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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

 1 var dp,s:array[0..500000]of int64;
 2     a,q:array[1..500000]of longint;
 3     n,m,i,t,w:longint;
 4
 5 function sum(x,y:longint):int64;
 6 begin
 7  exit(s[y]-s[x-1]);
 8 end;
 9
10 function clac(j,i:longint):int64;
11 begin
12  exit(dp[j]+sqr(sum(j+1,i))+m);
13 end;
14
15 function cmp(x,y,z:longint):boolean;
16 var x1,y1,x2,y2:int64;
17 begin
18  x1:=dp[x]-dp[y]+sqr(s[x])-sqr(s[y]);
19  y1:=2*(s[x]-s[y]);
20  x2:=dp[y]-dp[z]+sqr(s[y])-sqr(s[z]);
21  y2:=2*(s[y]-s[z]);
22  if x1*y2>=x2*y1 then exit(true);
23  exit(false);
24 end;
25
26 begin
27  assign(input,‘1.in‘); reset(input);
28  assign(output,‘1.out‘); rewrite(output);
29  while not eof do
30  begin
31   readln(n,m);
32   fillchar(dp,sizeof(dp),0);
33   for i:=1 to n do readln(a[i]);
34   s[0]:=0;
35   for i:=1 to n do s[i]:=s[i-1]+a[i];
36   t:=1; w:=1; q[1]:=0; dp[0]:=0;
37   for i:=1 to n do
38   begin
39    while (w-t>=1)and(clac(q[t],i)>=clac(q[t+1],i)) do inc(t);
40    dp[i]:=clac(q[t],i);
41    while (w-t>=1)and cmp(q[w-1],q[w],i) do dec(w);
42    inc(w); q[w]:=i;
43   end;
44   writeln(dp[n]);
45  end;
46  close(input);
47  close(output);
48 end.