省选模版复习——费用流

bzoj3876 支线剧情

其实也是2014江苏的题

上下界的费用流很裸吧

其实也可以利用图的特殊性把他转化成普通的费用流


比较一下时间,普通费用流有时还是很明显的

//普通费用流
#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;
const int Maxn=305, Maxm=200005, INF=1e9;
int node[Maxm],next[Maxm],flow[Maxm],cost[Maxm],q[Maxm];
int a[Maxn],g[Maxn][Maxn],way[Maxn],path[Maxn],d[Maxn],de[Maxn];
int n,K,i,j,k,tot,ans,minx,x,y,l,r,N,b,t;
bool v[Maxn];

void add(int x,int y,int z1,int z2){
  node[++tot]=y; next[tot]=a[x]; a[x]=tot; flow[tot]=z1; cost[tot]=z2;
  node[++tot]=x; next[tot]=a[y]; a[y]=tot; flow[tot]=0; cost[tot]=-z2;
}

void floyed(){
  for (k=1;k<=n;k++)
    for (i=1;i<=n;i++)
    if (i!=k && g[i][k]<g[0][0])
      for (j=1;j<=n;j++)
      if (k!=j && i!=j && g[i][j]>g[i][k]+g[k][j])
        g[i][j]=g[i][k]+g[k][j];
}

bool spfa(){
  memset(d,127/2,sizeof(d));
  d[1] = 0; v[1] = 1;
  for (q[l=r=1]=1;l<=r;v[q[l++]]=0)
    for (i=a[q[l]];i;i=next[i])
    if (flow[i]>0 && d[node[i]]>d[q[l]]+cost[i]){
      d[node[i]] = d[q[l]]+cost[i];
      path[node[i]] = q[l]; way[node[i]] = i;
      if (v[node[i]]==0) v[ q[++r]=node[i] ]=1;
    }
  if (d[N]>=d[0]) return 0;
  minx = INF;
  for (i=N;i>1;i=path[i])
    minx = min(minx,flow[way[i]]);
  ans += d[N]*minx;
  for (i=N;i>1;i=path[i])
    flow[way[i]]-=minx, flow[way[i]^1]+=minx;
  return 1;
}

int main(){
  freopen("story.in","r",stdin);
  freopen("story.out","w",stdout);
  scanf("%d",&n);
  memset(g,127/2,sizeof(g));
  for (i=1;i<=n;i++)
    g[i][i]=0;
  for (i=1;i<=n;i++){
  	scanf("%d",&K);
  	while (K--){
  	  scanf("%d%d",&b,&t);
  	  ans += t;
  	  g[i][b] = min(g[i][b],t);
  	  de[i]++; de[b]--;
  	}
  }
  floyed();
  tot = 1; N = n+2;
  for (i=2;i<=n;i++)
  if (de[i]>0) add(i+1,N,de[i],0);
    else add(1,i+1,-de[i],0);
  add(1,2,INF,0);
  for (i=1;i<=n;i++)
    for (j=1;j<=n;j++)
    if (i!=j && g[i][j]<g[0][0])
      add(i+1,j+1,INF,g[i][j]);
  while (spfa());
  printf("%d\n",ans);
  return 0;
}

//上下界费用流
#include <vector>
#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;
#define pb push_back
const int Maxn=305, Maxm=20000, INF=1e9;
int node[Maxm],next[Maxm],flow[Maxm],cost[Maxm],q[Maxm];
int a[Maxn],d[Maxn],path[Maxn],way[Maxn],K[Maxn],de[Maxn];
int n,N,l,r,i,j,tot,sum,fl,cnt,ans,L,R,Mid,minx,x,y;
bool v[Maxn];
vector <int> b[Maxn],t[Maxn];

void add(int x,int y,int z1,int z2){
  node[++tot]=y; next[tot]=a[x]; a[x]=tot; flow[tot]=z1; cost[tot]=z2;
  node[++tot]=x; next[tot]=a[y]; a[y]=tot; flow[tot]=0; cost[tot]=-z2;
}

bool spfa(){
  memset(d,10,sizeof(d));
  d[1] = 0; v[1] = 1;
  for (q[l=r=1]=1;l<=r;v[q[l++]]=0)
    for (i=a[q[l]];i;i=next[i])
    if (flow[i]>0 && d[node[i]]>d[q[l]]+cost[i]){
      d[node[i]] = d[q[l]]+cost[i];
      path[node[i]] = q[l]; way[node[i]] = i;
      if (v[node[i]]==0) v[ q[++r]=node[i] ]=1;
    }
  if (d[N]>=d[0]) return 0;
  minx = INF;
  for (i=N;i>1;i=path[i])
    minx = min(minx,flow[way[i]]);
  cnt += d[N]*minx; fl+=minx;
  for (i=N;i>1;i=path[i])
    flow[way[i]]-=minx, flow[way[i]^1]+=minx;
  return 1;
}

bool Judge(){
  memset(a,0,sizeof(a));
  memset(de,0,sizeof(de));
  de[1]=Mid; de[n+1]=-Mid;
  for (i=1,tot=1;i<=n;i++){
  	for (j=0;j<K[i];j++){
  	  add(i+1,b[i][j]+1,INF,t[i][j]);
  	  de[b[i][j]]++; de[i]--;
    }
	add(i+1,n+2,INF,0);
  }
  N = n+3;
  int SUM = 0;
  for (i=1;i<=n+1;i++)
  if (de[i]>0) SUM+=de[i], add(1,i+1,de[i],0);
    else add(i+1,N,-de[i],0);
  fl = 0; cnt = 0;
  while (spfa());
  if (fl==SUM && cnt<ans) ans=cnt;
  return (fl==SUM);
}

int main(){
  freopen("story.in","r",stdin);
  freopen("story.out","w",stdout);
  scanf("%d",&n);
  for (i=1;i<=n;i++){
  	scanf("%d",&K[i]);
  	for (j=0;j<K[i];j++){
  	  scanf("%d%d",&x,&y);
  	  b[i].pb(x); t[i].pb(y);
  	  sum += t[i][j];
    }
  }
  L = 1; R = 5000; ans=INF;
  while (L<=R){
  	Mid = (L+R)>>1;
  	if (Judge()) R = Mid-1;
  	  else L = Mid+1;
  }
  ans += sum;
  printf("%d\n",ans);
  return 0;
}


你可能感兴趣的:(费用流)