【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[0..500000]of int64;
    a,q:array[1..500000]of longint;
    n,m,i,t,w:longint;

function sum(x,y:longint):int64;
begin
 exit(s[y]-s[x-1]);
end;

function clac(j,i:longint):int64;
begin
 exit(dp[j]+sqr(sum(j+1,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:=2*(s[x]-s[y]);
 x2:=dp[y]-dp[z]+sqr(s[y])-sqr(s[z]);
 y2:=2*(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),0);
  for i:=1 to n do readln(a[i]);
  s[0]:=0;
  for i:=1 to n do s[i]:=s[i-1]+a[i];
  t:=1; w:=1; q[1]:=0; dp[0]:=0;
  for i:=1 to n do
  begin
   while (w-t>=1)and(clac(q[t],i)>=clac(q[t+1],i)) do inc(t);
   dp[i]:=clac(q[t],i);
   while (w-t>=1)and cmp(q[w-1],q[w],i) do dec(w);
   inc(w); q[w]:=i;
  end;
  writeln(dp[n]);
 end;
 close(input);
 close(output);
end.