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：

#include<bits/stdc++.h>
#define RI register
using namespace std;

const int maxn = 100020;
const int N = 100000;

int n,q;
char str[maxn];
int T[maxn<<2],a[maxn];
int RMQ[maxn][19],pw[maxn];

struct node{int l,r,nb;}qy[maxn];
int ans[maxn];
int sa[maxn],rk[maxn],X[maxn],Y[maxn];
int ht[maxn],h[maxn];

void fstread(int &x){
    char ch = getchar();x = 0;
    while(ch > '9' || ch < '0') ch = getchar();
    while(ch >= '0' && ch <= '9') x = x*10+ch-'0',ch=getchar();
}

int chk(int x,int k){
    return rk[sa[x]]==rk[sa[x-1]]&&rk[sa[x]+(1<<k)]==rk[sa[x-1]+(1<<k)];
}

void GetSA(){
    for(RI int i=0;i<n;i++) X[str[i]]++;
    for(RI int i=1;i<=N;i++) X[i] += X[i-1];
    for(RI int i=n-1;i>=0;i--) sa[X[str[i]]--] = i;
    for(RI int i = 2, num = 1;i <= n;i++)
    rk[sa[i]] = (str[sa[i]] == str[sa[i-1]]?num:++num);
    rk[sa[1]] = 1;
    for(int k=1;(1<<k-1)<=n;k++){
    for(RI int i=1;i<=N;i++) X[i] = 0;
    for(RI int i=n-(1<<k-1);i<n;i++) Y[i-n+(1<<k-1)+1]=i;
    for(RI int i=1,j=(1<<k-1)+1;i<=n;i++)
        if(sa[i]>=(1<<k-1))Y[j++]=sa[i]-(1<<k-1);
    for(RI int i=0;i<n;i++) X[rk[i]]++;
    for(RI int i=1;i<=N;i++) X[i]+=X[i-1];
    for(RI int i=n;i>=1;i--) sa[X[rk[Y[i]]]--] = Y[i];
    int num = 1; Y[sa[1]] = 1;
    for(RI int i=2;i<=n;i++) Y[sa[i]] = (chk(i,k-1)?num:++num);
    for(RI int i=0;i<n;i++) rk[i] = Y[i];
    if(num == n) break;
    }
}

void buildRMQ(){
    for(int i=1;i<=n;i++) RMQ[i][0] = ht[i];
    for(int i=0;(1<<i)<=n;i++) pw[(1<<i)] = i;
    for(int i=3;i<=n;i++) if(!pw[i]) pw[i] = pw[i-1];
    for(int k=1;(1<<k)<=n;k++){
    for(RI int i=1;i<=n;i++){
        if(i+(1<<k-1)>n) RMQ[i][k] = RMQ[i][k-1];
        else RMQ[i][k] = min(RMQ[i][k-1],RMQ[i+(1<<k-1)][k-1]);
    }
    }
}

void GetHeight(){
    for(RI int i=0;i<n;i++){
    if(i) h[i] = max(0,h[i-1]-1);
    if(rk[i] == 1) {h[i] = 0;continue;}
    while(str[i+h[i]] == str[sa[rk[i]-1]+h[i]]) h[i]++;
    }
    for(RI int i=0;i<n;i++) ht[rk[i]] = h[i];
}

int LCP(int l,int r){
    l = rk[l],r = rk[r]; if(l > r) swap(l,r);l++;
    int k = pw[r-l+1];
    return min(RMQ[l][k],RMQ[r-(1<<k)+1][k]);
}

void update(int now,int tl,int tr,int pos,int len){
    if(tl == tr){T[now] = max(T[now],len); return;}
    int mid = (tl+tr)/2;
    if(pos <= mid) update(now<<1,tl,mid,pos,len);
    else update(now<<1|1,mid+1,tr,pos,len);
    T[now] = max(T[now<<1],T[now<<1|1]);
}

int Query(int now,int tl,int tr,int l,int r,int mx){
    if(tl >= l && tr <= r){
    if(T[now] <= mx) return -1;
    else{
        while(tl < tr){
        int mid = (tl+tr)/2;
        if(T[now<<1|1] > mx) tl = mid+1,now = now*2+1;
        else tr = mid,now<<=1;
        }
        return tl;
    }
    }
    if(tl > r || tr < l) return -1;
    int mid = (tl+tr)/2;
    if(mid >= r) return Query(now<<1,tl,mid,l,r,mx);
    if(mid < l) return Query(now<<1|1,mid+1,tr,l,r,mx);
    int z = Query(now<<1|1,mid+1,tr,l,r,mx);
    if(z!=-1) return z;
    else return Query(now<<1,tl,mid,l,r,mx);
}

vector<int> mlgb[maxn];

namespace BruteForce{
    int minn[maxn<<2];
    
    pair<int,int> QueryRange(int now,int tl,int tr,int l,int r,int up,int d){
    if(tl >= l && tr <= r && d == 1){
        if(minn[now] < up){
        while(tl != tr){
            int mid = (tl+tr)/2;
            if(minn[now<<1|1] < up) tl = mid+1,now=now*2+1;
            else tr = mid,now<<=1;
        }
        return make_pair(minn[now],tl);
        }else return make_pair(0,0);
    }
    if(tl >= l && tr <= r && d == 0){
        if(minn[now] < up){
        while(tl != tr){
            int mid = (tl+tr)/2;
            if(minn[now<<1] < up) tr = mid,now<<=1;
            else tl = mid+1,now=now*2+1;
        }
        return make_pair(minn[now],tl);
        }else return make_pair(0,0);
    }
    if(tl > r || tr < l) return make_pair(0,0);
    int mid = (tl+tr)/2;
    if(mid>=r) return QueryRange(now<<1,tl,mid,l,r,up,d);
    if(mid<l) return QueryRange(now<<1|1,mid+1,tr,l,r,up,d);
    if(d){
        pair<int,int> z = QueryRange(now<<1|1,mid+1,tr,l,r,up,d);
        if(z.first) return z;
        else return QueryRange(now<<1,tl,mid,l,r,up,d);
    }else{
        pair<int,int> z = QueryRange(now<<1,tl,mid,l,r,up,d);
        if(z.first) return z;
        else return QueryRange(now<<1|1,mid+1,tr,l,r,up,d);
    }
    }
    void add(int now,int tl,int tr,int pos,int dt){
    if(tl == tr) {minn[now] = dt;return;}
    int mid = (tl+tr)/2;
    if(pos <= mid) add(now<<1,tl,mid,pos,dt);
    else add(now<<1|1,mid+1,tr,pos,dt);
    minn[now] = min(minn[now<<1],minn[now<<1|1]);
    }
    
    void holyshit(){
    memset(minn,0x3f,sizeof(minn));
    for(int i=n-1;i>=0;i--){
        int z = rk[i],p=19260817;
        add(1,1,n,z,i);
        while(true){
        pair<int,int> um = QueryRange(1,1,n,z+1,n,p,0);
        if(!um.first) break;
        mlgb[um.first].push_back(i);
        z = um.second; p = sa[z];
        }
        z = rk[i],p = 19260817;
        while(true){
        pair<int,int> um = QueryRange(1,1,n,1,z-1,p,1);
        if(!um.first) break;
        mlgb[um.first].push_back(i);
        z = um.second; p = sa[z];
        }
    }
    
    }
}

void work(){
    GetSA();
    GetHeight();
    buildRMQ();
    
    BruteForce::holyshit();
    int num = 1;
    for(int i=0;i<n;i++){
    for(int j=0;j<mlgb[i].size();j++){
        int z = LCP(mlgb[i][j],i);
        if(a[mlgb[i][j]] >= z) continue;
        a[mlgb[i][j]] = z;
        update(1,0,n-1,mlgb[i][j],z);
        
    }
    while(qy[num].r == i){
        int z = 0,pq = qy[num].r-1;
        while(pq >= qy[num].l){
        int hp = Query(1,0,n-1,0,pq,z);
        if(hp < qy[num].l) hp = qy[num].l-1;
        ans[qy[num].nb] += (pq-hp)*z;
        if(hp < 0) break;
        z = a[hp],pq = hp;
        }
        num++;
    }
    }
    for(int i=1;i<=q;i++) printf("%d
",ans[i]);
}

int cmp(node alpha,node beta){return alpha.r < beta.r;}
int main(){
    //freopen("1.in","r",stdin);
    fstread(n);fstread(q);
    for(int i=1;i<=n;i++){
    str[i-1] = getchar();
    while(str[i-1]!= '0' && str[i-1] != '1') str[i-1] = getchar();
    }
    for(int i=1;i<=q;i++) fstread(qy[i].l),fstread(qy[i].r),qy[i].nb=i;
    for(int i=1;i<=q;i++) qy[i].l--,qy[i].r--;
    sort(qy+1,qy+q+1,cmp);
    work();
    return 0;
}