HDU - 3157 Crazy Circuits(有下界的最小流)

题目大意：一个电路板，上面有N个接线柱，还有+,-两极

现在给出M条线路，每条线路都有相应的下限，即需要流至少多少的电流才能使该线路运行

问需要通多少的电流，才能使得所有的线路都能运行

解题思路：有下界的最小流，这个百度一下可以搜到，具体就不解释了

这边解释一下为什么先跑一下最大流，再添加边，再跑一下最大流

在没有添加边的情况下，先跑最大流，即保证能平衡的先尽量平衡，这样就可以减少后面的流量了

接着再添加边再跑最大流，既是为了确保平衡

[code]#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
#include <queue>
using namespace std;
const int MAXNODE = 210;
const int MAXEDGE = 100010;
typedef int Type;
const Type INF = 0x3f3f3f3f;

struct Edge{
    int u, v, next;
    Type cap, flow;
    Edge() {}
    Edge(int u, int v, Type cap, Type flow, int next) : u(u), v(v), cap(cap), flow(flow), next(next){}
};

struct Dinic{
    int n, m, s, t;
    Edge edges[MAXEDGE];
    int head[MAXNODE];
    int cur[MAXNODE];
    bool vis[MAXNODE];
    Type d[MAXNODE];
    vector<int> cut;

    void init(int n) {
        this->n = n;
        memset(head, -1, sizeof(head));
        m = 0;
    }

    void AddEdge(int u, int v, Type cap) {
        edges[m] = Edge(u, v, cap, 0, head[u]);
        head[u] = m++;
        edges[m] = Edge(v, u, 0, 0, head[v]);
        head[v] = m++;
    } 

    bool BFS() {
        memset(vis, 0, sizeof(vis));
        queue<int> Q;
        Q.push(s);
        d[s] = 0;
        vis[s] = 1;

        while (!Q.empty()) {
            int u = Q.front(); Q.pop();
            for (int i = head[u]; ~i; i = edges[i].next) {
                Edge &e = edges[i];
                if (!vis[e.v] && e.cap > e.flow) {
                    vis[e.v] = true;
                    d[e.v] = d[u] + 1;
                    Q.push(e.v);
                }
            }
        }
        return vis[t];
    }

    Type DFS(int u, Type a) {
        if (u == t || a == 0) return a;

        Type flow = 0, f;
        for (int &i = cur[u]; i != -1; i = edges[i].next) {
            Edge &e = edges[i];
            if (d[u] + 1 == d[e.v] && (f = DFS(e.v, min(a, e.cap - e.flow))) > 0) {
                e.flow += f;
                edges[i ^ 1].flow -= f;
                flow += f;
                a -= f;
                if (a == 0) break;
            }
        }
        return flow;
    }

    Type Maxflow(int s, int t) {
        this->s = s; this->t = t;
        Type flow = 0;
        while (BFS()) {
            for (int i = 0; i < n; i++)
                cur[i] = head[i];
            flow += DFS(s, INF);
        }
        return flow;
    }

    void Mincut() {
        cut.clear();
        for (int i = 0; i < m; i += 2) {
            if (vis[edges[i].u] && !vis[edges[i].v]) 
                cut.push_back(i);
        }
    }

    bool judge() {
        for (int i = head[s]; ~i; i = edges[i].next) 
            if (edges[i].cap - edges[i].flow != 0) return false;
        return true;
    }
}dinic;

#define maxn 60
int n, m;
int d[maxn];
char str[maxn];

void init() {
    memset(d, 0, sizeof(d));
    int source = n + 2, sink = n + 3;
    dinic.init(sink + 1);

    int u, v, c;
    for (int i = 1; i <= m; i++) {
        scanf("%s", str);
        if (str[0] == '+') u = 0;
        else sscanf(str, "%d", &u);

        scanf("%s", str);
        if (str[0] == '-') v = n + 1;
        else sscanf(str, "%d", &v);

        scanf("%d", &c);
        dinic.AddEdge(u, v, INF);
        d[u] -= c;
        d[v] += c;
    }   

    for (int i = 0; i <= n + 1; i++) {
        if (d[i] > 0) dinic.AddEdge(source, i, d[i]);
        if (d[i] < 0) dinic.AddEdge(i, sink, -d[i]);
    }
    dinic.Maxflow(source, sink);
    dinic.AddEdge(n + 1, 0, INF);
    dinic.Maxflow(source, sink);
    if (!dinic.judge()) printf("impossible\n");
    else printf("%d\n", dinic.edges[dinic.m - 2].flow);
}

int main() {

    while (scanf("%d%d", &n, &m) != EOF && n + m) {
        init();
    }
    return 0;
}