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ZOJ 2314 带上下界的可行流

对于无源汇问题,方法有两种.

1 从边的角度来处理. 新建超级源汇, 对于每一条有下界的边,x->y, 建立有向边 超级源->y ,容量为x->y下界,建立有向边 x-> 超级汇,容量为x->y下界.建立有向边 x->y,容量为x->y的上界减下界.

2 从点的角度来处理. 新建超级源汇,对于每个点流进的下界和为 in, 流出此点的下界和为out.如果in > out. 建立有向边 超级源->i,容量为in-out.反之,建立有向边 i->超级汇,容量为out-in.

如果超级源的每一条出边都满流,则存在一个可行流,可行流的流量就是每一条逆向边的流量+ 此边下界.

从点的角度的处理方法是边的处理方法的拓展.基于边的处理比较容易理解,但是复杂度较高.

下面是基于点的处理的程序:

   1:  /*
   2:      带上下界的可行流
   3:  */
   4:  #include<iostream>
   5:  #include<cmath>
   6:  #include<memory>
   7:  #include <string.h>
   8:  #include <cstdio>
   9:  using namespace std;
  10:   
  11:  #define V 300      // vertex
  12:  #define E  40800     // edge
  13:  #define INF 0x3F3F3F3F  // 1061109567
  14:   
  15:  int i,j,k;
  16:  #define REP(i,n) for((i)=0;(i)<(int)(n);(i)++)
  17:  #define snuke(c,itr) for(__typeof((c).begin()) itr=(c).begin();itr!=(c).end();itr++)
  18:   
  19:  struct MaxFlow
  20:  {
  21:      struct Edge
  22:      {
  23:          int v, w, next;     //w for capicity
  24:          int lb,up;
  25:      } edge[E];
  26:   
  27:      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
  28:      int e;                // the index of the edge
  29:      int src, sink;
  30:      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
  31:   
  32:   
  33:      void addedge(int  u, int v, int w, int lb = 0, int up = INF, int rw = 0)
  34:      {
  35:          edge[e].v = v;
  36:          edge[e].w= w;
  37:          edge[e].next = head[u];
  38:          edge[e].lb = lb, edge[e].up = up;
  39:          head[u] = e++;
  40:          // reverse edge  v -> u
  41:          edge[e].v = u;
  42:          edge[e].w = rw;
  43:          edge[e].lb = lb, edge[e].up = up;
  44:          edge[e].next = head[v];
  45:          head[v] = e++;
  46:      }
  47:   
  48:      int ISAP(int VertexNum )
  49:      {
  50:          int u, v, max_flow, aug, min_lev;
  51:          int curedge[V], parent[V], level[V];
  52:          int count[V], augment[V];
  53:   
  54:          memset(level, 0, sizeof(level));
  55:          memset(count, 0, sizeof(count));
  56:          REP(i,VertexNum+1) curedge[i] = head[i];
  57:          max_flow = 0;
  58:          augment[src] = INF;
  59:          parent[src] = -1;
  60:          u = src;
  61:   
  62:          while (level[src] < VertexNum)
  63:          {
  64:              if (u == sink)
  65:              {
  66:                  max_flow += augment[sink];
  67:                  aug = augment[sink];
  68:                  for (v = parent[sink]; v != -1; v = parent[v])
  69:                  {
  70:                      i = curedge[v];
  71:                      edge[i].w  -= aug;
  72:                      edge[i^1].w  += aug;
  73:                      augment[edge[i].v] -= aug;
  74:                      if (edge[i].w == 0) u = v;
  75:                  }
  76:              }
  77:              for (i = curedge[u]; i != -1; i = edge[i].next)
  78:              {
  79:                  v = edge[i].v;
  80:                  if (edge[i].w > 0 && level[u] == (level[v]+1))
  81:                  {
  82:                      augment[v] = min(augment[u], edge[i].w);
  83:                      curedge[u] = i;
  84:                      parent[v] = u;
  85:                      u = v;
  86:                      break;
  87:                  }
  88:              }
  89:              if (i == -1)
  90:              {
  91:                  if (--count[level[u]] == 0) break;
  92:                  curedge[u] = head[u];
  93:                  min_lev = VertexNum;
  94:                  for (i = head[u]; i != -1; i = edge[i].next)
  95:                      if (edge[i].w > 0)
  96:                          min_lev = min(level[edge[i].v], min_lev);
  97:                  level[u] = min_lev + 1;
  98:                  count[level[u]]++;
  99:                  if (u != src ) u = parent[u];
 100:              }
 101:          }
 102:          return max_flow;
 103:      }
 104:      void solve()
 105:      {
 106:          int T; cin>>T;
 107:          for(int cas =1; cas <=T; cas++)
 108:          {
 109:              int N,M; cin>>N>>M;
 110:              e = 0;
 111:              memset(head, -1, sizeof(head));
 112:              memset(net, 0, sizeof(net));
 113:              int a,b,c,d;
 114:              for(int i=1; i<=M;i++)
 115:              {
 116:                  scanf("%d%d%d%d", &a, &b, &c, &d);
 117:                  net[b] += c; net[a] -= c;
 118:                  addedge(a,b,d-c, c,d);
 119:              }
 120:              // 无源汇,这两个是super src, super sink.
 121:              src =http://www.mamicode.com/N+1; sink = N+2;
 122:              for(int i=1; i<=N; i++)
 123:              {
 124:                  if(net[i] > 0)
 125:                      addedge(src, i, net[i]);
 126:                  else
 127:                      addedge(i, sink, -net[i]);
 128:              }
 129:              ISAP(N+2);
 130:              bool flag = true;
 131:              for (i = head[src]; i != -1; i = edge[i].next)
 132:              {
 133:                  if(edge[i].w !=0)
 134:                  {
 135:                      flag = false;
 136:                      break;
 137:                  }
 138:              }
 139:              if(flag)
 140:              {
 141:                  cout<<"YES"<<endl;
 142:                  for(int i=0; i<M;i++)
 143:                  {
 144:                      cout<<edge[i*2+1].w + edge[i*2+1].lb<<endl;
 145:                  }
 146:                  cout<<endl;
 147:              }else
 148:              {
 149:                  cout<<"NO"<<endl;
 150:                  cout<<endl;
 151:              }
 152:          }
 153:   
 154:      }
 155:  }sap;
 156:   
 157:  int main()
 158:  {
 159:  //    freopen("1.txt","r",stdin);
 160:      sap.solve();
 161:      return 0;
 162:  }
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