LUOGUP3498 [POI2010]KOR-Beads (哈希)

传送门

解题思路

这是一道上周的考试题。。。当时考的时候看了一眼，"呀，这不是调和级数，nlogn么！！！" ，然后一写就写了个n^2的。。。。结果边界还弄错40分滚蛋了。。正解就是正着求一遍hash，倒着求一遍hash，再求个逆元，O(nlogn)

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>

using namespace std;
const int MAXN = 200005;
const int mod = 19260817;
typedef long long LL;

inline int rd(){
    int x=0,f=1;char ch=getchar();
    while(!isdigit(ch)) {f=ch=='-'?0:1;ch=getchar();}
    while(isdigit(ch))  {x=(x<<1)+(x<<3)+ch-'0';ch=getchar();}
    return f?x:-x;
}

int n,a[MAXN],base,cnt,ans,Ans[MAXN],num;
int hsh[MAXN],hsh_[MAXN];
int inv[MAXN],c[20000000];

int fast_pow(int x,int y){
    int ret=1;
    for(;y;y>>=1){
        if(y&1) ret=(LL)ret*x%mod;
        x=(LL)x*x%mod;
    }
    return ret;
}

int main(){
//    freopen("bead.in","r",stdin);
//    freopen("bead.out","w",stdout);
    n=rd();base=n+1;inv[0]=1;int now=1;
    for(int i=1;i<=n;i++) {
        now=(LL)now*base%mod;a[i]=rd();inv[i]=fast_pow(now,mod-2);
        hsh[i]=hsh[i-1]+(LL)now*a[i]%mod;hsh[i]%=mod;
    }now=1;
    for(int i=n;i;i--) {
        now=(LL)now*base%mod;
        hsh_[i]=hsh_[i+1]+(LL)a[i]*now%mod;
        hsh_[i]%=mod;
    }
//    cout<<hsh_[1]<<endl;cout<<inv[n]<<endl;    
    int tmp,tmp_;
    for(int i=1;i<=n;i++){
        cnt=0;
        if(n/i<ans) break;
        for(register int j=i;j<=n;j+=i) {
            if(j>n) break;
            tmp=((hsh[j]-hsh[j-i])%mod+mod)%mod;
            tmp_=((hsh_[j-i+1]-hsh_[j+1])%mod+mod)%mod;
            tmp=(LL)tmp*inv[j-i]%mod;tmp_=(LL)tmp_*inv[n-j]%mod;
            if(c[tmp]==i && c[tmp_]==i) continue;
            c[tmp]=c[tmp_]=i;cnt++;
        }    
        if(cnt>ans) {ans=cnt;num=0;Ans[++num]=i;}
        else if(cnt==ans) Ans[++num]=i;
    }
    printf("%d %d
",ans,num);
    for(int i=1;i<=num;i++) printf("%d ",Ans[i]);
    return 0;
}

/*
21
1 1 1 2 2 2 3 3 3 1 2 3 3 1 2 2 1 3 3 2 1
*/