APIO2010特别行动队（单调队列、斜率优化）

其实这题一看知道应该是DP，再一看数据范围肯定就是单调队列了。

不过我还不太懂神马单调队列、斜率优化……

附上天牛的题解：http://www.cnblogs.com/neverforget/archive/2012/04/19/2456483.html

var f,g:array[0..1000050] of int64;
    s,q:array[0..1000050] of longint;
    a,b,c,n,i,h,t,x:longint;
    bestk:double;
procedure init;
 begin
 readln(n);
 readln(a,b,c);
 s[0]:=0;
 for i:=1 to n do
  begin
  read(x);
  s[i]:=s[i-1]+x;
  end;
 end;
function k(x,y:longint):double;
 begin
 exit(double(g[y]-g[x])/(s[y]-s[x]));
 end;
procedure main;
 begin
 f[0]:=0;h:=1;t:=1;q[1]:=0;
 for i:=1 to n do
  begin
  bestk:=double(2*a*s[i]);
  while (h<t) and (k(q[h],q[h+1])>=bestk) do inc(h);
  f[i]:=int64(f[q[h]])+int64(a)*int64(s[i]-s[q[h]])*int64(s[i]-s[q[h]])
       +int64(b)*int64(s[i]-s[q[h]])+int64(c);
  g[i]:=int64(f[i])+int64(a)*int64(s[i])*int64(s[i])-int64(b)*int64(s[i]);
  while (h+1<=t) and (k(q[t],i)>k(q[t-1],q[t])) do dec(t);
  inc(t);
  q[t]:=i;
  end;
 end;
procedure print;
 begin
 writeln(f[n]);
 end;
begin
 init;
 main;
 print;
end.