[COGS 740]分配问题
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很明显是二分图最大权匹配。可以用匈牙利算法求解,但我比较弱……所以就写了个费用流。
注意最优解和最差解都要给出!
代码:
#include <cstdio>
#include <cstring>
#include <vector>
#include <queue>
#include <algorithm>
using namespace std;
const int maxn=205;
namespace MCMF{
struct Edge{
int u,v,cap,flow,cost;
};
vector<Edge> edges;
vector<int> G[maxn];
int m;
inline void AddEdge(int u,int v,int cap,int cost){
edges.push_back((Edge){u,v,cap,0,cost});
edges.push_back((Edge){v,u,0,0,-cost});
m=edges.size();
G[u].push_back(m-2);
G[v].push_back(m-1);
}
inline void ClearGraph(){
register int i;
edges.clear();
for(i=0;i<maxn;i++)
G[i].clear();
}
int a[maxn];
bool inQueue[maxn];
int d[maxn],p[maxn];
bool BellmanFord(int s,int t,long long& cost){
register int i,u;
queue<int> Q;
memset(d,0x7f,sizeof(d));
memset(inQueue,0,sizeof(inQueue));
d[s]=0;
inQueue[s]=true;
p[s]=0;
a[s]=0x7f7f7f7f;
Q.push(s);
while(!Q.empty()){
u=Q.front();
Q.pop();
inQueue[u]=false;
for(i=0;i<G[u].size();i++){
Edge& e=edges[G[u][i]];
if(e.cap>e.flow && d[e.v]>d[u]+e.cost){
d[e.v]=d[u]+e.cost;
p[e.v]=G[u][i];
a[e.v]=min(a[u],e.cap-e.flow);
if(!inQueue[e.v]){
Q.push(e.v);
inQueue[e.v]=true;
}
}
}
}
if(d[t]==0x7f7f7f7f)
return false;
cost+=((long long)d[t])*((long long)a[t]);
for(u=t;u!=s;u=edges[p[u]].u){
edges[p[u]].flow+=a[t];
edges[p[u]^1].flow-=a[t];
}
return true;
}
long long MincostMaxflow(int s,int t){
register long long ans=0;
while(BellmanFord(s,t,ans));
return ans;
}
};
int A[105][105];
int main(){
int n;
register int i,j;
freopen("job.in","r",stdin);
freopen("job.out","w+",stdout);
scanf("%d",&n);
for(i=1;i<=n;i++)
for(j=1;j<=n;j++){
scanf("%d",&A[i][j]);
MCMF::AddEdge(i,j+n,1,A[i][j]);
}
for(i=1;i<=n;i++)
MCMF::AddEdge(0,i,1,0);
for(i=n+1;i<=2*n;i++)
MCMF::AddEdge(i,2*n+1,1,0);
printf("%lld\n",MCMF::MincostMaxflow(0,2*n+1));
MCMF::ClearGraph();
for(i=1;i<=n;i++)
for(j=1;j<=n;j++){
MCMF::AddEdge(i,j+n,1,-A[i][j]);
}
for(i=1;i<=n;i++)
MCMF::AddEdge(0,i,1,0);
for(i=n+1;i<=2*n;i++)
MCMF::AddEdge(i,2*n+1,1,0);
printf("%lld\n",-(MCMF::MincostMaxflow(0,2*n+1)));
return 0;
}
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