[pku2288]Islands and Bridges

状态压缩的动态规划，设 opt[i][j][s] 表示最后访问的 I,j 各点的遍历情况为 s 的最好值，那么可以更新 opt[j][k][s+2^(k-1)] ，注意 dp 的循序为 s->i->j ，因为 s 更新的为 ss ， ss 总是大于 s 的。所以 s 应该从小到大的进行更新。

状态转移方程opt[i][j][s]+v[i]*v[j]*v[k]*map[i][k]+ v[j]*v[k]*map[j][k]+v[k] à opt[j][k][ss]

程序

{
  pku2288 Islands and Bridges
  By largelymfs
  Accepted 44208K 1375MS
  Date:2010-05-30 8:06
  状态压缩的动态规划
  Note：动态规划的枚举顺序
}
program ex;

const
  Infile  = 'pku2288.in';
  Outfile = 'pku2288.out';
  maxn    = 14;
  maxs    = 17000;
var
  n, m, t: longint;
  v:   array[0..maxn] of longint;
  map: array[0..maxn, 0..maxn] of longint;
  opt, way: array[0..maxn, 0..maxn, 0..maxs] of int64;

  procedure INit;
  var
    i, x, y: longint;
  begin
    Readln(n, m);
    for i := 1 to n do
      Read(v[i]);
    Fillchar(Map, sizeof(Map), $ff);
    for i := 1 to n do
      map[0][i] := 0;
    for i := 1 to m do
    begin
      Readln(x, y);
      map[x][y] := 0;
      map[y][x] := 0;
    end;
    v[0] := 0;
  end;

  procedure Prepare;
  var
    i, j, s: longint;
  begin
    for i := 0 to n do
      for j := 0 to n do
        for s := 0 to (1 shl n) - 1 do
          opt[i][j][s] := -1;
    opt[0][0][0] := 0;
    Fillchar(way, sizeof(way), 0);
    way[0][0][0] := 1;
  end;

  procedure Main;
  var
    target, k, s, i, j, ss: longint;
    max, now, maxway: int64;
  begin
    prepare;
    for s := 0 to (1 shl n) - 1 do
      for i := 0 to n do
        for j := 0 to n do
        begin
          if opt[i][j][s] = -1 then
            Continue;
          for k := 1 to n do
          begin
            ss := 1 shl (k - 1);
            if (map[j][k] = 0) and (s and ss = 0) then
            begin
              now := opt[i][j][s] + v[k] + v[j] * v[k];
              if map[i][k] = 0 then
                now := now + v[i] * v[j] * v[k];
              if now = opt[j][k][s + ss] then
              begin
                way[j][k][s + ss] := way[i][j][s] + way[j][k][s + ss];
              end;
              if now > opt[j][k][s + ss] then
              begin
                opt[j][k][s + ss] := now;
                way[j][k][ss + s] := way[i][j][s];
              end;
            end;
          end;
        end;
    target := 1 shl n;
    target := target - 1;
    max    := -1;
    maxway := 0;
    for i := 1 to n do
      for j := 1 to n do
      begin
        if max = opt[i][j][target] then
          maxway := maxway + way[i][j][target];
        if max < opt[i][j][target] then
        begin
          Max    := opt[i][j][target];
          maxway := way[i][j][target];
        end;
      end;
    if max = -1 then
      Writeln(0, ' ', 0)
    else
      Writeln(max, ' ', maxway div 2);
  end;

begin
  Assign(Input, Infile);
  Reset(input);
  Assign(Output, OUtfile);
  Rewrite(Output);
  Readln(t);
  while t > 0 do
  begin
    Dec(t);
    Init;
    IF n=1 Then Begin
      Writeln(v[1],' ', 1);
    end Else  Main;
  end;
  Close(Input);
  Close(Output);
end.