bool bounded_max_flow(graph_matrix upper, graph_matrix lower,
int beg, int end, int& max_flow)
{//流网络有g_cnt个节点，下标从0到g_cnt-1，upper为上界容量，lower为下界容量
//返回有源汇容量有上下界的流网络中是否存在可行流，若存在返回最大流max_flow
max_flow = 0;
//n_upper和n_lower是有源汇网络对应的无源汇网络
graph_matrix n_upper(upper), n_lower(lower);
//构造无源汇网络n_upper和n_lower，添加一条从end到beg的无穷大的边
construct_n(n_upper, beg, end);
//s_beg为超级源点，s_end为超级汇点
int s_beg, s_end;
graph_matrix residue(n_upper);
residue.g_cnt += 2;
s_beg = residue.g_cnt - 2;
s_end = residue.g_cnt - 1;
//将residue构造为无源汇网络对应的普通流网络
construct_c(n_upper, n_lower, s_beg, s_end, residue);
int lower_max_flow = distance_label(residue, s_beg, s_end);
int s_beg_out = beg_out(residue, s_beg, n_upper.g_cnt);
//若不相等则不存在可行流，也不存在最大流
if(lower_max_flow != s_beg_out)
return(false);
//若存在可行流，则计算最大流
//将residue中的超级源点超级汇点和原汇点到源点的边删去
deconstruct_c(residue, s_beg, s_end, beg, end);
int free_max_flow = distance_label(residue, beg, end);
max_flow = lower_max_flow + free_max_flow;
return(true);
}
bool bounded_min_flow(graph_matrix upper, graph_matrix lower,
int beg, int end, int& min_flow)
{//流网络有g_cnt个节点，下标从0到g_cnt-1，upper为上界容量，lower为下界容量
//返回有源汇容量有上下界的流网络中是否存在可行流，若存在返回最小流min_flow
min_flow = 0;
graph_matrix n_upper(upper), n_lower(lower);
int s_beg, s_end;
graph_matrix residue(n_upper);
residue.g_cnt += 2;
s_beg = residue.g_cnt - 2;
s_end = residue.g_cnt - 1;
construct_c(n_upper, n_lower, s_beg, s_end, residue);
//第一次计算最大流
int lower_max_flow = distance_label(residue, s_beg, s_end);
int s_beg_out = beg_out(residue, s_beg, n_upper.g_cnt);
//若第一次最大流已经等于超级源点所有出弧边容量之和，即已经满负荷
if(lower_max_flow == s_beg_out)
return(false);
//若lower_max_flow < s_beg_out，即尚未满负荷
//添加从汇点end到源点beg容量无穷大的边
construct_n(residue, beg, end);
//再次计算最大流
//由于计算从汇点end到源点beg边上的流需要更改distance_label代码，不方便扩展
//所以本文略去具体的代码(读者只需要对distance_label代码稍作更改即可求出min_flow)
int lower_max_flow2 = distance_label(residue, s_beg, s_end);
int s_beg_out2 = beg_out(residue, s_beg, n_upper.g_cnt);
if(lower_max_flow2 == s_beg_out2)
return(true);
else
return(false);
}
