POJ2396 Budget 上下界网络流

表示弱看了半天才能勉强看懂啊。。

为什么有上下界会流量不守恒，可以看这篇文章，里面有证明。

嗯。如果理解了原理的话，这题应该算是一个入门题了吧。

要注意的地方就是，因为给的条件有大于和小于，所以更新low和up的时候用cap-1，cap+1，而不是cap。。调了好久才发现的。。

#include <cstring>
#include <iostream>
#include <algorithm>
#include <cstdio>
#include <queue>

using namespace std;
const int MAXN = 1000;
const int MAXM = 2e6;
const int INF = 0x3f3f3f3f;
struct Edge
{
    int to,cap,flow,nex;
}edge[MAXM];

int n,m,tol,head[MAXN],dis[MAXN],low[MAXN][MAXN],up[MAXN][MAXN],cnt[MAXN],s,t,ss,tt,ans[MAXN][MAXN];

void addedge(int u,int v,int cap)
{
    edge[tol]={v,cap,0,head[u]}; head[u]=tol++;
    edge[tol]={u,0,0,head[v]}; head[v]=tol++;
}

void init()
{
    memset(head,-1,sizeof head);
    memset(low,0,sizeof low);
    memset(up,0x3f,sizeof up);
    memset(cnt,0,sizeof cnt);
    memset(ans,0,sizeof ans);
}

bool bfs(int s,int t)
{
    queue<int> que;
    memset(dis,-1,sizeof dis);
    dis[s]=0;
    que.push(s);
    while (!que.empty())
    {
        int u=que.front();que.pop();
        for (int i=head[u];~i;i=edge[i].nex)
        {
            int v=edge[i].to;
            if (dis[v]==-1 && edge[i].cap-edge[i].flow)
            {
                dis[v]=dis[u]+1;
                if (v==t) return true;
                que.push(v);
            }
        }
    }
    return false;
}

int dfs(int u,int t,int cap)
{
    if (u==t) return cap;
    int flow=0,f;
    for (int i=head[u];~i;i=edge[i].nex)
    {
        int v=edge[i].to;
        if (dis[v]==dis[u]+1 && edge[i].cap-edge[i].flow)
        {
            f=dfs(v,t,min(cap-flow,edge[i].cap-edge[i].flow));
            edge[i].flow += f;
            edge[i^1].flow -=f;
            flow += f;
            if (cap == flow) break;
        }
    }
    if (!flow) dis[u]=-1;
    return flow;
}

int dicnic(int s,int t)
{
    int flow=0,f;
    while (bfs(s,t))
        while ((f=dfs(s,t,INF))>0)
            flow += f;
    return flow;
}

bool paint(int a,int b,char c,int d)
{
    int fr,tr,fc,tc;
    if (b==0) fc=1,tc=m;
    else fc=tc=b;
    if (a==0) fr=1,tr=n;
    else fr=tr=a;
    for (int i=fr;i<=tr;i++)
        for (int j=fc;j<=tc;j++)
        {
            if (c == '>')
                low[i][j]=max(low[i][j],d+1);
            else if (c == '<')
                up[i][j]=min(up[i][j],d-1);
            else
            {
                if (low[i][j] > d || up[i][j] < d)
                    return false;
                low[i][j] = up[i][j] = d;
            }
            if (low[i][j]>up[i][j]) return false;
        }
    return true;
}

bool read()
{
    scanf("%d%d",&n,&m);
    s=n+m+1,t=n+m+2,ss=n+m+3,tt=n+m+4;
    for (int i=1;i<=n;i++)
    {
        int cap;
        scanf("%d",&cap);
        low[s][i] = up[s][i] = cap;
    }
    for (int i=1;i<=m;i++)
    {
        int cap;
        scanf("%d",&cap);
        low[i][t] = up[i][t] = cap;
    }
    int k;
    scanf("%d",&k);
    bool flag=true;
    while (k--)
    {
        int a,b,d;char c;
        scanf("%d %d %c %d",&a,&b,&c,&d);
        if (!paint(a,b,c,d)) flag=false;
    }
    return flag;
}

bool solve()
{
    int sum=0;
    for (int i=1;i<=n;i++)
    {
        addedge(s,i,0);
        cnt[s] -= low[s][i];
        cnt[i] += low[s][i];
    }
    for (int i=1;i<=m;i++)
    {
        addedge(i+n,t,0);
        cnt[i+n] -= low[i][t];
        cnt[t] += low[i][t];
    }
    for (int i=1;i<=n;i++)
        for (int j=1;j<=m;j++)
        {
            addedge(i,j+n,up[i][j] - low[i][j]);
            cnt[i] -= low[i][j];
            cnt[j+n] += low[i][j];
        }

    for (int i=1;i<=t;i++)
    {
        if (cnt[i]>0) addedge(ss,i,cnt[i]),sum+=cnt[i];
        else addedge(i,tt,-cnt[i]);
    }
    addedge(t,s,INF);
    if (dicnic(ss,tt) != sum) return false;
    for (int i=1;i<=n;i++)
    {
        for (int j=head[i];~j;j=edge[j].nex)
        {
            int v=edge[j].to;
            if (v>=n+1 && v<=n+m)
                ans[i][v-n] += edge[j].flow + low[i][v-n];
        }
    }
    return true;
}

int main()
{
//    freopen("in.txt","r",stdin);
//    freopen("out.txt","w",stdout);
    int t;
    cin>>t;
    while (t--)
    {
        init();
        if (!read())
        {
            printf("IMPOSSIBLE\n");
            if (t) printf("\n");
            continue;
        }
        if (!solve())
        {
            printf("IMPOSSIBLE\n");
            if (t) printf("\n");
            continue;
        }
        else
        {
            for (int i=1;i<=n;i++)
            {
                printf("%d",ans[i][1]);
                for (int j=2;j<=m;j++) printf(" %d",ans[i][j]);
                printf("\n");
            }
        }
        if (t) printf("\n");
    }
    return 0;
}