HDU 5772 String problem

最大权闭合子图。建图巧妙。

最大权闭合子图：

#pragma comment(linker, "/STACK:1024000000,1024000000")
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<vector>
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<iostream>
using namespace std;
typedef long long LL;
const double pi=acos(-1.0),eps=1e-8;
void File()
{
    freopen("D:\in.txt","r",stdin);
    freopen("D:\out.txt","w",stdout);
}
inline int read()
{
    char c = getchar();  while(!isdigit(c)) c = getchar();
    int x = 0;
    while(isdigit(c)) { x = x * 10 + c - '0'; c = getchar(); }
    return x;
}

const int maxn = 30000 + 10;
const int INF = 0x7FFFFFFF;
struct Edge
{
    int from, to, cap, flow;
    Edge(int u, int v, int c, int f) :from(u), to(v), cap(c), flow(f) {}
};
vector<Edge>edges;
vector<int>G[maxn];
bool vis[maxn];
int d[maxn];
int cur[maxn];
int n, m, s, t;

void init()
{
    for (int i = 0; i < maxn; i++) G[i].clear();
    edges.clear();
}
void AddEdge(int from, int to, int cap)
{
    edges.push_back(Edge(from, to, cap, 0));
    edges.push_back(Edge(to, from, 0, 0));
    int w = edges.size();
    G[from].push_back(w - 2);
    G[to].push_back(w - 1);
}
bool BFS()
{
    memset(vis, 0, sizeof(vis));
    queue<int>Q;
    Q.push(s);
    d[s] = 0;
    vis[s] = 1;
    while (!Q.empty())
    {
        int x = Q.front();
        Q.pop();
        for (int i = 0; i<G[x].size(); i++)
        {
            Edge e = edges[G[x][i]];
            if (!vis[e.to] && e.cap>e.flow)
            {
                vis[e.to] = 1;
                d[e.to] = d[x] + 1;
                Q.push(e.to);
            }
        }
    }
    return vis[t];
}
int DFS(int x, int a)
{
    if (x == t || a == 0)
        return a;
    int flow = 0, f;
    for (int &i = cur[x]; i<G[x].size(); i++)
    {
        Edge e = edges[G[x][i]];
        if (d[x]+1 == d[e.to]&&(f=DFS(e.to,min(a,e.cap-e.flow)))>0)
        {
            edges[G[x][i]].flow+=f;
            edges[G[x][i] ^ 1].flow-=f;
            flow+=f;
            a-=f;
            if(a==0) break;
        }
    }
    if(!flow) d[x] = -1;
    return flow;
}
int dinic(int s, int t)
{
    int flow = 0;
    while (BFS())
    {
        memset(cur, 0, sizeof(cur));
        flow += DFS(s, INF);
    }
    return flow;
}

const int MAXM=110;
int T,len,a[MAXM],b[MAXM],w[MAXM][MAXM],val[2*MAXM*MAXM],ans;
char str[MAXM];

int main()
{
    scanf("%d",&T); int cas=1;
    while(T--)
    {
        scanf("%d",&len); scanf("%s",str);
        for(int i=0;i<10;i++) scanf("%d%d",&a[i],&b[i]);
        for(int i=0;i<len;i++) for(int j=0;j<len;j++) scanf("%d",&w[i][j]);

        init(); ans=0;
        s=len*len+len+10; val[s]=0;
        t=len*len+len+10+1; val[t]=0;

        for(int i=0;i<len;i++) for(int j=i+1;j<len;j++)
        {
            val[i*len+j]=w[i][j]+w[j][i];
            AddEdge(i*len+j,len*len+i,INF);
            AddEdge(i*len+j,len*len+j,INF);
            if(val[i*len+j]>0) AddEdge(s,i*len+j,val[i*len+j]), ans=ans+val[i*len+j];
            else if(val[i*len+j]<0) AddEdge(i*len+j,t,-val[i*len+j]);
        }
        for(int i=len*len;i<=len*len+len-1;i++)
        {
            val[i]=-a[str[i-len*len]-'0'];
            AddEdge(i,len*len+len+str[i-len*len]-'0',INF);
            if(val[i]>0) AddEdge(s,i,val[i]), ans=ans+val[i];
            else if(val[i]<0) AddEdge(i,t,-val[i]);
        }
        for(int i=len*len+len;i<=len*len+len+10-1;i++)
        {
            val[i]=-b[i-(len*len+len)]+a[i-(len*len+len)];
            if(val[i]>0) AddEdge(s,i,val[i]), ans=ans+val[i];
            else if(val[i]<0) AddEdge(i,t,-val[i]);
        }
        ans=ans-dinic(s,t);
        printf("Case #%d: %d
",cas++,ans);
    }
    return 0;
}