Luogu3732 [HAOI2017] 供给侧改革 【后缀数组】【线段树】【乱搞】

题目分析:

这道题我是乱搞的,因为他说$01$串是随机的。

那么我们可以猜测能够让LCP变大的地方很少。求出后缀数组之后可能让LCP变大的地方就等价于从大到小往height里动态加点同时维护这个点左右两边的单调栈。

这个事情用线段树模拟就行了。

用暴力跑一下发现果然不大,只有200w,其中很多还是废点,把废点特判一下删除掉就行了。

然后把询问离线,按r排序,再作扫描线,每次扫到r的时候把前面变动的LCP更新一下。然后对于询问也做一个类似上面单调栈的操作。

代码:

  1 #include<bits/stdc++.h>
  2 #define RI register
  3 using namespace std;
  4 
  5 const int maxn = 100020;
  6 const int N = 100000;
  7 
  8 int n,q;
  9 char str[maxn];
 10 int T[maxn<<2],a[maxn];
 11 int RMQ[maxn][19],pw[maxn];
 12 
 13 struct node{int l,r,nb;}qy[maxn];
 14 int ans[maxn];
 15 int sa[maxn],rk[maxn],X[maxn],Y[maxn];
 16 int ht[maxn],h[maxn];
 17 
 18 void fstread(int &x){
 19     char ch = getchar();x = 0;
 20     while(ch > '9' || ch < '0') ch = getchar();
 21     while(ch >= '0' && ch <= '9') x = x*10+ch-'0',ch=getchar();
 22 }
 23 
 24 int chk(int x,int k){
 25     return rk[sa[x]]==rk[sa[x-1]]&&rk[sa[x]+(1<<k)]==rk[sa[x-1]+(1<<k)];
 26 }
 27 
 28 void GetSA(){
 29     for(RI int i=0;i<n;i++) X[str[i]]++;
 30     for(RI int i=1;i<=N;i++) X[i] += X[i-1];
 31     for(RI int i=n-1;i>=0;i--) sa[X[str[i]]--] = i;
 32     for(RI int i = 2, num = 1;i <= n;i++)
 33     rk[sa[i]] = (str[sa[i]] == str[sa[i-1]]?num:++num);
 34     rk[sa[1]] = 1;
 35     for(int k=1;(1<<k-1)<=n;k++){
 36     for(RI int i=1;i<=N;i++) X[i] = 0;
 37     for(RI int i=n-(1<<k-1);i<n;i++) Y[i-n+(1<<k-1)+1]=i;
 38     for(RI int i=1,j=(1<<k-1)+1;i<=n;i++)
 39         if(sa[i]>=(1<<k-1))Y[j++]=sa[i]-(1<<k-1);
 40     for(RI int i=0;i<n;i++) X[rk[i]]++;
 41     for(RI int i=1;i<=N;i++) X[i]+=X[i-1];
 42     for(RI int i=n;i>=1;i--) sa[X[rk[Y[i]]]--] = Y[i];
 43     int num = 1; Y[sa[1]] = 1;
 44     for(RI int i=2;i<=n;i++) Y[sa[i]] = (chk(i,k-1)?num:++num);
 45     for(RI int i=0;i<n;i++) rk[i] = Y[i];
 46     if(num == n) break;
 47     }
 48 }
 49 
 50 void buildRMQ(){
 51     for(int i=1;i<=n;i++) RMQ[i][0] = ht[i];
 52     for(int i=0;(1<<i)<=n;i++) pw[(1<<i)] = i;
 53     for(int i=3;i<=n;i++) if(!pw[i]) pw[i] = pw[i-1];
 54     for(int k=1;(1<<k)<=n;k++){
 55     for(RI int i=1;i<=n;i++){
 56         if(i+(1<<k-1)>n) RMQ[i][k] = RMQ[i][k-1];
 57         else RMQ[i][k] = min(RMQ[i][k-1],RMQ[i+(1<<k-1)][k-1]);
 58     }
 59     }
 60 }
 61 
 62 void GetHeight(){
 63     for(RI int i=0;i<n;i++){
 64     if(i) h[i] = max(0,h[i-1]-1);
 65     if(rk[i] == 1) {h[i] = 0;continue;}
 66     while(str[i+h[i]] == str[sa[rk[i]-1]+h[i]]) h[i]++;
 67     }
 68     for(RI int i=0;i<n;i++) ht[rk[i]] = h[i];
 69 }
 70 
 71 int LCP(int l,int r){
 72     l = rk[l],r = rk[r]; if(l > r) swap(l,r);l++;
 73     int k = pw[r-l+1];
 74     return min(RMQ[l][k],RMQ[r-(1<<k)+1][k]);
 75 }
 76 
 77 void update(int now,int tl,int tr,int pos,int len){
 78     if(tl == tr){T[now] = max(T[now],len); return;}
 79     int mid = (tl+tr)/2;
 80     if(pos <= mid) update(now<<1,tl,mid,pos,len);
 81     else update(now<<1|1,mid+1,tr,pos,len);
 82     T[now] = max(T[now<<1],T[now<<1|1]);
 83 }
 84 
 85 int Query(int now,int tl,int tr,int l,int r,int mx){
 86     if(tl >= l && tr <= r){
 87     if(T[now] <= mx) return -1;
 88     else{
 89         while(tl < tr){
 90         int mid = (tl+tr)/2;
 91         if(T[now<<1|1] > mx) tl = mid+1,now = now*2+1;
 92         else tr = mid,now<<=1;
 93         }
 94         return tl;
 95     }
 96     }
 97     if(tl > r || tr < l) return -1;
 98     int mid = (tl+tr)/2;
 99     if(mid >= r) return Query(now<<1,tl,mid,l,r,mx);
100     if(mid < l) return Query(now<<1|1,mid+1,tr,l,r,mx);
101     int z = Query(now<<1|1,mid+1,tr,l,r,mx);
102     if(z!=-1) return z;
103     else return Query(now<<1,tl,mid,l,r,mx);
104 }
105 
106 vector<int> mlgb[maxn];
107 
108 namespace BruteForce{
109     int minn[maxn<<2];
110     
111     pair<int,int> QueryRange(int now,int tl,int tr,int l,int r,int up,int d){
112     if(tl >= l && tr <= r && d == 1){
113         if(minn[now] < up){
114         while(tl != tr){
115             int mid = (tl+tr)/2;
116             if(minn[now<<1|1] < up) tl = mid+1,now=now*2+1;
117             else tr = mid,now<<=1;
118         }
119         return make_pair(minn[now],tl);
120         }else return make_pair(0,0);
121     }
122     if(tl >= l && tr <= r && d == 0){
123         if(minn[now] < up){
124         while(tl != tr){
125             int mid = (tl+tr)/2;
126             if(minn[now<<1] < up) tr = mid,now<<=1;
127             else tl = mid+1,now=now*2+1;
128         }
129         return make_pair(minn[now],tl);
130         }else return make_pair(0,0);
131     }
132     if(tl > r || tr < l) return make_pair(0,0);
133     int mid = (tl+tr)/2;
134     if(mid>=r) return QueryRange(now<<1,tl,mid,l,r,up,d);
135     if(mid<l) return QueryRange(now<<1|1,mid+1,tr,l,r,up,d);
136     if(d){
137         pair<int,int> z = QueryRange(now<<1|1,mid+1,tr,l,r,up,d);
138         if(z.first) return z;
139         else return QueryRange(now<<1,tl,mid,l,r,up,d);
140     }else{
141         pair<int,int> z = QueryRange(now<<1,tl,mid,l,r,up,d);
142         if(z.first) return z;
143         else return QueryRange(now<<1|1,mid+1,tr,l,r,up,d);
144     }
145     }
146     void add(int now,int tl,int tr,int pos,int dt){
147     if(tl == tr) {minn[now] = dt;return;}
148     int mid = (tl+tr)/2;
149     if(pos <= mid) add(now<<1,tl,mid,pos,dt);
150     else add(now<<1|1,mid+1,tr,pos,dt);
151     minn[now] = min(minn[now<<1],minn[now<<1|1]);
152     }
153     
154     void holyshit(){
155     memset(minn,0x3f,sizeof(minn));
156     for(int i=n-1;i>=0;i--){
157         int z = rk[i],p=19260817;
158         add(1,1,n,z,i);
159         while(true){
160         pair<int,int> um = QueryRange(1,1,n,z+1,n,p,0);
161         if(!um.first) break;
162         mlgb[um.first].push_back(i);
163         z = um.second; p = sa[z];
164         }
165         z = rk[i],p = 19260817;
166         while(true){
167         pair<int,int> um = QueryRange(1,1,n,1,z-1,p,1);
168         if(!um.first) break;
169         mlgb[um.first].push_back(i);
170         z = um.second; p = sa[z];
171         }
172     }
173     
174     }
175 }
176 
177 void work(){
178     GetSA();
179     GetHeight();
180     buildRMQ();
181     
182     BruteForce::holyshit();
183     int num = 1;
184     for(int i=0;i<n;i++){
185     for(int j=0;j<mlgb[i].size();j++){
186         int z = LCP(mlgb[i][j],i);
187         if(a[mlgb[i][j]] >= z) continue;
188         a[mlgb[i][j]] = z;
189         update(1,0,n-1,mlgb[i][j],z);
190         
191     }
192     while(qy[num].r == i){
193         int z = 0,pq = qy[num].r-1;
194         while(pq >= qy[num].l){
195         int hp = Query(1,0,n-1,0,pq,z);
196         if(hp < qy[num].l) hp = qy[num].l-1;
197         ans[qy[num].nb] += (pq-hp)*z;
198         if(hp < 0) break;
199         z = a[hp],pq = hp;
200         }
201         num++;
202     }
203     }
204     for(int i=1;i<=q;i++) printf("%d\n",ans[i]);
205 }
206 
207 int cmp(node alpha,node beta){return alpha.r < beta.r;}
208 int main(){
209     freopen("1.in","r",stdin);
210     fstread(n);fstread(q);
211     for(int i=1;i<=n;i++){
212     str[i-1] = getchar();
213     while(str[i-1]!= '0' && str[i-1] != '1') str[i-1] = getchar();
214     }
215     for(int i=1;i<=q;i++) fstread(qy[i].l),fstread(qy[i].r),qy[i].nb=i;
216     for(int i=1;i<=q;i++) qy[i].l--,qy[i].r--;
217     sort(qy+1,qy+q+1,cmp);
218     work();
219     return 0;
220 }

 

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