合并类动态规划——石子合并

43

54

来源：NOI 1996

代码:

var n,i,j,k,l,minf,maxf:longint;
    a,s:array[0..300] of longint;
    f:array[1..300,1..300] of longint;
function min(x,y:longint):longint;
begin
  if x<y then exit(x) else exit(y);
end;
function max(x,y:longint):longint;
begin
  if x>y then exit(x) else exit(y);
end;
begin
  readln(n);
  for i:=1 to n do
    begin
      read(a[i]);
      a[i+n]:=a[i];
    end;


  for i:=1 to 2*n-1 do
       s[i]:=s[i-1]+a[i];   
  for l:=2 to n do           //枚举可能的长度
    for i:=1 to 2*n-l do     //环形扩展到链
      begin
        j:=i+l-1;
        f[i,j]:=maxlongint;
        for k:=i to j-1 do
          f[i,j]:=min(f[i,j], f[i,k]+f[k+1,j]+s[j]-s[i-1]);
      end;
  minf:=maxlongint;
  for i:=1 to n do minf:=min(minf,f[i,i+n-1]); //求出最小的值

  fillchar(f,sizeof(f),0);
  for l:=2 to n do
    for i:=1 to 2*n-1 do
      begin
        j:=i+l-1;
        f[i,j]:=0;
        for k:=i to j-1 do
          f[i,j]:=max(f[i,j], f[i,k]+f[k+1,j]+s[j]-s[i-1]);
      end;
  maxf:=0;
  for i:=1 to n do maxf:=max(maxf,f[i,i+n-1]);

  writeln(minf);
  writeln(maxf);
end.