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

 1 var f,g:array[0..1000050] of int64;

 2     s,q:array[0..1000050] of longint;

 3     a,b,c,n,i,h,t,x:longint;

 4     bestk:double;

 5 procedure init;

 6  begin

 7  readln(n);

 8  readln(a,b,c);

 9  s[0]:=0;

10  for i:=1 to n do

11   begin

12   read(x);

13   s[i]:=s[i-1]+x;

14   end;

15  end;

16 function k(x,y:longint):double;

17  begin

18  exit(double(g[y]-g[x])/(s[y]-s[x]));

19  end;

20 procedure main;

21  begin

22  f[0]:=0;h:=1;t:=1;q[1]:=0;

23  for i:=1 to n do

24   begin

25   bestk:=double(2*a*s[i]);

26   while (h<t) and (k(q[h],q[h+1])>=bestk) do inc(h);

27   f[i]:=int64(f[q[h]])+int64(a)*int64(s[i]-s[q[h]])*int64(s[i]-s[q[h]])

28        +int64(b)*int64(s[i]-s[q[h]])+int64(c);

29   g[i]:=int64(f[i])+int64(a)*int64(s[i])*int64(s[i])-int64(b)*int64(s[i]);

30   while (h+1<=t) and (k(q[t],i)>k(q[t-1],q[t])) do dec(t);

31   inc(t);

32   q[t]:=i;

33   end;

34  end;

35 procedure print;

36  begin

37  writeln(f[n]);

38  end;

39 begin

40  init;

41  main;

42  print;

43 end.                                                                                  

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