POJ 3801 有上下界最小流

   1:  /**

   2:      POJ 3801 有上下界的最小流

   3:  

   4:  1、对supersrc到supersink 求一次最大流，记为f1。（在有源汇的情况下，先使整个网络趋向必须边尽量满足的情况）

   5:  2、添加一条边sink -> src，流量上限为INF，这条边记为p。（构造无源汇网络）

   6:  3、对supersrc到supersink再次求最大流，记为f2,这里判断是否为可行流。（要判断可行，必须先构造无源汇网络流，因此要再次求最大流）

   7:  

   8:      此网络流的最小流即为 sink -> src 的流量

   9:  */

  10:   

  11:  #include<iostream>

  12:  #include<cmath>

  13:  #include<memory>

  14:  #include <string.h>

  15:  #include <cstdio>

  16:  #include <vector>

  17:  using namespace std;

  18:   

  19:  #define V 150      // vertex

  20:  #define E  (V*V)     // edge

  21:  #define INF 0x3F3F3F3F  // 1061109567

  22:   

  23:  int i,j,k;

  24:  #define REP(i,n) for((i)=0;(i)<(int)(n);(i)++)

  25:  #define snuke(c,itr) for(__typeof((c).begin()) itr=(c).begin();itr!=(c).end();itr++)

  26:   

  27:  struct MaxFlow

  28:  {

  29:      struct Edge

  30:      {

  31:          int v, w, next;     //w for capicity

  32:          int lb,up;

  33:      } edge[E];

  34:   

  35:      int head[V];          // head[u]表示顶点u第一条邻接边的序号, 若head[u] = -1, u没有邻接边

  36:      int e;                // the index of the edge

  37:      int src, sink;

  38:      int net[V];              // 流入此节点的流的下界和 - 流出此节点的流的下界和,对于带上下界的来进行使用

  39:   

  40:   

  41:      void addedge(int  u, int v, int w, int lb = 0, int up = INF, int rw = 0)

  42:      {

  43:          edge[e].v = v;

  44:          edge[e].w= w;

  45:          edge[e].next = head[u];

  46:          edge[e].lb = lb, edge[e].up = up;

  47:          head[u] = e++;

  48:          // reverse edge  v -> u

  49:          edge[e].v = u;

  50:          edge[e].w = rw;

  51:          edge[e].lb = lb, edge[e].up = up;

  52:          edge[e].next = head[v];

  53:          head[v] = e++;

  54:      }

  55:   

  56:      int ISAP(int VertexNum )

  57:      {

  58:          int u, v, max_flow, aug, min_lev;

  59:          int curedge[V], parent[V], level[V];

  60:          int count[V], augment[V];

  61:   

  62:          memset(level, 0, sizeof(level));

  63:          memset(count, 0, sizeof(count));

  64:          REP(i,VertexNum+1) curedge[i] = head[i];

  65:          max_flow = 0;

  66:          augment[src] = INF;

  67:          parent[src] = -1;

  68:          u = src;

  69:   

  70:          while (level[src] < VertexNum)

  71:          {

  72:              if (u == sink)

  73:              {

  74:                  max_flow += augment[sink];

  75:                  aug = augment[sink];

  76:                  for (v = parent[sink]; v != -1; v = parent[v])

  77:                  {

  78:                      i = curedge[v];

  79:                      edge[i].w  -= aug;

  80:                      edge[i^1].w  += aug;

  81:                      augment[edge[i].v] -= aug;

  82:                      if (edge[i].w == 0) u = v;

  83:                  }

  84:              }

  85:              for (i = curedge[u]; i != -1; i = edge[i].next)

  86:              {

  87:                  v = edge[i].v;

  88:                  if (edge[i].w > 0 && level[u] == (level[v]+1))

  89:                  {

  90:                      augment[v] = min(augment[u], edge[i].w);

  91:                      curedge[u] = i;

  92:                      parent[v] = u;

  93:                      u = v;

  94:                      break;

  95:                  }

  96:              }

  97:              if (i == -1)

  98:              {

  99:                  if (--count[level[u]] == 0) break;

 100:                  curedge[u] = head[u];

 101:                  min_lev = VertexNum;

 102:                  for (i = head[u]; i != -1; i = edge[i].next)

 103:                      if (edge[i].w > 0)

 104:                          min_lev = min(level[edge[i].v], min_lev);

 105:                  level[u] = min_lev + 1;

 106:                  count[level[u]]++;

 107:                  if (u != src ) u = parent[u];

 108:              }

 109:          }

 110:          return max_flow;

 111:      }

 112:      void solve()

 113:      {

 114:          int n, m;

 115:          while (scanf("%d %d", &n, &m) != EOF)

 116:          {

 117:              if (n+m == 0) break;

 118:              e = 0;

 119:              memset(head, -1, sizeof(head));

 120:              memset(net, 0, sizeof(net));

 121:   

 122:              int s = n+1, t = n+2;

 123:              src = n+3, sink = n+4;

 124:              char a[5], b[5];

 125:              int c;

 126:              while (m--)

 127:              {

 128:                  scanf("%s %s %d", a, b, &c);

 129:                  int u, v;

 130:                  if (a[0] == ‘+‘) u = s;

 131:                  else sscanf(a, "%d", &u);   // 注意这里读取信息

 132:                  if (b[0] == ‘-‘) v = t;

 133:                  else sscanf(b, "%d", &v);

 134:                  net[v] += c, net[u] -= c;

 135:                  addedge(u,v,INF,c, INF);

 136:              }

 137:              vector<int> CE;

 138:              for(int i=1; i<=n+2; i++)

 139:              {

 140:                  if(net[i] >=0)

 141:                  {

 142:                      CE.push_back(e);

 143:                      addedge(src, i, net[i]);

 144:                  }

 145:                  else

 146:                  {

 147:                      CE.push_back(e);

 148:                      addedge(i, sink, -net[i]);

 149:                  }

 150:              }

 151:              int flow = 0;

 152:              flow =  ISAP(n+4);

 153:              int p = e;

 154:              addedge(t, s, INF, 0, INF);

 155:              flow += ISAP(n+4);

 156:              bool flag = true;

 157:              for(int i= 0; i< CE.size(); i++)

 158:              {

 159:                  if(edge[CE[i]].w !=0)

 160:                  {

 161:                      flag = false;

 162:                      break;

 163:                  }

 164:              }

 165:              if (!flag)

 166:                  printf("impossible\n");

 167:              else

 168:                  printf("%d\n", edge[p^1].w);

 169:          }

 170:      }

 171:  } sap;

 172:   

 173:  int main()

 174:  {

 175:  //    freopen("1.txt","r",stdin);

 176:      sap.solve();

 177:      return 0;

 178:  }