以前的空间Poj 3071 Cut the Sequence

Posted 2020-09-02 Macaulish

dp+单调性+平衡树

    在看某篇论文中看到这道题，但是那篇论文不如这个http://www.cnblogs.com/staginner/archive/2012/04/02/2429850.html 大神的空间写的好（还是说我太弱需要详解……）。

   其实要说的在大神的博客里面已经说的很好……

   比如f[i]，然后j表示满足a[j+1]+a[j+2]+……+a[i]<=m的最小值。然后我们假定a[j]--a[i]中最大数的下标为k，那么就有j+1<=l<=k时，f[j+1]+a[k]<=f[j+2]+a[k]<=f[j+3]+a[k]……<=f[k-1]+a[k]，也就是只要在把在k前或者k到i的区间分为一个区间，那么这个区间的最大值就是a[k]。这样f数组就是递增的。

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var
  left,right,s,q,d:array[0..501000]of longint;
  key,a,sum,f:array[0..500100]of int64;
  i,j,k,l,n,tot,t,head,tail,deci:longint;
  m:int64;
   
procedure rightrotate(var t:longint);
var
  k:longint;
begin
  k:=left[t];
  left[t]:=right[k];
  right[k]:=t;
  s[k]:=s[t];
  s[t]:=s[left[t]]+s[right[t]]+1;
  t:=k;
end;
   
procedure leftrotate(Var t:longint);
var
  k:longint;
begin
  k:=right[t];
  right[t]:=left[k];
  left[k]:=t;
  s[k]:=s[t];
  s[t]:=s[left[t]]+s[right[t]]+1;
  t:=k;
end;
   
procedure maintain(var t:longint);
begin
  if s[left[left[t]]]>s[right[t]] then begin
    rightrotate(t);
    maintain(right[t]);
    maintain(t);
  end;
  if s[right[left[t]]]>s[right[t]] then begin
    leftrotate(left[t]);
    rightrotate(t);
    maintain(left[t]);
    maintain(right[t]);
    maintain(t);
  end;
  if s[right[right[t]]]>s[left[t]] then begin
    leftrotate(t);
    maintain(left[t]);
    maintain(t);
  end;
  if s[left[right[t]]]>s[left[t]] then begin
    rightrotate(right[t]);
    leftrotate(t);
    maintain(left[t]);
    maintain(right[t]);
    maintain(t);
  end;
end;
   
procedure insert(var t:longint;v:int64);
begin
  if t=0 then begin
    inc(tot);
    t:=tot;
    key[t]:=v;
    s[t]:=1;
    left[t]:=0;
    right[t]:=0;
  end
  else begin
    inc(s[t]);
    if v<key[t] then insert(left[t],v)
      else insert(right[t],v);
    maintain(t);
  end;
end;
   
function delete(var t:longint;v:int64):int64;
begin
  dec(s[t]);
  if (key[t]=v) or( (v<key[t]) and (left[t]=0) )or ((v>=key[t]) and (right[t]=0)) then begin
    delete:=key[t];
    if (left[t]=0) or (right[t]=0) then
      t:=left[t]+right[t]
    else key[t]:=delete(left[t],key[t]+1);
  end
  else
    if v<key[t] then
      delete:=delete(left[t],v)
    else delete:=delete(right[t],v);
end;
   
function searchmin(var t:longint):int64;
begin
  if left[t]=0 then exit(key[t]);
  exit(searchmin(left[t]));
end;
   
function into:boolean;
begin
  readln(n,m);
  sum[0]:=0;
  for i:=1 to n do begin
    read(a[i]);
    sum[i]:=sum[i-1]+a[i];
    if a[i]>m then exit(false);
  end;
  exit(true);
end;
   
begin
  if into then begin
    t:=0;
    tot:=0;
    head:=1;
    tail:=1;
    deci:=0;
    for i:=1 to n do begin
      while sum[i]-sum[deci]>m do inc(deci);
      while (head<tail) and (q[head]<=deci) do begin
        delete(t,f[d[head]]+a[q[head]]);
        inc(head);
      end;
      while (head<tail) and (a[i]>=a[q[tail-1]]) do begin
        delete(t,f[d[tail-1]]+a[q[tail-1]]);
        dec(tail);
      end;
      q[tail]:=i;
      if head<tail then
        d[tail]:=q[tail-1]
      else d[tail]:=deci;
      insert(t,f[d[tail]]+a[i]);
      inc(tail);
      if d[head]<deci then begin
        delete(t,f[d[head]]+a[q[head]]);
        d[head]:=deci;
        insert(t,f[deci]+a[q[head]]);
      end;
      f[i]:=searchmin(t);
    end;
    writeln(f[n]);
  end
    else writeln(\'-1\');
  readln;
  readln;
end.

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