[SD2014集訓(xùn)]查詢（分塊+數(shù)學(xué)相關(guān)）

2019-11-14 10:14:07

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供稿：網(wǎng)友

題目描述

這里寫圖片描述

題解

看模數(shù)那么奇怪找一下規(guī)律看看有沒(méi)有奇怪的性質(zhì) 發(fā)現(xiàn)每一個(gè)數(shù)立方48次后回到原數(shù) 線段樹(shù)不如分塊好寫維護(hù)每個(gè)數(shù)立方k次后得到的數(shù)，每一個(gè)塊所有的數(shù)分別立方k次后的和修改時(shí)，對(duì)于整塊記錄立方的次數(shù)，其余的暴力重構(gòu) 重構(gòu)即把塊內(nèi)的點(diǎn)維護(hù)的立方旋轉(zhuǎn)t次，然后重新計(jì)算和查詢時(shí)，整塊直接查詢，其余暴力時(shí)間復(fù)雜度O(m(block+n?szblock)) $O(m(block+{n*sz/over block}))$ ，可以發(fā)現(xiàn)當(dāng)block=n?sz?????√ $block=/sqrt {n*sz}$ 時(shí)有最小值，O(mn?sz?????√)≈2.19s $O(m/sqrt{n*sz})/ap<a >PR</a>ox 2.19s$

代碼

#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)); }}