【HDU3507】Print Article（斜率优化DP）

单调队列DP复出练手题

朴素方程dp[i]=min(dp[j]+(s[i]-s[j-1])^2+m

你懂得

 var dp,s:array[..]of int64;
     a,q:array[..]of longint;
     n,m,i,t,w:longint;

 function sum(x,y:longint):int64;
 begin
  exit(s[y]-s[x-]);
 end;

 function clac(j,i:longint):int64;
 begin
  exit(dp[j]+sqr(sum(j+,i))+m);
 end;

 function cmp(x,y,z:longint):boolean;
 var x1,y1,x2,y2:int64;
 begin
  x1:=dp[x]-dp[y]+sqr(s[x])-sqr(s[y]);
  y1:=*(s[x]-s[y]);
  x2:=dp[y]-dp[z]+sqr(s[y])-sqr(s[z]);
  y2:=*(s[y]-s[z]);
  if x1*y2>=x2*y1 then exit(true);
  exit(false);
 end;

 begin
  assign(input,'1.in'); reset(input);
  assign(output,'1.out'); rewrite(output);
  while not eof do
  begin
   readln(n,m);
   fillchar(dp,sizeof(dp),);
   for i:= to n do readln(a[i]);
   s[]:=;
   for i:= to n do s[i]:=s[i-]+a[i];
   t:=; w:=; q[]:=; dp[]:=;
   for i:= to n do
   begin
    while (w-t>=)and(clac(q[t],i)>=clac(q[t+],i)) do inc(t);
    dp[i]:=clac(q[t],i);
    while (w-t>=)and cmp(q[w-],q[w],i) do dec(w);
    inc(w); q[w]:=i;
   end;
   writeln(dp[n]);
  end;
  close(input);
  close(output);
 end.