题意：
一些人，和他们可能加入的组号。问每个组，最小的最大人数是多少
分析：
二分的是最大流的容量。设置一个超级源点，连向所有的人，容量为1。设置一个超级汇点，使所有的组连向超级汇点，二分的就是这里的容量（0～n）。然后根据题目给出的人和组的关系连接人和组，容量为1。二分时，若当前状态求出的最大流等于人数，则下界等于mid，若不等于，则上界等于mid。二分出的容量，就是组中的最小的最大人数。
输入：
3 2
John 0 1
Rose 1
Mary 1
5 4
ACM 1 2 3
ICPC 0 1
Asian 0 2 3
Regional 1 2
ShangHai 0 2
0 0
输出：
2
2
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <queue>
#include <vector>
#include <sstream>
using namespace std;
const int maxn=3010;
const int inf=1e9;
int n,m;
structEdge
{
int u,v;
int flow,cap;
Edge(int uu,int cc,int fl,int ca):u(uu),v(cc),flow(fl),cap(ca)
{
}
};
vector<Edge>edge;
structISAP
{
vector<int>G[maxn];
vector<Edge>edge;
int s,t;
int d[maxn];
int cur[maxn];
int p[maxn];
int num[maxn];
int flow;
void init()
{
for(int i=0;i<=n+m+1;i++)
G[i].clear();
s=0;
t=n+m+1;
}
bool bfs()
{
memset(d,-1,sizeof(d));
queue<int>q;
q.push(t);
d[t]=0;
while(!q.empty())
{
int u=q.front();
q.pop();
for(int i=0;i<G[u].size();i++)
{
Edge& e=edge[G[u][i]];
if(e.cap==0&&d[e.v]==-1)
{
d[e.v]=d[u]+1;
q.push(e.v);
}
}
}
return d[s]!=-1;
}
int Augment()
{
int x=t,a=inf;
while(x!=s)
{
Edge& e=edge[p[x]];
a=min(a,e.cap-e.flow);
x=edge[p[x]].u;
}
x=t;
while(x!=s)
{
edge[p[x]].flow+=a;
edge[p[x]^1].flow-=a;
x=edge[p[x]].u;
}
return a;
}
int maxflow(int s,int t)
{
this->s=s;
this->t=t;
flow=0;
bfs();
for(int i=0;i<=n+m+1;i++)
num[d[i]]++;
int x=s;
memset(cur,0,sizeof(cur));
while(d[s]<n+m+2)
{
if(x==t)
{
flow+=Augment();
x=s;
}
bool ok=false;
for(int i=cur[x];i<G[x].size();i++)
{
Edge& e=edge[G[x][i]];
if(e.cap>e.flow&&d[x]==d[e.v]+1)
{
ok=true;
p[e.v]=G[x][i];
cur[x]=i;
x=e.v;
break;
}
}
if(!ok)
{
int k=n+m+1;
for(int i=0;i<G[x].size();i++)
{
Edge& e=edge[G[x][i]];
if(e.cap>e.flow)
k=min(k,d[e.v]);
}
if(--num[d[x]]==0)
break;
num[d[x]=k+1]++;
cur[x]=0;
if(x!=s)
x=edge[p[x]].u;
}
}
return flow;
}
}solver;
char buffer[11000];
void add(int s,int t,int cap)
{
edge.push_back(Edge(s,t,0,cap));
edge.push_back(Edge(t,s,0,0));
int x=edge.size();
solver.G[s].push_back(x-2);
solver.G[t].push_back(x-1);
}
void input()
{
solver.init();
int x;
edge.clear();
char ch[100];
for (int i = 1 ; i <= n ; ++i)
{
add(0,i,1);
scanf("%*s");
gets(buffer);
char * p = strtok(buffer, " ");
while (p) {
sscanf(p,"%d",&x);
add(i,x+1+n,1);
p = strtok(NULL," ");
}
}
int sz=edge.size();
for(int i=n+1;i<=n+m;i++)
{
sz+=2;
solver.G[i].push_back(sz-2);
solver.G[n+m+1].push_back(sz-1);
}
}
void build(int up)
{
solver.edge=edge;
for(int i=n+1;i<=n+m;i++)
{
solver.edge.push_back(Edge(i,n+m+1,0,up));
solver.edge.push_back(Edge(n+m+1,i,0,0));
}
}
void solve()
{
int left=1,right=n;
int mid=(left+right)>>1;
int ans=n;
while(left<=right)
{
build(mid);
if (solver.maxflow(0,n+m+1)==n)
{
right = mid-1;
ans = min(ans,mid);
}
else
{
left = mid+1;
}
mid = (left+right)>>1;
}
printf("%d\n",ans);
}
int main()
{
while(scanf("%d%d",&n,&m)==2,n+m)
{
input();
solve();
}
}
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <queue>
#include <vector>
#include <sstream>
using namespace std;
const int maxn=3010;
const int inf=1e9;
int n,m;
structEdge
{
int u,v;
int flow,cap;
Edge(int uu,int cc,int fl,int ca):u(uu),v(cc),flow(fl),cap(ca)
{
}
};
vector<Edge>edge;
structISAP
{
vector<int>G[maxn];
vector<Edge>edge;
int s,t;
int d[maxn];
int cur[maxn];
int p[maxn];
int num[maxn];
int flow;
void init()
{
for(int i=0;i<=n+m+1;i++)
G[i].clear();
s=0;
t=n+m+1;
}
bool bfs()
{
memset(d,-1,sizeof(d));
queue<int>q;
q.push(t);
d[t]=0;
while(!q.empty())
{
int u=q.front();
q.pop();
for(int i=0;i<G[u].size();i++)
{
Edge& e=edge[G[u][i]];
if(e.cap==0&&d[e.v]==-1)
{
d[e.v]=d[u]+1;
q.push(e.v);
}
}
}
return d[s]!=-1;
}
int Augment()
{
int x=t,a=inf;
while(x!=s)
{
Edge& e=edge[p[x]];
a=min(a,e.cap-e.flow);
x=edge[p[x]].u;
}
x=t;
while(x!=s)
{
edge[p[x]].flow+=a;
edge[p[x]^1].flow-=a;
x=edge[p[x]].u;
}
return a;
}
int maxflow(int s,int t)
{
this->s=s;
this->t=t;
flow=0;
bfs();
for(int i=0;i<=n+m+1;i++)
num[d[i]]++;
int x=s;
memset(cur,0,sizeof(cur));
while(d[s]<n+m+2)
{
if(x==t)
{
flow+=Augment();
x=s;
}
bool ok=false;
for(int i=cur[x];i<G[x].size();i++)
{
Edge& e=edge[G[x][i]];
if(e.cap>e.flow&&d[x]==d[e.v]+1)
{
ok=true;
p[e.v]=G[x][i];
cur[x]=i;
x=e.v;
break;
}
}
if(!ok)
{
int k=n+m+1;
for(int i=0;i<G[x].size();i++)
{
Edge& e=edge[G[x][i]];
if(e.cap>e.flow)
k=min(k,d[e.v]);
}
if(--num[d[x]]==0)
break;
num[d[x]=k+1]++;
cur[x]=0;
if(x!=s)
x=edge[p[x]].u;
}
}
return flow;
}
}solver;
char buffer[11000];
void add(int s,int t,int cap)
{
edge.push_back(Edge(s,t,0,cap));
edge.push_back(Edge(t,s,0,0));
int x=edge.size();
solver.G[s].push_back(x-2);
solver.G[t].push_back(x-1);
}
void input()
{
solver.init();
int x;
edge.clear();
char ch[100];
for (int i = 1 ; i <= n ; ++i)
{
add(0,i,1);
scanf("%*s");
gets(buffer);
char * p = strtok(buffer, " ");
while (p) {
sscanf(p,"%d",&x);
add(i,x+1+n,1);
p = strtok(NULL," ");
}
}
int sz=edge.size();
for(int i=n+1;i<=n+m;i++)
{
sz+=2;
solver.G[i].push_back(sz-2);
solver.G[n+m+1].push_back(sz-1);
}
}
void build(int up)
{
solver.edge=edge;
for(int i=n+1;i<=n+m;i++)
{
solver.edge.push_back(Edge(i,n+m+1,0,up));
solver.edge.push_back(Edge(n+m+1,i,0,0));
}
}
void solve()
{
int left=1,right=n;
int mid=(left+right)>>1;
int ans=n;
while(left<=right)
{
build(mid);
if (solver.maxflow(0,n+m+1)==n)
{
right = mid-1;
ans = min(ans,mid);
}
else
{
left = mid+1;
}
mid = (left+right)>>1;
}
printf("%d\n",ans);
}
int main()
{
while(scanf("%d%d",&n,&m)==2,n+m)
{
input();
solve();
}
}
UVA 1345 Jamie's Contact Groups
时间： 2024-09-29 22:09:18