]+d2[i]-a[f[i]][i])){ f[i]=x; f2[i]=l; }
                }
                if(flag!=-1)break;
            }
            if(flag!=-1){ workback(flag); break; }
            long long dd=1000000000000000ll;
            for(int i=1;i<=n;i++)if(bo2[i]<ii)dd=min(dd,d[f[i]]+d2[i]-a[f[i]][i]);
            for(int i=1;i<=n;i++)if(bo[i]==ii)d[i]-=dd;
            for(int i=1;i<=n;i++)if(bo2[i]==ii)d2[i]+=dd;
            for(int i=1;i<=n;i++)if((bo2[i]<ii)and(d[f[i]]+d2[i]-a[f[i]][i]==0))
            {
                bo2[i]=ii; if(p[i]==0){ p[i]=f[i]; flag=f2[i]; break; }
                r++; lb[r][0]=i; lb[r][1]=p[i]; lb[r][2]=f2[i];
            }
            if(flag!=-1){ workback(flag); break; }    
        }
    }
    for(int i=1;i<=n;i++)ans+=d[i]+d2[i];
    printf("%lld
",ans);
    for(int i=1;i<=n;i++)p1[p[i]]=i;
    for(int i=1;i<=n1;i++)if(a[i][p1[i]]>0)printf("%d ",p1[i]);else printf("0 ");
    printf("
");
}