# ACM/ICPC 之 有流量上下界的网络流-Dinic(可做模板)(POJ2396)

```//有流量上下界的网络流
//Time:47Ms     Memory:1788K
#include<iostream>
#include<cstring>
#include<cstdio>
#include<algorithm>
#include<queue>
using namespace std;

#define MAXC 25
#define MAXN 250
#define MAXE 100000
#define INF 0x3f3f3f3f

struct Edge{
int u,v,f,next;
Edge(){}
Edge(int uu, int vv, int ff, int nn):u(uu), v(vv), f(ff), next(nn){}
}e[MAXE];

int n, m;
int S,T,s,t;
int sn[MAXN], sm[MAXC]; //行和，列和
int up[MAXN][MAXC], down[MAXN][MAXC];      //上界与下界
int in[MAXN], out[MAXN];    //出入度
int h[MAXN], le;
int d[MAXN];
int ans[MAXN][MAXC];

void add(int u,int v,int f)
{
e[le] = Edge(u, v, f, h[u]);    h[u] = le++;
e[le] = Edge(v, u, 0, h[v]);    h[v] = le++;
}

bool Init()
{
int TT;
bool result = true;
scanf("%d", &TT);
while(TT--){
int x, y, v;
int x1,x2,y1,y2;
char op[2];
scanf("%d%d%s%d", &x, &y, op, &v);
if(!result) continue;
x1 = x2 = x;    y1 = y2 = y;
if(x == 0){ x1 = 1; x2 = n;}
if(y == 0){ y1 = 1; y2 = m;}
for(int i = x1; i <= x2; i++)
{
for(int j = y1; j <= y2; j++)
{
if(op[0] == '='){
if(v > up[i][j] || v < down[i][j]) result = false;
up[i][j] = down[i][j] = v;
}
else if(op[0] == '>')
down[i][j] = max(down[i][j], v+1);
else up[i][j] = min(up[i][j], v-1);
if(up[i][j] < down[i][j]) result = false;
}
}
}
return result;
}

void Build()    //建图
{
memset(h, -1, sizeof(h));
memset(in,0,sizeof(in));
memset(out,0,sizeof(out));
le = 0;
s = 0;  t = n+m+1;  //原图源汇点
S = t+1;  T = t+2;  //超级源汇点
for(int i =1; i <= n; i++)  //建立初始各边
{
for(int j = 1; j <= m; j++)
{
int x = i, y = j + n;
add(x, y, up[i][j] - down[i][j]);
in[y] += down[i][j];    out[x] += down[i][j];
}
}
for(int i = 1; i <= n; i++)   //从s流出的流量
{
in[i] += sn[i];   out[s] += sn[i];
}
for(int i = 1; i <= m; i++) //到t的流量
{
in[t] += sm[i]; out[i+n] += sm[i];
}
for(int i = 0; i <= n+m+1; i++) //新建补边
{
int x,y,w;
if(in[i] > out[i])  {
out[S] += in[i] - out[i];
}
else if(in[i] < out[i]) add(i, T, out[i] - in[i]);
}
}

bool BFS()
{
memset(d, -1, sizeof(d));
queue<int> q;
q.push(S);  d[S] = 0;
while(!q.empty()){
int cur = q.front();
q.pop();
for(int i = h[cur]; i != -1; i = e[i].next)
{
int v = e[i].v;
if(d[v] == -1 && e[i].f)
{
d[v] = d[cur] + 1;
if(v == T) return true;
q.push(v);
}
}
}
return false;
}

int DFS(int x, int sum)
{
if (x == T || sum == 0) return sum;
int src = sum;
for (int i = h[x]; i != -1; i = e[i].next)
{
int v = e[i].v;
if (d[v] == d[x] + 1 && e[i].f)
{
int tmp = DFS(v, min(sum, e[i].f));
e[i].f -= tmp;
e[i^1].f += tmp;
sum -= tmp;
}
}
return src - sum;
}

int Dinic()
{
int maxflow = 0;
while(BFS()){
maxflow += DFS(S, INF);
}
return maxflow;
}

int main()
{
//freopen("in.txt", "r", stdin);
//freopen("out.txt", "w", stdout);
int TT;
scanf("%d",&TT);
while(TT--){
memset(e, 0, sizeof(e));
memset(up, INF, sizeof(up));
memset(down, 0 ,sizeof(down));
scanf("%d%d", &n,&m);
for(int i = 1; i <= n; i++)
scanf("%d", &sn[i]);
for(int i = 1; i <= m; i++)
scanf("%d", &sm[i]);
if(!Init()){   //预处理得到矛盾
printf("IMPOSSIBLE\n\n");
continue;
}
Build();    //构图
if(Dinic() != out[S])   printf("IMPOSSIBLE\n\n");
else{
for(int i = 1; i <= n; i++)
for(int j = h[i]; j != -1; j = e[j].next)
ans[i][e[j].v-n] = e[j^1].f + down[i][e[j].v-n];
for(int i = 1; i <= n; i++)
{
for(int j = 1; j < m; j++)
printf("%d ", ans[i][j]);
printf("%d\n", ans[i][m]);
}
printf("\n");
}
}
return 0;
}
```

原文作者：Inkblots
原文地址: https://www.cnblogs.com/Inkblots/p/5740650.html
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