P5161 WD與數列(字尾自動機+線段樹合併)
阿新 • • 發佈:2019-01-02
沒想出來→_→
首先不難看出要差分之後計算不相交也不相鄰的相等子串對數,於是差分之後建SAM,在parent樹上用線段樹合併維護endpos集合,然後用啟發式合併維護一個節點對另一個節點的貢獻,於是總的時間複雜度為\(O(n\log^2n)\)
//minamoto #include<bits/stdc++.h> #define R register #define ll long long #define IT vector<int>::iterator #define fp(i,a,b) for(R int i=a,I=b+1;i<I;++i) #define fd(i,a,b) for(R int i=a,I=b-1;i>I;--i) #define go(u) for(int i=head[u],v=e[i].v;i;i=e[i].nx,v=e[i].v) #define gg(u) for(IT it=f[u].begin();it!=f[u].end();++it) using namespace std; char buf[1<<21],*p1=buf,*p2=buf; inline char getc(){return p1==p2&&(p2=(p1=buf)+fread(buf,1,1<<21,stdin),p1==p2)?EOF:*p1++;} int read(){ R int res,f=1;R char ch; while((ch=getc())>'9'||ch<'0')(ch=='-')&&(f=-1); for(res=ch-'0';(ch=getc())>='0'&&ch<='9';res=res*10+ch-'0'); return res*f; } const int N=6e5+5; struct eg{int v,nx;}e[N];int head[N],tot; inline void add(R int u,R int v){e[++tot]={v,head[u]},head[u]=tot;} int fa[N],l[N],a[N],rt[N];map<int,int>ch[N]; struct node{int s,ls,rs;ll xs;}t[N<<5];vector<int>*f[N],tmp[N]; int n,m,ctot,cnt,las;ll ans; void ins(int c){ int p=las,np=++cnt;las=np,l[np]=l[p]+1; for(;p&&!ch[p].count(c);p=fa[p])ch[p][c]=np; if(!p)fa[np]=1; else{ int q=ch[p][c]; if(l[q]==l[p]+1)fa[np]=q; else{ int nq=++cnt;l[nq]=l[p]+1; ch[nq]=ch[q],fa[nq]=fa[q],fa[np]=fa[q]=nq; for(;p&&ch[p][c]==q;p=fa[p])ch[p][c]=nq; } } } void update(int &p,int l,int r,int x){ if(!p)p=++ctot;++t[p].s,t[p].xs+=x; if(l==r)return; int mid=(l+r)>>1; x<=mid?update(t[p].ls,l,mid,x):update(t[p].rs,mid+1,r,x); } int qaqs(int p,int l,int r,int ql,int qr){ if(!p)return 0;if(ql<=l&&qr>=r)return t[p].s; int mid=(l+r)>>1,res=0; if(ql<=mid)res+=qaqs(t[p].ls,l,mid,ql,qr); if(qr>mid)res+=qaqs(t[p].rs,mid+1,r,ql,qr); return res; } inline int querys(R int p,R int l,R int r){return (l>r||r<1||l>n)?0:qaqs(p,1,n,l,r);} ll qaqxs(int p,int l,int r,int ql,int qr){ if(!p)return 0;if(ql<=l&&qr>=r)return t[p].xs; int mid=(l+r)>>1;ll res=0; if(ql<=mid)res+=qaqxs(t[p].ls,l,mid,ql,qr); if(qr>mid)res+=qaqxs(t[p].rs,mid+1,r,ql,qr); return res; } inline ll queryxs(R int p,R int l,R int r){return (l>r||r<1||l>n)?0:qaqxs(p,1,n,l,r);} int merge(int x,int y){ if(!x||!y)return x|y; t[x].s+=t[y].s,t[x].xs+=t[y].xs; t[x].ls=merge(t[x].ls,t[y].ls),t[x].rs=merge(t[x].rs,t[y].rs); return x; } void dfs(int u){ int k=l[u]; go(u){ dfs(v);if(f[u]->size()<f[v]->size())swap(f[u],f[v]),swap(rt[u],rt[v]); gg(v){ int x=*it; ll A=1ll*querys(rt[u],x-k-1,x-2)*(x-1)-queryxs(rt[u],x-k-1,x-2)+1ll*querys(rt[u],1,x-k-2)*k; ll B=1ll*queryxs(rt[u],x+2,x+k+1)-1ll*querys(rt[u],x+2,x+k+1)*(x+1)+1ll*querys(rt[u],x+k+2,n)*k; ans+=A+B,f[u]->push_back(x); }rt[u]=merge(rt[u],rt[v]); } } int main(){ // freopen("testdata.in","r",stdin); n=read(); fp(i,1,n)a[i]=read(); fp(i,1,n-1)a[i]=a[i+1]-a[i],f[i]=&tmp[i]; ans=1ll*n*(n-1)>>1; --n,las=cnt=1; fp(i,1,n)ins(a[i]),f[las].push_back(i),update(rt[las],1,n,i); fp(i,2,cnt)add(fa[i],i); dfs(1);printf("%lld\n",ans); return 0; }