[POJ3020 Antenna Placement]

[题目来源]：POJ3023

[关键字]：二分图最小路径覆盖

[题目大意]：在一个坐标图中有一些点需要覆盖，每在一个点上覆盖就可在覆盖它上下左右4个点中任一个，问最小放几个。

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[分析]：利用黑白染色法把每一个点都和与之相邻的4个点连边，就构成了一个二分图。要求的就是有最小的点数覆盖全部边，即求最小路径覆盖=最大独立集=所有点-最大匹配由此可以求出最优解。实现方法——匈牙利算法即可。注意的是，这里的点是所有可以放得点*2，而匹配数也是正常匹配数的二倍（A到B连了，B到A也连了），所以最后是n-最大匹配/2。

[代码]：

View Code

  1 program Project1;
  2 const
  3   dx: array[1..4] of -1..1=(-1,1,0,0);
  4   dy: array[1..4] of -1..1=(0,0,1,-1);
  5 var
  6   tc, n, m, tot: longint;
  7   link: array[0..500] of longint;
  8   map: array[0..100,0..100] of char;
  9   d: array[0..500,0..500] of boolean;
 10   b: array[0..500] of boolean;
 11 
 12 function judge(x, y: longint):boolean;
 13 begin
 14   if (x > n) or (x < 1) or (y > m) or (y < 1) then exit(false);
 15   if map[x,y] <> '*' then exit(false);
 16   exit(true);
 17 end;
 18 
 19 procedure init;
 20 var
 21   i, j, k, xx, yy, s, s2: longint;
 22 begin
 23   readln(n,m);
 24   tot := 0;
 25   for i := 1 to n do
 26     begin
 27       for j := 1 to m do
 28         begin
 29           read(map[i,j]);
 30           if map[i,j] = '*' then inc(tot);
 31         end;
 32       readln;
 33     end;
 34   fillchar(d,sizeof(d),false);
 35   for i := 1 to n do
 36     for j := 1 to m do
 37       if map[i,j] = '*' then
 38         begin
 39           s := (i-1)*m+j;
 40           //writeln(s);
 41           for k := 1 to 4 do
 42             begin
 43               xx := i+dx[k];
 44               yy := j+dy[k];
 45               //writeln(xx,' ',yy);
 46               if judge(xx,yy) then
 47                 begin
 48                   s2 := (xx-1)*m+yy;
 49                   //writeln(s2);
 50                   d[s,s2] := true;
 51                 end;
 52             end;
 53         end;
 54   {for i := 1 to n*m do
 55     begin
 56       for j := 1 to n*m do write(d[i,j],'   ');
 57       writeln;
 58     end;}
 59 end;
 60 
 61 function dfs(k: longint):boolean;
 62 var
 63   i: longint;
 64 begin
 65   b[k] := false;
 66   for i := 1 to n*m do
 67     if (d[k,i]) and (b[i]) then
 68       begin
 69         b[i] := false;
 70         if (link[i] = 0) or (dfs(link[i])) then
 71           begin
 72             link[i] := k;
 73             exit(true);
 74           end;
 75       end;
 76   exit(false);
 77 end;
 78 
 79 procedure work;
 80 var
 81   i, j, ans, maxmatch, s: longint;
 82 begin
 83   maxmatch := 0;
 84   fillchar(link,sizeof(link),0);
 85   for i := 1 to n do
 86     for j := 1 to m do
 87       if map[i,j] = '*' then
 88         begin
 89           s := (i-1)*m+j;
 90           fillchar(b,sizeof(b),true);
 91           if dfs(s) then inc(maxmatch);
 92         end;
 93 //  writeln(tot,' ',maxmatch);
 94   ans := tot-maxmatch div 2;
 95   writeln(ans);
 96 end;
 97 
 98 begin
 99   readln(tc);
100   while tc > 0 do
101     begin
102       init;
103       work;
104       dec(tc);
105     end;
106 end.