[SD2014集训]查询（分块+数学相关）

2019-11-14 10:42:34

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题目描述

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题解

看模数那么奇怪找一下规律看看有没有奇怪的性质发现每一个数立方48次后回到原数线段树不如分块好写维护每个数立方k次后得到的数，每一个块所有的数分别立方k次后的和修改时，对于整块记录立方的次数，其余的暴力重构重构即把块内的点维护的立方旋转t次，然后重新计算和查询时，整块直接查询，其余暴力时间复杂度O(m(block+n∗szblock)) $O(m(block+{n*sz/over block}))$ ，可以发现当block=n∗sz−−−−−√ $block=/sqrt {n*sz}$ 时有最小值，O(mn∗sz−−−−−√)≈2.19s $O(m/sqrt{n*sz})/ap<a href="http://pr.VeVb.com/">PR</a>ox 2.19s$

代码

#include<algorithm>#include<iostream>#include<cstring>#include<cstdio>#include<cmath>using namespace std;#define LL long long#define Mod 329701061#define sz 48#define N 100005char opt;int n,m,x,y,block,tot;int t[N],num[N],l[N],r[N];LL a[N],cub[N][sz],Cub[N][sz],s[sz];void init(){ for (int i=1;i<=n;++i) { cub[i][0]=a[i]; for (int j=1;j<sz;++j) cub[i][j]=cub[i][j-1]*cub[i][j-1]%Mod*cub[i][j-1]%Mod; } for (int i=1;i<=tot;++i) for (int j=0;j<sz;++j) for (int k=l[i];k<=r[i];++k) { Cub[i][j]+=cub[k][j]; if (Cub[i][j]>=Mod) Cub[i][j]-=Mod; }}void move(int id,int rad){ if (!rad) return; for (int i=0;i<rad;++i) s[i]=cub[id][i]; for (int i=rad;i<sz;++i) cub[id][i-rad]=cub[id][i]; for (int i=0;i<rad;++i) cub[id][i+sz-rad]=s[i];}void calc(int id){ for (int i=0;i<sz;++i) { Cub[id][i]=0; for (int j=l[id];j<=r[id];++j) { Cub[id][i]+=cub[j][i]; if (Cub[id][i]>=Mod) Cub[id][i]-=Mod; } }}void change(int x,int y){ if (num[x]==num[y]) { for (int i=l[num[x]];i<x;++i) move(i,t[num[x]]); for (int i=y+1;i<=r[num[y]];++i) move(i,t[num[x]]); ++t[num[x]];if (t[num[x]]==sz) t[num[x]]=0; for (int i=x;i<=y;++i) move(i,t[num[x]]); t[num[x]]=0; calc(num[x]); return; } if (x==l[num[x]]) x=num[x]; else { for (int i=l[num[x]];i<x;++i) move(i,t[num[x]]); ++t[num[x]];if (t[num[x]]==sz) t[num[x]]=0; for (int i=x;i<=r[num[x]];++i) move(i,t[num[x]]); t[num[x]]=0; calc(num[x]); x=num[x]+1; } if (y==r[num[y]]) y=num[y]; else { for (int i=y+1;i<=r[num[y]];++i) move(i,t[num[y]]); ++t[num[y]];if (t[num[y]]==sz) t[num[y]]=0; for (int i=l[num[y]];i<=y;++i) move(i,t[num[y]]); t[num[y]]=0; calc(num[y]); y=num[y]-1; } for (int i=x;i<=y;++i) { ++t[i]; if (t[i]==sz) t[i]=0; }}LL query(int x,int y){ LL ans=0; if (num[x]==num[y]) { for (int i=x;i<=y;++i) { ans+=cub[i][t[num[x]]]; if (ans>=Mod) ans-=Mod; } return ans; } if (x==l[num[x]]) x=num[x]; else { for (int i=x;i<=r[num[x]];++i) { ans+=cub[i][t[num[x]]]; if (ans>=Mod) ans-=Mod; } x=num[x]+1; } if (y==r[num[y]]) y=num[y]; else { for (int i=l[num[y]];i<=y;++i) { ans+=cub[i][t[num[y]]]; if (ans>=Mod) ans-=Mod; } y=num[y]-1; } for (int i=x;i<=y;++i) { ans+=Cub[i][t[i]]; if (ans>=Mod) ans-=Mod; } return ans;}int main(){ scanf("%d",&n); for (int i=1;i<=n;++i) scanf("%I64d",&a[i]); block=n/floor(sqrt(n*sz)); if (!block) ++block; tot=(n-1)/block+1; for (int i=1;i<=n;++i) { num[i]=(i-1)/block+1; if (num[i]!=num[i-1]) r[num[i-1]]=i-1,l[num[i]]=i; } r[tot]=n; init(); scanf("%d",&m); for (int i=1;i<=m;++i) { opt=getchar(); while (opt!='C'&&opt!='Q') opt=getchar(); scanf("%d%d",&x,&y); if (x>y) swap(x,y); if (opt=='C') change(x,y); else printf("%I64d/n",query(x,y)); }}