Redraw Beautiful Drawings

2 2 4
4 2
4 2  
4 2 2
2 2 5 0
5 4
1 4 3
9
1 2 3 3

Not Unique
Impossible
Unique
1 2 3 3

已知一个矩阵，n行m列。已知每一行，每一列的和，推断是否存在这种矩阵，而且推断是否唯一。

非常裸的最大流模型，前面的部分非常水，关键是，最大流判环部分有点纠结。

代码：

/* ***********************************************
Author :rabbit
Created Time :2014/8/4 18:18:37
File Name :11.cpp
************************************************ */
#pragma comment(linker, "/STACK:102400000,102400000")
#include <stdio.h>
#include <iostream>
#include <algorithm>
#include <sstream>
#include <stdlib.h>
#include <string.h>
#include <limits.h>
#include <string>
#include <time.h>
#include <math.h>
#include <queue>
#include <stack>
#include <set>
#include <map>
using namespace std;
#define INF 0x3f3f3f3f
#define eps 1e-8
#define pi acos(-1.0)
typedef long long ll;
const int maxn=20100;
const int maxm=1002000;
struct Edge{
	int next,to,cap;
	Edge(){};
	Edge(int _next,int _to,int _cap){
		next=_next;to=_to;cap=_cap;
	}
}edge[maxm];
int head[maxn],tol,dep[maxn],gap[maxn];
void addedge(int u,int v,int flow){
    edge[tol]=Edge(head[u],v,flow);head[u]=tol++;
    edge[tol]=Edge(head[v],u,0);head[v]=tol++;
}
void bfs(int start,int end){
    memset(dep,-1,sizeof(dep));
    memset(gap,0,sizeof(gap));
    gap[0]++;int front=0,rear=0,Q[maxn];
    dep[end]=0;Q[rear++]=end;
    while(front!=rear){
        int u=Q[front++];
        for(int i=head[u];i!=-1;i=edge[i].next){
            int v=edge[i].to;if(dep[v]==-1)
                Q[rear++]=v,dep[v]=dep[u]+1,gap[dep[v]]++;
        }
    }
}
int cur[maxn],S[maxn];
int sap(int s,int t,int N){
	int res=0;bfs(s,t);
	int top=0,u=s,i;
	memcpy(cur,head,sizeof(head));
	while(dep[s]<N){
		if(u==t){
			int temp=INF,id;
		    for( i=0;i<top;i++)
			   if(temp>edge[S[i]].cap)
				   temp=edge[S[i]].cap,id=i;
		    for( i=0;i<top;i++)
			      edge[S[i]].cap-=temp,edge[S[i]^1].cap+=temp;
		    res+=temp;top=id;u=edge[S[top]^1].to;
		}
		if(u!=t&&gap[dep[u]-1]==0)break;
		for( i=cur[u];i!=-1;i=edge[i].next)
			if(edge[i].cap&&dep[u]==dep[edge[i].to]+1)break;
		if(i!=-1)cur[u]=i,S[top++]=i,u=edge[i].to;
		else{
			int MIN=N;
			for( i=head[u];i!=-1;i=edge[i].next)
				if(edge[i].cap&&MIN>dep[edge[i].to])
					MIN=dep[edge[i].to],cur[u]=i;
			--gap[dep[u]];++gap[dep[u]=MIN+1];
			if(u!=s)u=edge[S[--top]^1].to;
		}
	}
	return res;
}
int hang[500],lie[500];
int flow[500][500],vis[maxn],m,n,k;
bool dfs(int u,int fa){
	if(vis[u])return 1;
	vis[u]=1;
	for(int i=head[u];i!=-1;i=edge[i].next){
		int v=edge[i].to;
		if(v==fa||v==0||v==n+m+1||edge[i].cap==0)continue;
		if(dfs(v,u))return 1;
	}
	vis[u]=0;
	return 0;
}
int main()
{
     freopen("1002.in","r",stdin);
     freopen("data.out","w",stdout);
	 while(~scanf("%d%d%d",&n,&m,&k)){
		 memset(head,-1,sizeof(head));tol=0;
		 int L=0,R=0;
		 for(int i=1;i<=n;i++)scanf("%d",&hang[i]),L+=hang[i];
		 for(int i=1;i<=m;i++)scanf("%d",&lie[i]),R+=lie[i];
		 if(L!=R){
			 puts("Impossible");continue;
		 }
		 for(int i=1;i<=n;i++)
			 addedge(0,i,hang[i]);
		 for(int i=1;i<=m;i++)
			 addedge(i+n,n+m+1,lie[i]);
		 for(int i=1;i<=n;i++)
			 for(int j=n+1;j<=n+m;j++)
				 addedge(i,j,k);
		 int ans=sap(0,n+m+1,m+n+100);
		 if(ans!=L){
			 puts("Impossible");continue;
		 }
		 int flag=0;
		 memset(vis,0,sizeof(vis));
		 for(int i=1;i<=n;i++)
			 if(dfs(i,-1)){
				 flag=1;break;
			 }
		 if(flag)puts("Not Unique");
		 else {
			 puts("Unique");
			 for(int i=1;i<=n;i++)
				 for(int j=head[i];j!=-1;j=edge[j].next){
					 int v=edge[j].to;
					 if(v>n&&v<=n+m)
						 flow[i][v-n]=k-edge[j].cap;
				 }
			 for(int i=1;i<=n;i++){
				 printf("%d",flow[i][1]);
				 for(int j=2;j<=m;j++)
					 printf(" %d",flow[i][j]);
				 puts("");
			 }
		 }
	 }
     return 0;
}