CF：358C 暴力DP筛选素数预处理

C. Bear and Prime Numbers

time limit per test
2 seconds

memory limit per test
512 megabytes

input
standard input

output
standard output

Recently, the bear started studying data structures and faced the following problem.

You are given a sequence of integers x1, x2, ..., xn of
length n and m queries, each of them is characterized
by two integers li, ri.
Let's introduce f(p) to represent the number of such indexes k,
that xk is divisible
by p. The answer to the query li, ri is
the sum:

,
where S(li, ri) is
a set of prime numbers from segment [li, ri] (both
borders are included in the segment).

Help the bear cope with the problem.

Input

The first line contains integer n (1 ≤ n ≤ 106).
The second line contains n integers x1, x2, ..., xn (2 ≤ xi ≤ 107).
The numbers are not necessarily distinct.

The third line contains integer m (1 ≤ m ≤ 50000).
Each of the following m lines contains a pair of space-separated integers, li and ri(2 ≤ li ≤ ri ≤ 2·109) —
the numbers that characterize the current query.

Output

Print m integers — the answers to the queries on the order the queries appear in the input.

Sample test(s)

input

6
5 5 7 10 14 15
3
2 11
3 12
4 4

output

9
7
0

input

7
2 3 5 7 11 4 8
2
8 10
2 123

output

0
7

Note

Consider the first sample. Overall, the first sample has 3 queries.

The first query l = 2, r = 11 comes. You need to
count f(2) + f(3) + f(5) + f(7) + f(11) = 2 + 1 + 4 + 2 + 0 = 9.

The second query comes l = 3, r = 12. You need to
count f(3) + f(5) + f(7) + f(11) = 1 + 4 + 2 + 0 = 7.

The third query comes l = 4, r = 4. As this interval
has no prime numbers, then the sum equals 0.

这题太神了！比赛的时候不知道怎么做，唉……没想到可以这样暴力的。太神了……递推的DP，查询时间复杂为O(1)，比线段树还快，这个能这样暴力真是服了，见识短浅啊……

dp[i]表示当前2到 i 这中间能被 那n 个数整除的数之和……然后求 l 到 r 的时候就可以直接dp [ r ] - dp [ l-1] 了。

#include <iostream>
#include <cstdio>
#include <fstream>
#include <algorithm>
#include <cmath>
#include <deque>
#include <vector>
#include <list>
#include <queue>
#include <string>
#include <cstring>
#include <map>
#include <stack>
#include <set>
#define PI acos(-1.0)
#define mem(a,b) memset(a,b,sizeof(a))
#define sca(a) scanf("%d",&a)
#define pri(a) printf("%d\n",a)
#define lson i<<1,l,mid
#define rson i<<1|1,mid+1,r
#define MM 10000005
#define MN 3005
#define INF 10000007
#define eps 1e-7
using namespace std;
typedef long long ll;
int vis[MM],dp[MM],is[MM];
void getprime()
{
    int i,j;
    for(i=2;i<=MM;i++)
        if(!is[i])
        {
            if(vis[i]) dp[i]+=vis[i];
            for(j=i+i;j<=MM;j+=i)
            {
                if(vis[j]) dp[i]+=vis[j];
                is[j]=1;
            }
        }
    for(i=2;i<=MM;i++)
        dp[i]+=dp[i-1];
}
int main()
{
    int n,m,i,a,l,r;
    sca(n);
    for(i=0;i<n;i++)
        sca(a),vis[a]++;
    getprime();
    sca(m);
    while(m--)
    {
        scanf("%d%d",&l,&r);
        l=l>MM?MM:l;
        r=r>MM?MM:r;
        pri(dp[r]-dp[l-1]);
    }
    return 0;
}