两道有上下界有源汇最小流。 步骤之前写的笔记里有。但是原理。。。确实不太懂。 步骤： 1. 按照无源汇有上下界的最大流的做法找出可行流（但不要建立t->s）； 2. 添加t->s，流量上界INF； 3. 再次运行最大流，找出ss->st可行流； 4. 若ss不满载，则无可行流。反之，最小流为t->s的流量，每条边的流量为逆向边的流量（加上下界b）。
SGU176 - Flow construction 1
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127//下界网络流
using namespace std;
struct Edge {
int c, f, id;
unsigned v, flip;
Edge(unsigned v, int c, int f, unsigned flip, int id) :v(v), c(c), f(f), flip(flip), id(id) {}
};
class Dinic {
public:
bool b[Maxn];
int a[Maxn];
unsigned p[Maxn], cur[Maxn], d[Maxn];
vector<Edge> G[Maxn];
unsigned s, t;
void Init(unsigned n) {
for (int i = 0; i <= n; ++i)
G[i].clear();
}
void AddEdge(unsigned u, unsigned v, int c, int id) {
G[u].push_back(Edge(v, c, 0, G[v].size(),0));
G[v].push_back(Edge(u, 0, 0, G[u].size() - 1, id)); // 使用无向图时将0改为c即可
}
bool BFS() {
unsigned u, v;
queue<unsigned> q;
memset(b, 0, sizeof(b));
q.push(s);
d[s] = 0;
b[s] = 1;
while (!q.empty()) {
u = q.front();
q.pop();
for (auto it = G[u].begin(); it != G[u].end(); ++it) {
Edge &e = *it;
if (!b[e.v] && e.c>e.f) {
b[e.v] = 1;
d[e.v] = d[u] + 1;
q.push(e.v);
}
}
}
return b[t];
}
int DFS(unsigned u, int a) {
if (u == t || a == 0)
return a;
int flow = 0, f;
for (unsigned &i = cur[u]; i<G[u].size(); ++i) {
Edge &e = G[u][i];
if (d[u] + 1 == d[e.v] && (f = DFS(e.v, min(a, e.c - e.f)))>0) {
a -= f;
e.f += f;
G[e.v][e.flip].f -= f;
flow += f;
if (!a) break;
}
}
return flow;
}
int MaxFlow(unsigned s, unsigned t) {
int flow = 0;
this->s = s;
this->t = t;
while (BFS()) {
memset(cur, 0, sizeof(cur));
flow += DFS(s, INF);
}
return flow;
}
};
int Flow[10000+23];
int N, M;
int Dif[Maxn];
int main() {
ios::sync_with_stdio(false);
while (cin >> N >> M) {
const int ss = N + 1, st = N + 2;
memset(Dif, 0, sizeof(Dif));
memset(Flow, 0, sizeof(Flow));
Dinic Din;
Din.Init(N);
int u, v, b, c;
for (int i = 1; i <= M; ++i) {
cin >> u >> v >> c >> b;
if (b) {
b = c;
Dif[u] -= b;
Dif[v] += b;
Flow[i] = b;
}
else Din.AddEdge(u, v, c - b, i);
}
int sum = 0;
for (int i = 1; i <= N; ++i) {
if (Dif[i] > 0) {
Din.AddEdge(ss, i, Dif[i], 0);
sum += Dif[i];
}
if (Dif[i] < 0) Din.AddEdge(i, st, -Dif[i], 0);
}
int ans = Din.MaxFlow(ss, st);
Din.AddEdge(N, 1, INF, 0);
ans += Din.MaxFlow(ss, st);
if (sum != ans) cout << "Impossible\n";
else {
cout << Din.G[N].rbegin()->f << '\n';
for (int i = 1; i <= N; ++i) for (const auto &e : Din.G[i]) {
if (e.id) Flow[e.id] += -e.f;
}
for (int i = 1; i < M; ++i) cout << Flow[i] << ' ';
cout << Flow[M] << '\n';
}
}
return 0;
}
HDU3157 - Crazy Circuits 1
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using namespace std;
const int Maxn = 100;
int N, M, S, T, SS, ST;
int Dif[Maxn];
bool QIn(int &x) {
char c;
while ((c = getchar()) != EOF && (!isdigit(c) && (c != '+'&&c != '-')));
switch (c) {
case '+':x = S; return true;
case '-':x = T; return true;
case EOF: return false;
}
x = 0;
do {
x *= 10;
x += c - '0';
} while ((c = getchar()) != EOF&&isdigit(c));
return true;
}
struct Edge {
int c, f;
unsigned v, flip;
Edge(unsigned v, int c, int f, unsigned flip) :v(v), c(c), f(f), flip(flip) {}
};
class Dinic {
private:
bool b[Maxn];
int a[Maxn];
unsigned p[Maxn], cur[Maxn], d[Maxn];
public:
vector<Edge> G[Maxn];
unsigned s, t;
void Init(unsigned n) {
for (int i = 0; i <= n; ++i)
G[i].clear();
}
void AddEdge(unsigned u, unsigned v, int c) {
G[u].push_back(Edge(v, c, 0, G[v].size()));
G[v].push_back(Edge(u, 0, 0, G[u].size() - 1)); //使用无向图时将0改为c即可
}
bool BFS() {
unsigned u, v;
queue<unsigned> q;
memset(b, 0, sizeof(b));
q.push(s);
d[s] = 0;
b[s] = 1;
while (!q.empty()) {
u = q.front();
q.pop();
for (auto it = G[u].begin(); it != G[u].end(); ++it) {
Edge &e = *it;
if (!b[e.v] && e.c>e.f) {
b[e.v] = 1;
d[e.v] = d[u] + 1;
q.push(e.v);
}
}
}
return b[t];
}
int DFS(unsigned u, int a) {
if (u == t || a == 0)
return a;
int flow = 0, f;
for (unsigned &i = cur[u]; i<G[u].size(); ++i) {
Edge &e = G[u][i];
if (d[u] + 1 == d[e.v] && (f = DFS(e.v, min(a, e.c - e.f)))>0) {
a -= f;
e.f += f;
G[e.v][e.flip].f -= f;
flow += f;
if (!a) break;
}
}
return flow;
}
int MaxFlow(unsigned s, unsigned t) {
int flow = 0;
this->s = s;
this->t = t;
while (BFS()) {
memset(cur, 0, sizeof(cur));
flow += DFS(s, INF);
}
return flow;
}
};
void Input(Dinic &d) {
memset(Dif, 0, sizeof(Dif));
int u, v, b;
char c;
for (int i = 1; i <= M; ++i) {
QIn(u);
QIn(v);
QIn(b);
d.AddEdge(u, v, INF); //由于无上界，直接写INF好了，反正流量不可能达到INF-b
Dif[u] -= b;
Dif[v] += b;
}
}
int main() {
while (~scanf("%d %d",&N,&M) && M) { //N可以等于0！
S = N + 1, T = N + 2;
SS = S + 2, ST = T + 2;
Dinic D;
Input(D);
int sum = 0;
for (int i = 1; i <= T; ++i) { //建立与超级源汇点ss、st的边（别漏了源汇点！）
if (Dif[i] > 0) {
D.AddEdge(SS, i, Dif[i]);
sum += Dif[i];
}
if (Dif[i] < 0) D.AddEdge(i, ST, -Dif[i]);
}
int ans=D.MaxFlow(SS, ST);
D.AddEdge(T, S, INF);
ans += D.MaxFlow(SS, ST);
if (ans != sum) {
puts("impossible");
}
else {
printf("%d\n", D.G[T].rbegin()->f);
}
}
return 0;
}