HDU 4888 Redraw Beautiful Drawings

网络流。

$s$向每一个$r[i]$连边，容量为$r[i]$。

每一个$r[i]$向每一个$c[j]$连边，容量为$k$。

每一个$c[j]$向$t$连边容量为$c[j]$。

跑最大流，中间每一条边上的容量就是那一个格子所填的数字。

唯一性判定：如果残留网络上有环，那么不唯一。

#include<map>
#include<set>
#include<ctime>
#include<cmath>
#include<queue>
#include<string>
#include<vector>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<functional>
using namespace std;
#define ms(x,y) memset(x,y,sizeof(x))
#define rep(i,j,k) for(int i=j;i<=k;i++)
#define per(i,j,k) for(int i=j;i>=k;i--)
#define loop(i,j,k) for (int i=j;i!=-1;i=k[i])
#define inone(x) scanf("%d",&x)
#define intwo(x,y) scanf("%d%d",&x,&y)
#define inthr(x,y,z) scanf("%d%d%d",&x,&y,&z)
#define infou(x,y,z,p) scanf("%d%d%d%d",&x,&y,&z,&p)
#define lson x<<1,l,mid
#define rson x<<1|1,mid+1,r
#define mp(i,j) make_pair(i,j)
#define ft first
#define sd second
typedef long long LL;
typedef pair<int, int> pii;
const int low(int x) { return x&-x; }
const int INF = 0x7FFFFFFF;
const int mod = 1e9 + 7;
const int N = 4e5 + 10;
const double eps = 1e-10;

int n,m,k;

const int maxn = 1000 + 10;
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],GG[maxn];
bool vis[maxn];
int d[maxn];
int cur[maxn],q[maxn];
int s, t,FF,sz;

void init()
{
    for (int i = 0; i < maxn; i++) G[i].clear();
    for (int i = 0; i < maxn; i++) GG[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;
}

void D(int x,int y)
{
    for(int i=0;i<GG[x].size();i++)
    {
        if(GG[x][i]==y) continue;
        if(q[GG[x][i]]) { FF=1; return; }
        q[GG[x][i]]=1;
        D(GG[x][i],x); if(FF ) return ;
        q[GG[x][i]]=0;
    }
}

int main()
{
    while(~scanf("%d%d%d",&n,&m,&k))
    {
        init();
        s=0, t=n+m+1;
        for(int i=1;i<=n;i++)
        {
            int x; scanf("%d",&x);
            AddEdge(s,i,x);
        }
        for(int i=1;i<=m;i++)
        {
            int x; scanf("%d",&x);
            AddEdge(n+i,t,x);
        }

        for(int i=1;i<=n;i++)
            for(int j=1;j<=m;j++)
                AddEdge(i,n+j,k);

        dinic(s,t);

        bool fail=0;
        for(int i=0;i<edges.size();i=i+2)
        {
            if(edges[i].from==s && edges[i].flow<edges[i].cap) fail=1;
            if(edges[i].to==t && edges[i].flow<edges[i].cap) fail=1;
        }

        if(fail) printf("Impossible\n");
        else
        {
            FF=0; memset(vis,0,sizeof vis);

            for(int i=0;i<edges.size();i=i+1)
            {
                if(edges[i].flow<edges[i].cap)
                {
                    if(edges[i].from==s||edges[i].from==t) continue;
                    if(edges[i].to==s||edges[i].to==t) continue;

                    GG[edges[i].to].push_back(edges[i].from);
                }
            }

            for(int i=1 ;i<=n ;i++)
            {
                memset(q,0,sizeof q);
                q[i]=1; D(i,-1);
                if(FF) break;
            }

            if(FF==1)
            {
                printf("Not Unique\n");
                continue;
            }

            printf("Unique\n");
            int now=1;
            for(int i=0;i<edges.size();i=i+2)
            {
                if(edges[i].from==s) continue;
                if(edges[i].to==t) continue;
                printf("%d",edges[i].flow);
                if(now%m==0) printf("\n");
                else printf(" ");
                now++;
            }
        }
    }

    return 0;
}