HDU 3157 Crazy Circuits (有源汇上下界最小流)

时间：2022-10-20 18:19:53

题意：一个电路板，上面有N个接线柱(标号1~N)   还有两个电源接线柱  +  - 然后是 给出M个部件正负极的接线柱和最小电流，求一个可以让所有部件正常工作的总电流。

析：这是一个有源汇有上下界的最小流。

有源汇有上下界最大流：

1.构造附加网络

2.对ss、tt求最大流(ss、tt满流则有解)

3.若有解，对s、t求最大流

有源汇有上下界最小流：

1.构造附加网络(不添加[t,s]边)

2.对ss、tt求最大流

3.添加[t,s]边

4.对ss、tt求最大流

5.若ss、tt满流，则[t,s]的流量就是最小流

代码如下：

#pragma comment(linker, "/STACK:1024000000,1024000000")

#include <cstdio>

#include <string>

#include <cstdlib>

#include <cmath>

#include <iostream>

#include <cstring>

#include <set>

#include <queue>

#include <algorithm>

#include <vector>

#include <map>

#include <cctype>

#include <cmath>

#include <stack>

#include <sstream>

#include <list>

#include <assert.h>

#include <bitset>

#define debug() puts("++++");

#define gcd(a, b) __gcd(a, b)

#define lson l,m,rt<<1

#define rson m+1,r,rt<<1|1

#define fi first

#define se second

#define pb push_back

#define sqr(x) ((x)*(x))

#define ms(a,b) memset(a, b, sizeof a)

#define sz size()

#define pu push_up

#define pd push_down

#define cl clear()

#define all 1,n,1

#define FOR(i,x,n)  for(int i = (x); i < (n); ++i)

#define freopenr freopen("in.txt", "r", stdin)

#define freopenw freopen("out.txt", "w", stdout)

using namespace std;

typedef long long LL;

typedef unsigned long long ULL;

typedef pair<int, int> P;

const int INF = 0x3f3f3f3f;

const double inf = 1e20;

const double PI = acos(-1.0);

const double eps = 1e-8;

const int maxn = 80 + 10;

const int maxm = 1e5 + 10;

const int mod = 50007;

const int dr[] = {-1, 0, 1, 0};

const int dc[] = {0, -1, 0, 1};

const char *de[] = {"0000", "0001", "0010", "0011", "0100", "0101", "0110", "0111", "1000", "1001", "1010", "1011", "1100", "1101", "1110", "1111"};

int n, m;

const int mon[] = {0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};

const int monn[] = {0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};

inline bool is_in(int r, int c) {

  return r >= 0 && r < n && c >= 0 && c < m;

}

struct Edge{

  int from, to, cap, flow;

};

struct Dinic{

  int n, m, s, t;

  vector<Edge> edges;

  vector<int> G[maxn];

  int d[maxn];

  bool vis[maxn];

  int cur[maxn];

  void init(int n){

    this-> n = n;

    for(int i = 0; i < n; ++i)  G[i].cl;

    edges.cl;

  }

  void addEdge(int from, int to, int cap){

    edges.pb((Edge){from, to, cap, 0});

    edges.pb((Edge){to, from, 0, 0});

    m = edges.sz;

    G[from].pb(m-2);  G[to].pb(m-1);

  }

  bool bfs(){

    ms(vis, 0);  vis[s] = 1;

    d[s] = 1;

    queue<int> q;

    q.push(s);

    while(!q.empty()){

      int x = q.front();  q.pop();

      for(int i = 0; i < G[x].sz; ++i){

        Edge &e = edges[G[x][i]];

        if(!vis[e.to] && e.cap > e.flow){

          d[e.to] = d[x] + 1;

          vis[e.to] = 1;

          q.push(e.to);

        }

      }

    }

    return vis[t];

  }

  int dfs(int x, int a){

    if(x == t || a == 0)  return a;

    int flow = 0, f;

    for(int &i = cur[x]; i < G[x].sz; ++i){

      Edge &e = edges[G[x][i]];

      if(d[e.to] == d[x] + 1 && (f = dfs(e.to, min(a, e.cap - e.flow))) > 0){

        e.flow += f;

        edges[G[x][i]^1].flow -= f;

        a -= f;

        flow += f;

        if(a == 0)  break;

      }

    }

    return flow;

  }

  int maxflow(int s, int t){

    this->s = s;  this-> t = t;

    int flow = 0;

    while(bfs()){ ms(cur, 0);  flow += dfs(s, INF); }

    return flow;

  }

  void solve(int t){

    for(int i = 0; i < G[s].sz; ++i){

      Edge &e = edges[G[s][i]];

      if(e.cap > e.flow){

        puts("impossible");

        return ;

      }

    }

    printf("%d\n", edges[*G[t].rbegin()].flow);

  }

};

Dinic dinic;

int in[maxn];

int main(){

  while(scanf("%d %d", &n, &m) == 2 && n+m){

    int s = n + 2, t = n + 3;

    dinic.init(n + 10);

    char a[15], b[15], c[15];

    ms(in, 0);

    for(int i = 0; i < m; ++i){

      scanf("%s %s %s", a, b, c);

      int u = a[0] == '+' ? 0 : atoi(a);

      int v = b[0] == '-' ? n+1 : atoi(b);

      int val = atoi(c);

      in[v] += val;

      in[u] -= val;

      dinic.addEdge(u, v, INF);

    }

    for(int i = 0; i <= n+1; ++i){

      if(in[i] > 0)  dinic.addEdge(s, i, in[i]);

      if(in[i] < 0)  dinic.addEdge(i, t, -in[i]);

    }

    dinic.maxflow(s, t);

    dinic.addEdge(n+1, 0, INF);

    dinic.maxflow(s, t);

    dinic.solve(n+1);

  }

  return 0;

}

　　

Crazy Circuits

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