省选模版复习——费用流

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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_backconst 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;}

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