[SD2014集訓]查詢（分塊+數學相關）

2019-11-14 11:38:09

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題目描述

這里寫圖片描述

題解

看模數那么奇怪找一下規律看看有沒有奇怪的性質發現每一個數立方48次后回到原數線段樹不如分塊好寫維護每個數立方k次后得到的數，每一個塊所有的數分別立方k次后的和修改時，對于整塊記錄立方的次數，其余的暴力重構重構即把塊內的點維護的立方旋轉t次，然后重新計算和查詢時，整塊直接查詢，其余暴力時間復雜度O(m(block+n?szblock)) $O(m(block+{n*sz/over block}))$ ，可以發現當block=n?sz?????√ $block=/sqrt {n*sz}$ 時有最小值，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)); }}