POJ2396 Budget（有源汇流量有上下界网络的可行流）

  1 #include<cstdio>
  2 #include<cstring>
  3 #include<queue>
  4 #include<algorithm>
  5 using namespace std;
  6 #define INF (1<<30)
  7 #define MAXN 444
  8 #define MAXM 444*888
  9 
 10 struct Edge{
 11     int v,cap,flow,next;
 12 }edge[MAXM];
 13 int vs,vt,NE,NV;
 14 int head[MAXN];
 15 
 16 void addEdge(int u,int v,int cap){
 17     edge[NE].v=v; edge[NE].cap=cap; edge[NE].flow=0;
 18     edge[NE].next=head[u]; head[u]=NE++;
 19     edge[NE].v=u; edge[NE].cap=0; edge[NE].flow=0;
 20     edge[NE].next=head[v]; head[v]=NE++;
 21 }
 22 
 23 int level[MAXN];
 24 int gap[MAXN];
 25 void bfs(){
 26     memset(level,-1,sizeof(level));
 27     memset(gap,0,sizeof(gap));
 28     level[vt]=0;
 29     gap[level[vt]]++;
 30     queue<int> que;
 31     que.push(vt);
 32     while(!que.empty()){
 33         int u=que.front(); que.pop();
 34         for(int i=head[u]; i!=-1; i=edge[i].next){
 35             int v=edge[i].v;
 36             if(level[v]!=-1) continue;
 37             level[v]=level[u]+1;
 38             gap[level[v]]++;
 39             que.push(v);
 40         }
 41     }
 42 }
 43 
 44 int pre[MAXN];
 45 int cur[MAXN];
 46 int ISAP(){
 47     bfs();
 48     memset(pre,-1,sizeof(pre));
 49     memcpy(cur,head,sizeof(head));
 50     int u=pre[vs]=vs,flow=0,aug=INF;
 51     gap[0]=NV;
 52     while(level[vs]<NV){
 53         bool flag=false;
 54         for(int &i=cur[u]; i!=-1; i=edge[i].next){
 55             int v=edge[i].v;
 56             if(edge[i].cap!=edge[i].flow && level[u]==level[v]+1){
 57                 flag=true;
 58                 pre[v]=u;
 59                 u=v;
 60                 //aug=(aug==-1?edge[i].cap:min(aug,edge[i].cap));
 61                 aug=min(aug,edge[i].cap-edge[i].flow);
 62                 if(v==vt){
 63                     flow+=aug;
 64                     for(u=pre[v]; v!=vs; v=u,u=pre[u]){
 65                         edge[cur[u]].flow+=aug;
 66                         edge[cur[u]^1].flow-=aug;
 67                     }
 68                     //aug=-1;
 69                     aug=INF;
 70                 }
 71                 break;
 72             }
 73         }
 74         if(flag) continue;
 75         int minlevel=NV;
 76         for(int i=head[u]; i!=-1; i=edge[i].next){
 77             int v=edge[i].v;
 78             if(edge[i].cap!=edge[i].flow && level[v]<minlevel){
 79                 minlevel=level[v];
 80                 cur[u]=i;
 81             }
 82         }
 83         if(--gap[level[u]]==0) break;
 84         level[u]=minlevel+1;
 85         gap[level[u]]++;
 86         u=pre[u];
 87     }
 88     return flow;
 89 }
 90 int d[MAXN];
 91 int low[MAXN][MAXN],up[MAXN][MAXN];
 92 int main(){
 93     int t,n,m,a,b,c;
 94     char ch;
 95     scanf("%d",&t);
 96     while(t--){
 97         scanf("%d%d",&n,&m);
 98         memset(d,0,sizeof(d));
 99         int S=0,T=n+m+1;
100         vs=T+1; vt=vs+1; NV=vt+1; NE=0;
101         memset(head,-1,sizeof(head));
102         addEdge(T,S,INF);
103         bool flag=0;
104         for(int i=1; i<=n; ++i){
105             scanf("%d",&a);
106             d[i]-=a;
107             if(a<0) flag=1;
108         }
109         for(int i=1; i<=m; ++i){
110             scanf("%d",&a);
111             d[i+n]+=a;
112             if(a<0) flag=1;
113         }
114         for(int i=1; i<=n; ++i){
115             for(int j=1; j<=m; ++j){
116                 low[i][j]=0; up[i][j]=INF;
117             }
118         }
119         int k;
120         scanf("%d",&k);
121         while(k--){
122             scanf("%d%d",&a,&b); scanf(" %c",&ch); scanf("%d",&c);
123             if(ch==‘>‘) ++c;
124             else if(ch==‘<‘) --c;
125             if(ch==‘<‘ && c<0) flag=1;
126             if(c<0) c=0;
127             if(a==0 && b==0){
128                 for(int i=1; i<=n; ++i){
129                     for(int j=1; j<=m; ++j){
130                         if(ch==‘=‘) low[i][j]=up[i][j]=c;
131                         else if(ch==‘>‘) low[i][j]=c;
132                         else up[i][j]=c;
133                     }
134                 }
135             }else if(a==0){
136                 for(int i=1; i<=n; ++i){
137                     if(ch==‘=‘) low[i][b]=up[i][b]=c;
138                     else if(ch==‘>‘) low[i][b]=c;
139                     else up[i][b]=c;
140                 }
141             }else if(b==0){
142                 for(int i=1; i<=m; ++i){
143                     if(ch==‘=‘) low[a][i]=up[a][i]=c;
144                     else if(ch==‘>‘) low[a][i]=c;
145                     else up[a][i]=c;
146                 }
147             }else{
148                 if(ch==‘=‘) low[a][b]=up[a][b]=c;
149                 else if(ch==‘>‘) low[a][b]=c;
150                 else up[a][b]=c;
151             }
152         }
153         for(int i=1; i<=n; ++i){
154             for(int j=1; j<=m; ++j){
155                 addEdge(i,j+n,up[i][j]-low[i][j]);
156                 d[i]+=low[i][j];
157                 d[j+n]-=low[i][j];
158             }
159         }
160         int tot=0;
161         for(int i=S; i<=T; ++i){
162             if(d[i]<0) addEdge(vs,i,-d[i]);
163             else addEdge(i,vt,d[i]),tot+=d[i];
164         }
165         if(flag || ISAP()!=tot){
166             puts("IMPOSSIBLE\n");
167             continue;
168         }
169         for(int u=1; u<=n; ++u){
170             for(int i=head[u]; i!=-1; i=edge[i].next){
171                 if(i&1) continue;
172                 int v=edge[i].v;
173                 low[u][v-n]+=edge[i].flow;
174             }
175         }
176         for(int i=1; i<=n; ++i){
177             for(int j=1; j<=m; ++j){
178                 printf("%d ",low[i][j]);
179             }
180             putchar(‘\n‘);
181         }
182         putchar(‘\n‘);
183     }
184     return 0;
185 }