PKU1191 chessboard devision

       在市图的电子阅览室搞了这道DP。估计这个就是我这个假期的最后一道题了。难度不大，状态转移也比较好想，分横纵两次切割。F[xa,ya,xb,yb,k] 表示把矩阵 [xa,ya,xb,yb] 分割成 k 份的最小数值。

       开学之后可能不会很有时间，应该会弄一弄简单图论，在巩固一下搜索跟DP。

program chessboard;const inf=200000000;var data,sum:array[0..9,0..9] of longint; score:array[0..9,0..9,0..9,0..9] of longint; f:array[0..9,0..9,0..9,0..9,0..16] of real; n,count:longint; aver:real;function getmin(a,b:real):real;begin if a<b then exit(a) else exit(b);end;procedure init;var i,j:longint;begin fillchar(data,sizeof(data),0); count:=0; readln(n); for i:=1 to 8 do for j:=1 to 8 do read(data[i,j]);end;procedure calcsum;var i,j:longint;begin fillchar(sum,sizeof(sum),0); for i:=1 to 8 do for j:=1 to 8 do sum[i,j]:=data[i,j]-sum[i-1,j-1]+sum[i-1,j]+sum[i,j-1]; aver:=sum[8,8]/n;end;procedure calcscore;var xa,ya,xb,yb:longint;begin for xa:=1 to 8 do for ya:=1 to 8 do for xb:=xa to 8 do for yb:=ya to 8 do score[xa,ya,xb,yb]:=sum[xb,yb]+sum[xa-1,ya-1]-sum[xa-1,yb]-sum[xb,ya-1];end;function dp(xa,ya,xb,yb,k:longint):real;var i,j:longint; tmpa,tmpb:real;begin if f[xa,ya,xb,yb,k]>0 then exit(f[xa,ya,xb,yb,k]); if k=1 then begin f[xa,ya,xb,yb,k]:=sqr(score[xa,ya,xb,yb]-aver); exit(f[xa,ya,xb,yb,k]); end; tmpa:=inf; tmpb:=inf; for i:=xa to xb-1 do begin tmpa:=getmin(dp(xa,ya,i,yb,k-1)+sqr(score[i+1,ya,xb,yb]-aver),tmpa); tmpa:=getmin(sqr(score[xa,ya,i,yb]-aver)+dp(i+1,ya,xb,yb,k-1),tmpa); end; for j:=ya to yb-1 do begin tmpb:=getmin(dp(xa,ya,xb,j,k-1)+sqr(score[xa,j+1,xb,yb]-aver),tmpb); tmpb:=getmin(sqr(score[xa,ya,xb,j]-aver)+dp(xa,j+1,xb,yb,k-1),tmpb); end; f[xa,ya,xb,yb,k]:=getmin(tmpa,tmpb); exit(f[xa,ya,xb,yb,k]);end;procedure main;begin fillchar(f,sizeof(f),0); f[1,1,8,8,n]:=dp(1,1,8,8,n);end;procedure outit;var ans:real;begin ans:=sqrt(f[1,1,8,8,n]/n); writeln(ans:0:3);end;begin assign(input,'a.in'); reset(input); assign(output,'a.out'); rewrite(output); init; calcsum; calcscore; main; outit; close(input); close(output);end.