线性规划与网络流24题 运输问题（最裸的费用流了）

存费用流模板

用sfpa算出最小费用和路径，沿这条路径增广

 

  1 const

  2         inf=maxlongint;

  3 var

  4         n,m:longint;

  5         map,a,w:array[0..120,0..120]of longint;

  6 

  7 procedure init;

  8 var

  9         i,j:longint;

 10 begin

 11         read(m,n);

 12         for i:=1 to m do

 13           read(map[0,i]);

 14         for i:=1 to n do

 15           read(map[m+i,n+m+1]);

 16         for i:=1 to m do

 17           for j:=1 to n do

 18             begin

 19               read(w[i,m+j]);

 20               w[m+j,i]:=-w[i,m+j];

 21               map[i,m+j]:=inf;

 22             end;

 23 end;

 24 

 25 var

 26         flag,d,dis,pre:array[0..120]of longint;

 27         time:longint;

 28 

 29 function spfa:boolean;

 30 var

 31         i,head,tail,num:longint;

 32 begin

 33         head:=1;

 34         tail:=1;

 35         num:=1;

 36         inc(time);

 37         for i:=1 to n+m+1 do

 38           dis[i]:=inf;

 39         dis[0]:=0;

 40         d[1]:=0;

 41         flag[0]:=time;

 42         while num>0 do

 43           begin

 44                 for i:=1 to n+m+1 do

 45                   if (a[d[head],i]>0)and(dis[d[head]]+w[d[head],i]<dis[i]) then

 46                   begin

 47                         dis[i]:=dis[d[head]]+w[d[head],i];

 48                         pre[i]:=d[head];

 49                         if flag[i]<>time then

 50                         begin

 51                           flag[i]:=time;

 52                           inc(num);

 53                           tail:=tail mod(n+m+1)+1;

 54                           d[tail]:=i;

 55                         end;

 56                   end;

 57                 flag[d[head]]:=time-1;

 58                 head:=head mod(n+m+1)+1;

 59                 dec(num);

 60           end;

 61         if dis[n+m+1]=inf then exit(false);

 62         exit(true);

 63 end;

 64 

 65 procedure work;

 66 var

 67         i,j,aug,ans:longint;

 68 begin

 69         for i:=0 to n+m+1 do

 70           for j:=0 to n+m+1 do

 71             a[i,j]:=map[i,j];

 72         ans:=0;

 73         while spfa do

 74           begin

 75             aug:=inf;

 76             i:=n+m+1;

 77             while i<>0 do

 78               begin

 79                 j:=pre[i];

 80                 if a[j,i]<aug then aug:=a[j,i];

 81                 i:=j;

 82               end;

 83             inc(ans,dis[n+m+1]*aug);

 84             i:=n+m+1;

 85             while i<>0 do

 86               begin

 87                 j:=pre[i];

 88                 inc(a[i,j],aug);

 89                 dec(a[j,i],aug);

 90                 i:=j;

 91               end;

 92           end;

 93         writeln(ans);

 94         ans:=0;

 95         for i:=1 to m do

 96           for j:=1 to n do

 97             begin

 98               w[i,j+m]:=-w[i,j+m];

 99               w[j+m,i]:=-w[j+m,i];

100             end;

101         for i:=0 to n+m+1 do

102           for j:=0 to n+m+1 do

103             a[i,j]:=map[i,j];

104         ans:=0;

105         while spfa do

106           begin

107             aug:=inf;

108             i:=n+m+1;

109             while i<>0 do

110               begin

111                 j:=pre[i];

112                 if a[j,i]<aug then aug:=a[j,i];

113                 i:=j;

114               end;

115             inc(ans,dis[n+m+1]*aug);

116             i:=n+m+1;

117             while i<>0 do

118               begin

119                 j:=pre[i];

120                 inc(a[i,j],aug);

121                 dec(a[j,i],aug);

122                 i:=j;

123               end;

124           end;

125         writeln(-ans);

126 end;

127 

128 begin

129     assign(input,'trans.in');

130     reset(input);

131     assign(output,'trans.out');

132     rewrite(output);

133         init;

134         work;

135     close(input);

136     close(output);

137 end.

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