仓库建设（ZJOI2007）

算法：DP
 
分析：搞了半个上午的这道题，然后查知识发现是斜率优化，弄了半天还是弄不懂。
      不过还算有一些收获……

program storage;



const 

 maxn=1000001;



var 

 n,i,j,h,t:longint;

 f,s,y,p,x,w,c:array[0..maxn] of int64;

 q:array[0..maxn] of longint;



function pan(j,k:longint):boolean;

begin

 if y[j]-y[k]+x[i]*(w[j]-w[k])>=0 then exit(true) else exit(false);

end;



function cha(i,j,k:longint):boolean;

begin

 if (y[j]-y[i])*(w[k]-w[j])-(y[k]-y[j])*(w[j]-w[i])<=0 then exit(true) else exit(false);

end;



begin

 assign(input,'storage.in'); reset(input);

 assign(output,'storage.out'); rewrite(output);



 readln(n);

 for i:=1 to n do

  begin

   readln(x[i],p[i],c[i]);

   p[i]:=p[i-1]+p[i]; 

   s[i]:=s[i-1]+p[i-1]*(x[i]-x[i-1]);

  end;



 for i:=1 to n do

  begin

   while (h<t) and (pan(q[h],q[h+1])) do inc(h);

   j:=q[h];

   f[i]:=f[j]+s[i]-s[j]-p[j]*(x[i]-x[j])+c[i];

   y[i]:=f[i]-s[i]+p[i]*x[i];

   w[i]:=-p[i];

   while (h<t) and (cha(q[t-1],q[t],i)) do dec(t);

   inc(t); 

   q[t]:=i;

  end;



 writeln(f[n]);



 close(input); close(output);

end.