BZOJ1099: [POI2007] Tree Drz

First 1 with I exchange, n with I exchange, I with i+1 exchangeable can $o (n) $ calculated.

Then just consider I and x Exchange (1<i,x<n and |i-x|>1).

Set

A[I]=H[I-1]

B[I]=H[I+1]

f[i]=|h[i-1]-h[i]|+|h[i+1]-h[i]|

C[i]=min (A[i],b[i])

D[i]=max (A[i],b[i])

Then the exchange I with x contributes to the answer as

-F[I]-F[X]

+|a[i]-h[x]|+|b[i]-h[x]|

+|h[i]-a[x]|+|h[i]-b[x]|

The second row is categorized as a discussion:

1.h[x]<=min (A[i],b[i])

A[i]+b[i]-h[x]*2

2.min (A[i],b[i]) <=h[x]<=max (A[i],b[i])

|a[i]-b[i]|

3.h[x]>=max (A[i],b[i])

H[x]*2-a[i]-b[i]

The third row is categorized as a discussion:

1.h[i]<=min (A[x],b[x])

A[x]+b[x]-h[i]*2

2.min (A[x],b[x]) <=h[i]<=max (A[x],b[x])

|a[x]-b[x]|

3.h[i]>=max (A[x],b[x])

H[I]*2-A[X]-B[X]

So in 9 kinds of situations to discuss, with the scan line + line tree to complete the inquiry. Time Complexity $o (n\log N) $.

#include <cstdio> #include <algorithm>using namespace std;typedef long long ll;const int n=50010,inf=~0u> >1;int n,m,i,now,h[n],a[n],b[n],c[n],d[n],f[n],loc[n],v[131073],ans[n];ll H[N],B[N],sum;struct Q{int x,l,r,z,t; Q () {}q (int _x,int _l,int _r,int _z,int _t) {x=_x,l=_l,r=_r,z=_z,t=_t;}} q[n*3];inline bool Cmp1 (Q a,q b) {return a.x==b.x?a.t<b.t:a.x<b.x;} inline bool Cmp2 (Q a,q b) {return a.x==b.x?a.t<b.t:a.x>b.x;}  inline int Getl (ll x) {x=x*n;  int l=1,r=n,mid,t;  while (l<=r) if (b[mid= (l+r) >>1]>=x) r= (t=mid) -1;else l=mid+1; return t;}  inline int Getr (ll x) {x=x*n+n-1;  int l=1,r=n,mid,t;  while (l<=r) if (b[mid= (l+r) >>1]<=x) l= (t=mid) +1;else r=mid-1; return t;}  inline int Getx (ll x) {int l=1,r=n,mid,t;  while (l<=r) if (b[mid= (l+r) >>1]>=x) r= (t=mid) -1;else l=mid+1; return t;} inline int abs (int x) {return x>0?x:-x;} inline void up (Int&a,int b) {if (a>b) a=b;} inline void Read (int&a) {char c;while (!) ( ((C=getchar ()) >= ' 0 ') &&(c<= ' 9 ')), a=c-' 0 ', while (((C=getchar ()) >= ' 0 ') && (c<= ' 9 ')) (a*=10) +=c-' 0 ';}  void build (int x,int A,int b) {v[x]=inf;  if (a==b) return;  int mid= (A+B) >>1; Build (X<<1,a,mid), build (X&LT;&LT;1|1,MID+1,B);}  void change (int x,int a,int b,int c,int p) {if (a==b) {V[x]=p;return;}  int mid= (A+B) >>1;  C<=mid?change (x<<1,a,mid,c,p): Change (X&LT;&LT;1|1,MID+1,B,C,P); V[x]=min (v[x<<1],v[x<<1|1]);} void Ask (int x,int a,int b,int c,int D) {if (c>d| |  V[x]>=now) return;  if (C<=a&&b<=d) {up (now,v[x]); return;}  int mid= (A+B) >>1;  if (C<=mid) ask (X&LT;&LT;1,A,MID,C,D); if (D>mid) ask (X<<1|1,mid+1,b,c,d);}  inline void query (int l,int r,int p) {int x=loc[p-1],y=loc[p+1];  if (x>y) swap (x, y); if (y<l| |    X>r) {ask (1,1,n,l,r);  Return    } if (l<=x&&y<=r) {ask (1,1,n,l,x-1);    Ask (1,1,n,x+1,y-1);    Ask (1,1,n,y+1,r);  Return    } if (l<=x) {ask (1,1,n,l,x-1);    Ask (1,1,n,x+1,r);  Return } ASK (1,1,n,l,y-1); Ask (1,1,n,y+1,r);}    void S11 () {for (m=0,i=2;i<n;i++) {q[++m]=q (c[i],loc[i],0,a[i]+b[i]-h[i]*2-f[i],0);  Q[++m]=q (H[i],getr (C[i]), 0,a[i]+b[i]-h[i]*2-f[i],i);    } for (sort (Q+1,Q+M+1,CMP2), Build (1,1,n), i=1;i<=m;i++) {if (!q[i].t) change (1,1,N,Q[I].L,Q[I].Z);      else{now=inf,query (1,q[i].l,q[i].t);    if (Now<inf) up (Ans[q[i].t],q[i].z+now);    }}}void S12 () {for (m=0,i=2;i<n;i++) {q[++m]=q (C[i],loc[i],0,abs (A[i]-b[i])-h[i]*2-f[i],0);    Q[++m]=q (D[i],loc[i],0,0,n);  Q[++m]=q (H[i],getr (C[i]), 0,a[i]+b[i]-f[i],i);    } for (sort (Q+1,Q+M+1,CMP1), Build (1,1,n), i=1;i<=m;i++) {if (!q[i].t) change (1,1,N,Q[I].L,Q[I].Z);    else if (q[i].t==n) change (1,1,n,q[i].l,inf);      else{now=inf,query (1,q[i].l,q[i].t);    if (Now<inf) up (Ans[q[i].t],q[i].z+now);    }}}void S13 () {for (m=0,i=2;i<n;i++) {q[++m]=q (d[i],loc[i],0,-h[i]*2-a[i]-b[i]-f[i],0);  Q[++m]=q (H[i],getr (C[i]), 0,a[i]+b[i]+h[i]*2-f[i],i); } for (sort (Q+1,Q+M+1,CMP1), build (1,1,n), i=1;i<=m;i++) {if (!q[i].t) change (1,1,N,Q[I].L,Q[I].Z);      else{now=inf,query (1,q[i].l,q[i].t);    if (Now<inf) up (Ans[q[i].t],q[i].z+now);    }}}void S21 () {for (m=0,i=2;i<n;i++) {q[++m]=q (c[i],loc[i],0,a[i]+b[i]-f[i],0);  Q[++m]=q (H[i],getl (C[i]), GETR (D[i]), ABS (A[i]-b[i])-h[i]*2-f[i],i);    } for (sort (Q+1,Q+M+1,CMP2), Build (1,1,n), i=1;i<=m;i++) {if (!q[i].t) change (1,1,N,Q[I].L,Q[I].Z);      else{now=inf,query (q[i].l,q[i].r,q[i].t);    if (Now<inf) up (Ans[q[i].t],q[i].z+now);    }}}void S22 () {for (m=0,i=2;i<n;i++) {q[++m]=q (C[i],loc[i],0,abs (A[i]-b[i])-f[i],0);    Q[++m]=q (D[i],loc[i],0,0,n);  Q[++m]=q (H[i],getl (C[i]), GETR (D[i]), ABS (A[i]-b[i])-f[i],i);    } for (sort (Q+1,Q+M+1,CMP1), Build (1,1,n), i=1;i<=m;i++) {if (!q[i].t) change (1,1,N,Q[I].L,Q[I].Z);    else if (q[i].t==n) change (1,1,n,q[i].l,inf);      else{now=inf,query (q[i].l,q[i].r,q[i].t);    if (Now<inf) up (Ans[q[i].t],q[i].z+now); }}}void S23 () {for (m=0,i=2;i<n;i++){q[++m]=q (d[i],loc[i],0,-a[i]-b[i]-f[i],0);  Q[++m]=q (H[i],getl (C[i]), GETR (D[i]), ABS (A[i]-b[i]) +h[i]*2-f[i],i);    } for (sort (Q+1,Q+M+1,CMP1), Build (1,1,n), i=1;i<=m;i++) {if (!q[i].t) change (1,1,N,Q[I].L,Q[I].Z);      else{now=inf,query (q[i].l,q[i].r,q[i].t);    if (Now<inf) up (Ans[q[i].t],q[i].z+now);    }}}void S31 () {for (m=0,i=2;i<n;i++) {q[++m]=q (c[i],loc[i],0,a[i]+b[i]+h[i]*2-f[i],0);  Q[++m]=q (H[i],getl (D[i]), 0,-a[i]-b[i]-h[i]*2-f[i],i);    } for (sort (Q+1,Q+M+1,CMP2), Build (1,1,n), i=1;i<=m;i++) {if (!q[i].t) change (1,1,N,Q[I].L,Q[I].Z);      else{now=inf,query (q[i].l,n,q[i].t);    if (Now<inf) up (Ans[q[i].t],q[i].z+now);    }}}void S32 () {for (m=0,i=2;i<n;i++) {q[++m]=q (C[i],loc[i],0,abs (A[i]-b[i]) +h[i]*2-f[i],0);    Q[++m]=q (D[i],loc[i],0,0,n);  Q[++m]=q (H[i],getl (D[i]), 0,-a[i]-b[i]-f[i],i);    } for (sort (Q+1,Q+M+1,CMP1), Build (1,1,n), i=1;i<=m;i++) {if (!q[i].t) change (1,1,N,Q[I].L,Q[I].Z); else if (q[i].t==n) Change (1,1,n,q[i].l,iNF);      else{now=inf,query (q[i].l,n,q[i].t);    if (Now<inf) up (Ans[q[i].t],q[i].z+now);    }}}void S33 () {for (m=0,i=2;i<n;i++) {q[++m]=q (d[i],loc[i],0,h[i]*2-a[i]-b[i]-f[i],0);  Q[++m]=q (H[i],getl (D[i]), 0,h[i]*2-a[i]-b[i]-f[i],i);    } for (sort (Q+1,Q+M+1,CMP1), Build (1,1,n), i=1;i<=m;i++) {if (!q[i].t) change (1,1,N,Q[I].L,Q[I].Z);      else{now=inf,query (q[i].l,n,q[i].t);    if (Now<inf) up (Ans[q[i].t],q[i].z+now);  }}}int Main () {for (read (n), i=1;i<=n;i++) read (H[i]);  for (i=1;i<n;i++) Sum+=abs (h[i]-h[i+1]);    if (n>2) {f[1]=abs (h[1]-h[2]), F[n]=abs (h[n]-h[n-1]);      for (i=2;i<n;i++) {a[i]=h[i-1],b[i]=h[i+1];      C[i]=min (A[i],b[i]), D[i]=max (A[i],b[i]);    F[i]=abs (H[i]-h[i-1]) +abs (h[i]-h[i+1]);      } for (i=3;i<n;i++) {Up (Ans[1],abs (h[i]-h[2]) +abs (h[1]-h[i-1]) +abs (h[1]-h[i+1])-f[1]-f[i]);    Up (Ans[i],abs (h[i]-h[2]) +abs (h[1]-h[i-1]) +abs (h[1]-h[i+1)-f[1]-f[i]); } for (i=2;i<n-1;i++) {Up (Ans[n],abs (h[i]-h[n-1]) +ABS (H[n]-h[i-1]) +abs (h[n]-h[i+1])-f[n]-f[i]);    Up (Ans[i],abs (h[i]-h[n-1]) +abs (h[n]-h[i-1]) +abs (h[n]-h[i+1)-f[n]-f[i]);    } Up (Ans[1],abs (h[1]-h[n-1]) +abs (h[n]-h[2])-f[1]-f[n]);    Up (Ans[n],abs (h[1]-h[n-1]) +abs (h[n]-h[2])-f[1]-f[n]); if (n>2) {for (i=2;i<n-1;i++) {Up (Ans[i],abs (h[i-1]-h[i+1]) +abs (h[i]-h[i+1]) +abs (H[i+2]-h[i])-f[i]-f[i+1]+        ABS (h[i]-h[i+1]));      Up (Ans[i+1],abs (h[i-1]-h[i+1]) +abs (h[i]-h[i+1]) +abs (H[i+2]-h[i])-f[i]-f[i+1]+abs (h[i]-h[i+1]));      } Up (Ans[1],abs (h[1]-h[3])-abs (h[2]-h[3]));      Up (Ans[2],abs (h[1]-h[3])-abs (h[2]-h[3]));      Up (Ans[n],abs (h[n]-h[n-2])-abs (h[n-1]-h[n-2]));    Up (Ans[n-1],abs (h[n]-h[n-2])-abs (h[n-1]-h[n-2]));      } if (n>4) {for (i=1;i<=n;i++) b[i]=h[i]= (LL) h[i]*n+i-1;      Sort (b+1,b+n+1);      for (i=1;i<=n;i++) Loc[i]=getx (H[i]);    S11 (), S12 (), S13 (), S21 (), S22 (), S23 (), S31 (), S32 (), S33 ();  }} for (i=1;i<=n;i++) printf ("%lld\n", Sum+ans[i]); return 0;}

　　

BZOJ1099: [POI2007] Tree Drz