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题解
- SA+并查集
- 把ht按大小倒序加入,并查集合并维护答案的变化;
- SAM
- 翻转串,求出SAM的parent树就是后缀树,两个串的最长公共后缀是他们lca的len值;
- 考率一个节点x,那么它子树里的后缀点两两都是len[x]相似的,所以在prent树上做dp即可;
- 第二问的统计比较麻烦,可以直接写一个后缀树的dfs来统计u的当前儿子和之前的儿子的答案,这样子不用维护次大值;
- dp的具体方式见bzoj3238
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1 #include<bits/stdc++.h> 2 #define fp(i,a,b) for(register int i=a,I=b+1;i<I;++i) 3 #define fd(i,a,b) for(register int i=a,I=b-1;i>I;--i) 4 #define go(u) for(register int i=fi[u],v=e[i].to;i;v=e[i=e[i].nx].to) 5 #define file(s) freopen(s".in","r",stdin),freopen(s".out","w",stdout) 6 template<class T>inline bool cmax(T&a,const T&b){return a<b?a=b,1:0;} 7 template<class T>inline bool cmin(T&a,const T&b){return a>b?a=b,1:0;} 8 using namespace std; 9 char ss[1<<17],*A=ss,*B=ss; 10 inline char gc(){return A==B&&(B=(A=ss)+fread(ss,1,1<<17,stdin),A==B)?-1:*A++;} 11 template<class T>inline void sd(T&x){ 12 char c;T y=1;while(c=gc(),(c<48||57<c)&&c!=-1)if(c==45)y=-1;x=c-48; 13 while(c=gc(),47<c&&c<58)x=x*10+c-48;x*=y; 14 } 15 inline void gs(char*s){char c;while(c=gc(),c<32);*s++=c;while(c=gc(),c>32)*s++=c;} 16 char sr[1<<21],z[20];int C=-1,Z; 17 inline void Ot(){fwrite(sr,1,C+1,stdout),C=-1;} 18 template<class T>inline void we(T x){ 19 if(C>1<<20)Ot();if(x<0)sr[++C]=45,x=-x; 20 while(z[++Z]=x%10+48,x/=10); 21 while(sr[++C]=z[Z],--Z);sr[++C]=' '; 22 } 23 const int N=3e5+5,M=2*N,inf=1e9+7; 24 typedef long long ll; 25 typedef int arr[M]; 26 int n,w[N];char s[N]; 27 struct SAM{ 28 int las,T,ch[M][26];arr fa,len,sz; 29 SAM(){las=T=1;} 30 inline void ins(int c,int w){ 31 int p=las,np;fa[np=las=++T]=1,len[np]=len[p]+1; 32 for(;p&&!ch[p][c];p=fa[p])ch[p][c]=np; 33 mx[T]=mi[T]=w,mx2[T]=-inf,mi2[T]=inf,sz[T]=1; 34 if(p){ 35 int q=ch[p][c],nq; 36 if(len[p]+1==len[q])fa[np]=q; 37 else{ 38 nq=++T;mx[T]=mx2[T]=-inf,mi[T]=mi2[T]=inf; 39 fa[nq]=fa[q],len[nq]=len[p]+1,memcpy(ch[nq],ch[q],4*26); 40 for(fa[np]=fa[q]=nq;ch[p][c]==q;p=fa[p])ch[p][c]=nq; 41 } 42 } 43 } 44 struct eg{int nx,to;}e[M]; 45 int ce;arr fi,mx,mx2,mi,mi2,sx;ll sum[M],ans[M]; 46 inline void add(int u,int v){e[++ce]=(eg){fi[u],v},fi[u]=ce;} 47 inline void ck1(int u,int w){if(w>mx[u])mx2[u]=mx[u],mx[u]=w;else if(w>mx2[u])mx2[u]=w;} 48 inline void ck2(int u,int w){if(w<mi[u])mi2[u]=mi[u],mi[u]=w;else if(w<mi2[u])mi2[u]=w;} 49 void dfs(int u){ 50 int siz=0; 51 go(u){ 52 dfs(v);siz+=sz[v]; 53 ck1(u,mx[v]),ck1(u,mx2[v]); 54 ck2(u,mi[v]),ck2(u,mi2[v]); 55 56 }if(siz+sz[u]<2)return; 57 cmax(ans[len[u]],max((ll)mx[u]*mx2[u],(ll)mi[u]*mi2[u])); 58 go(u)sum[len[u]]+=(ll)sz[u]*sz[v],sz[u]+=sz[v]; 59 } 60 inline void sol(){ 61 mx[1]=mx2[1]=-inf,mi[1]=mi2[1]=inf; 62 memset(ans,-63,sizeof ans); 63 fp(i,2,T)add(fa[i],i);dfs(1); 64 fd(i,n-1,0)sum[i]+=sum[i+1],cmax(ans[i],ans[i+1]); 65 fp(i,0,n-1)we(sum[i]),we(!sum[i]?0:ans[i]),sr[++C]='\n'; 66 } 67 }p; 68 int main(){ 69 #ifndef ONLINE_JUDGE 70 file("s"); 71 #endif 72 sd(n),gs(s+1);fp(i,1,n)sd(w[i]); 73 fd(i,n,1)p.ins(s[i]-'a',w[i]);p.sol(); 74 return Ot(),0; 75 } 76 //https://kelin.blog.luogu.org/solution-p2178
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1 #include<bits/stdc++.h> 2 #define inf 0x3f3f3f3f 3 #define ll long long 4 #define il inline 5 using namespace std; 6 const int N=600010; 7 int n,lst,w[N],len[N],sz,pa[N],mx0[N],mx1[N],mn0[N],mn1[N],ch[N][26],c[N],id[N],cnt[N]; 8 char s[N]; 9 ll ans1[N],ans2[N]; 10 il bool upd1(int x,int y){ 11 if(y==inf)return false; 12 if(mx0[x]==inf||y>mx0[x]){mx1[x]=mx0[x];mx0[x]=y;return true;} 13 if(mx1[x]==inf||y>mx1[x]){mx1[x]=y;return false;} 14 return false; 15 } 16 il bool upd2(int x,int y){ 17 if(y==inf)return false; 18 if(mn0[x]==inf||y<mn0[x]){mn1[x]=mn0[x];mn0[x]=y;return true;} 19 if(mn1[x]==inf||y<mn1[x]){mn1[x]=y;return false;} 20 return false; 21 } 22 il void ins(int now,int x){ 23 int p=lst; int np=lst=++sz; 24 cnt[np]=1; 25 mx0[np]=mn0[np]=w[now]; 26 mx1[np]=mn1[np]=inf; 27 len[np]=len[p]+1; 28 while(p&&!ch[p][x])ch[p][x]=np,p=pa[p]; 29 if(!p){pa[np]=1;return;} 30 int q=ch[p][x]; 31 if(len[q]==len[p]+1){pa[np]=q;} 32 else { 33 int nq=++sz; len[nq]=len[p]+1; 34 memcpy(ch[nq],ch[q],sizeof(ch[q])); 35 pa[nq]=pa[q]; pa[q]=pa[np]=nq; 36 while(p&&ch[p][x]==q)ch[p][x]=nq,p=pa[p]; 37 } 38 } 39 inline ll max(ll x,ll y){return x>y?x:y;} 40 int main(){ 41 freopen("bzoj4199.in","r",stdin); 42 freopen("bzoj4199.out","w",stdout); 43 lst=sz=1; 44 memset(mx0,0x3f,sizeof(mx0)); 45 memset(mx1,0x3f,sizeof(mx1)); 46 memset(mn0,0x3f,sizeof(mn0)); 47 memset(mn1,0x3f,sizeof(mn1)); 48 scanf("%d%s",&n,s+1); 49 for(int i=1;i<=n>>1;i++)swap(s[i],s[n-i+1]); 50 for(int i=1;i<=n;i++)scanf("%d",&w[n-i+1]); 51 for(int i=1;i<=n;i++)ins(i,s[i]-'a'); 52 for(int i=1;i<=sz;i++)c[len[i]]++; 53 for(int i=1;i<=n;i++)c[i]+=c[i-1]; 54 for(int i=sz;i;i--)id[c[len[i]]--]=i,ans2[i]=-1e18; 55 len[0]=-1; 56 for(int i=sz;i;i--){ 57 int u=id[i]; 58 ll t1=(ll)cnt[u]*(cnt[u]-1)/2; 59 ll t2=max((ll)mx0[u]*mx1[u], (ll)mn0[u]*mn1[u]); 60 ans1[len[u]]+=t1; 61 if(t1)ans2[len[u]]=max(ans2[len[u]],t2); 62 ans1[len[pa[u]]]-=t1; 63 cnt[pa[u]]+=cnt[u]; 64 if(upd1(pa[u],mx0[u]))upd1(pa[u],mx1[u]); 65 if(upd2(pa[u],mn0[u]))upd2(pa[u],mn1[u]); 66 } 67 for(int i=n-1;~i;i--){ 68 ans1[i]+=ans1[i+1]; 69 ans2[i]=max(ans2[i],ans2[i+1]); 70 } 71 for(int i=0;i<n;i++){ 72 if(ans1[i])printf("%lld %lld\n",ans1[i],ans2[i]); 73 else puts("0 0"); 74 } 75 return 0; 76 }
【bzoj4199】【Noi2015】品酒大会
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转载自www.cnblogs.com/Paul-Guderian/p/10230485.html
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